From 80c46382fa32b9e0db2a028d2c11ecfdf42902c0 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Mon, 28 Aug 2017 16:02:19 +0900 Subject: [PATCH 01/34] [BugFix] Plot with errorbar --- tool/corplot.F90 | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tool/corplot.F90 b/tool/corplot.F90 index 81bf075c..cceb46a8 100644 --- a/tool/corplot.F90 +++ b/tool/corplot.F90 @@ -447,7 +447,7 @@ SUBROUTINE write_gnuplot() DO iwfc = 1, nwfc ! WRITE(fo, '(a,i0,a,i0,a,i0,a)',advance='no') & - & "'correlation.dat' u 1:2:($", iwfc+2, "-$", iwfc+2+nwfc, ") w l tit '", iwfc, "-'" + & "'correlation.dat' u 1:2:($", iwfc+2, "-$", iwfc+2+nwfc, ") w l tit '", iwfc, "-', " WRITE(fo, '(a,i0,a,i0,a,i0,a)',advance='no') & & "'correlation.dat' u 1:2:($", iwfc+2, "+$", iwfc+2+nwfc, ") w l tit '", iwfc, "+'" ! From 7edf24876238949a57473c32932bd7b121ee9182 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Tue, 29 Aug 2017 17:29:24 +0900 Subject: [PATCH 02/34] Modify the definition of correlation functions --- doc/fourier/en/fourier_overview_en.rst | 8 ++++---- doc/fourier/ja/fourier_overview_ja.rst | 11 ++++++----- src/StdFace/StdFace_main.c | 12 +++++++++--- tool/fourier.F90 | 7 +++++-- 4 files changed, 24 insertions(+), 14 deletions(-) diff --git a/doc/fourier/en/fourier_overview_en.rst b/doc/fourier/en/fourier_overview_en.rst index 359ee767..63c2bc91 100644 --- a/doc/fourier/en/fourier_overview_en.rst +++ b/doc/fourier/en/fourier_overview_en.rst @@ -38,7 +38,7 @@ Density-density correlation \begin{align} \langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle - \equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} \langle {\hat \rho}_{i} {\hat \rho}_{j}\rangle \end{align} @@ -49,15 +49,15 @@ Spin-Spin correlations \begin{align} \langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} \langle {\hat S}_{i}^{z} {\hat S}_{j}^{z} \rangle \\ \langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} \langle {\hat S}_{i}^{+} {\hat S}_{j}^{-} \rangle \\ \langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} \langle {\hat {\bf S}}_{i} \cdot {\hat {\bf S}}_{j} \rangle \end{align} diff --git a/doc/fourier/ja/fourier_overview_ja.rst b/doc/fourier/ja/fourier_overview_ja.rst index 6bf0b313..6a32c9a8 100644 --- a/doc/fourier/ja/fourier_overview_ja.rst +++ b/doc/fourier/ja/fourier_overview_ja.rst @@ -37,8 +37,9 @@ \begin{align} \langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle - \equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat \rho}_{i} {\hat \rho}_{j}\rangle + \equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle ({\hat \rho}_{i} - \langle {\hat \rho}_{i} \rangle) + ({\hat \rho}_{j} - \langle {\hat \rho}_{j} \rangle) \rangle \end{align} スピン-スピン相関 @@ -48,15 +49,15 @@ \begin{align} \langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} \langle {\hat S}_{i}^{z} {\hat S}_{j}^{z} \rangle \\ \langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} \langle {\hat S}_{i}^{+} {\hat S}_{j}^{-} \rangle \\ \langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} \langle {\hat {\bf S}}_{i} \cdot {\hat {\bf S}}_{j} \rangle \end{align} diff --git a/src/StdFace/StdFace_main.c b/src/StdFace/StdFace_main.c index 4fee32bd..ed55d6df 100644 --- a/src/StdFace/StdFace_main.c +++ b/src/StdFace/StdFace_main.c @@ -323,6 +323,12 @@ static void PrintExcitation(struct StdIntList *StdI) { isite += 1; } } + if (strcmp(StdI->model, "kondo") == 0) { + for (isite = 0; isite < StdI->nsite / 2; isite++) { + fourier_r[isite + StdI->nsite / 2] = fourier_r[isite]; + fourier_i[isite + StdI->nsite / 2] = fourier_i[isite]; + }/*for (isite = 0; isite < StdI->nsite; isite++)*/ + }/*if (strcmp(StdI->model, "kondo") == 0)*/ if (StdI->SpectrumBody == 1) { fp = fopen("single.def", "w"); @@ -2144,6 +2150,8 @@ void StdFace_main( PrintLocSpin(StdI); PrintTrans(StdI); PrintInteractions(StdI); + CheckModPara(StdI); + PrintModPara(StdI); #if defined(_HPhi) PrintExcitation(StdI); PrintCalcMod(StdI); @@ -2161,8 +2169,6 @@ void StdFace_main( PrintGutzwiller(StdI); PrintOrb(StdI); #endif - CheckModPara(StdI); - PrintModPara(StdI); CheckOutputMode(StdI); Print1Green(StdI); Print2Green(StdI); @@ -2245,4 +2251,4 @@ The non-local term is as follows: For more details, please see each functions. StdFace_Kagome_Boost()? Forget!! -*/ \ No newline at end of file +*/ diff --git a/tool/fourier.F90 b/tool/fourier.F90 index e916d9f6..d50c60e1 100644 --- a/tool/fourier.F90 +++ b/tool/fourier.F90 @@ -683,7 +683,9 @@ SUBROUTINE read_corrfile() cor(isite, jsite, 3, iwfc) = cor0(indx(isite,jsite,3)) & & + cor0(indx(isite,jsite,4)) & & + cor0(indx(isite,jsite,5)) & - & + cor0(indx(isite,jsite,6)) + & + cor0(indx(isite,jsite,6)) & + & - SUM(cor(isite, isite, 1:2, iwfc)) & + & * SUM(cor(jsite, jsite, 1:2, iwfc)) ! cor(isite, jsite, 4, iwfc) = cor0(indx(isite,jsite,3)) & & - cor0(indx(isite,jsite,4)) & @@ -756,7 +758,8 @@ SUBROUTINE fourier_cor() CALL zgemm('N', 'N', nk, 6*nwfc, nsite*nsite, CMPLX(1d0, 0d0, KIND(1d0)), fmat, nk, & & cor, nsite*nsite, CMPLX(0d0,0d0,KIND(1d0)), cor_k, nk) ! - cor_k(1:nk,1:6,1:nwfc) = cor_k(1:nk,1:6,1:nwfc) / dble(nk) + cor_k(1:nk,1:2,1:nwfc) = cor_k(1:nk,1:2,1:nwfc) / dble(nk) + cor_k(1:nk,3:6,1:nwfc) = cor_k(1:nk,3:6,1:nwfc) / dble(nk*nk) ! DEALLOCATE(fmat, cor, site) ! From b15c2039fc5e68896417e20b2fbbf3735844e5f8 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Tue, 29 Aug 2017 22:08:19 +0900 Subject: [PATCH 03/34] #180 comment out "set view equal" --- tool/corplot.F90 | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tool/corplot.F90 b/tool/corplot.F90 index cceb46a8..20350e70 100644 --- a/tool/corplot.F90 +++ b/tool/corplot.F90 @@ -419,7 +419,7 @@ SUBROUTINE write_gnuplot() WRITE(fo,'(a)') "#set view 60.0, 30.0" ! WRITE(fo,*) - WRITE(fo,'(a)') "set view equal xy" + WRITE(fo,'(a)') "#set view equal xy" WRITE(fo,'(a)') "set ticslevel 0" WRITE(fo,'(a)') "set hidden3d" WRITE(fo,'(a)') "set xlabel 'kx'" From 6eb2699f1e840f73454a8cd0fc24368b75d41677 Mon Sep 17 00:00:00 2001 From: tmisawa Date: Tue, 5 Sep 2017 17:57:29 +0900 Subject: [PATCH 04/34] #182 fixed bugs InJastrow --- src/mVMC/readdef.c | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/src/mVMC/readdef.c b/src/mVMC/readdef.c index 78105d2b..72f36875 100644 --- a/src/mVMC/readdef.c +++ b/src/mVMC/readdef.c @@ -1033,7 +1033,7 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { } for (i = 0; i < NGutzwillerIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); - Proj[idx] = tmp_real + I * tmp_comp; + Proj[i] = tmp_real + I * tmp_comp; } break; @@ -1046,7 +1046,7 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { count = NGutzwillerIdx; for (i = count; i < count + NJastrowIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); - Proj[idx] = tmp_real + I * tmp_comp; + Proj[i] = tmp_real + I * tmp_comp; } break; @@ -1059,7 +1059,7 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { count = NGutzwillerIdx + NJastrowIdx; for (i = count; i < count + 2 * 3 * NDoublonHolon2siteIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); - Proj[idx] = tmp_real + I * tmp_comp; + Proj[i] = tmp_real + I * tmp_comp; } break; @@ -1072,7 +1072,7 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { count = NGutzwillerIdx + NJastrowIdx + 2 * 3 * NDoublonHolon2siteIdx; for (i = count; i < count + 2 * 5 * NDoublonHolon4siteIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); - Proj[idx] = tmp_real + I * tmp_comp; + Proj[i] = tmp_real + I * tmp_comp; } break; From 9fa1a0426741583e28e4ef9b03708e795fc57130 Mon Sep 17 00:00:00 2001 From: Yuichi Motoyama Date: Tue, 5 Sep 2017 18:20:32 +0900 Subject: [PATCH 05/34] fixed #182 #183 --- src/mVMC/readdef.c | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/src/mVMC/readdef.c b/src/mVMC/readdef.c index 72f36875..911fb0aa 100644 --- a/src/mVMC/readdef.c +++ b/src/mVMC/readdef.c @@ -1031,9 +1031,10 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { info = 1; continue; } + count = 0 for (i = 0; i < NGutzwillerIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); - Proj[i] = tmp_real + I * tmp_comp; + Proj[idx+count] = tmp_real + I * tmp_comp; } break; @@ -1046,7 +1047,7 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { count = NGutzwillerIdx; for (i = count; i < count + NJastrowIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); - Proj[i] = tmp_real + I * tmp_comp; + Proj[idx+count] = tmp_real + I * tmp_comp; } break; @@ -1059,7 +1060,7 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { count = NGutzwillerIdx + NJastrowIdx; for (i = count; i < count + 2 * 3 * NDoublonHolon2siteIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); - Proj[i] = tmp_real + I * tmp_comp; + Proj[idx+count] = tmp_real + I * tmp_comp; } break; @@ -1072,7 +1073,7 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { count = NGutzwillerIdx + NJastrowIdx + 2 * 3 * NDoublonHolon2siteIdx; for (i = count; i < count + 2 * 5 * NDoublonHolon4siteIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); - Proj[i] = tmp_real + I * tmp_comp; + Proj[idx+count] = tmp_real + I * tmp_comp; } break; From 04c5addde51dd061d5f02cf41dcf59d1464760ce Mon Sep 17 00:00:00 2001 From: Yuichi Motoyama Date: Wed, 6 Sep 2017 10:47:51 +0900 Subject: [PATCH 06/34] added a missing ';' --- src/mVMC/readdef.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/mVMC/readdef.c b/src/mVMC/readdef.c index 911fb0aa..162bf082 100644 --- a/src/mVMC/readdef.c +++ b/src/mVMC/readdef.c @@ -1031,7 +1031,7 @@ int ReadInputParameters(char *xNameListFile, MPI_Comm comm) { info = 1; continue; } - count = 0 + count = 0; for (i = 0; i < NGutzwillerIdx; i++) { fscanf(fp, "%d %lf %lf ", &idx, &tmp_real, &tmp_comp); Proj[idx+count] = tmp_real + I * tmp_comp; From f88713f66bc7b1d3223df8dc1e30ca42229a0d3f Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Wed, 27 Sep 2017 10:52:55 +0900 Subject: [PATCH 07/34] Standard mode: Unify with HPhi. Bugfix in tthe face-centered orthorhombic lattice. Add tool for generating FermiSurfer file. --- src/StdFace/FCOrtho.c | 4 +-- src/StdFace/StdFace_ModelUtil.c | 12 ++++---- src/StdFace/StdFace_main.c | 35 +++++++++++++++------ tool/gen_frmsf.sh | 54 +++++++++++++++++++++++++++++++++ 4 files changed, 87 insertions(+), 18 deletions(-) create mode 100755 tool/gen_frmsf.sh diff --git a/src/StdFace/FCOrtho.c b/src/StdFace/FCOrtho.c index fcdd14db..2981be37 100644 --- a/src/StdFace/FCOrtho.c +++ b/src/StdFace/FCOrtho.c @@ -243,7 +243,7 @@ void StdFace_FCOrtho( /* (5) Nearest neighbor along L */ - StdFace_FindSite(StdI, iW, iL, iH, -1, 1, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, -1, 0, 1, 0, 0, &isite, &jsite, &Cphase); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); @@ -267,7 +267,7 @@ void StdFace_FCOrtho( /* (7) Nearest neighbor along H */ - StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 0, 0, 0, &isite, &jsite, &Cphase); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); diff --git a/src/StdFace/StdFace_ModelUtil.c b/src/StdFace/StdFace_ModelUtil.c index dc2a50f0..59bfcf7c 100644 --- a/src/StdFace/StdFace_ModelUtil.c +++ b/src/StdFace/StdFace_ModelUtil.c @@ -1413,11 +1413,11 @@ static void StdFace_InitSiteSub(struct StdIntList *StdI) StdI->NCellsub = 0; for (ii = 0; ii < 3; ii++) { StdI->NCellsub += StdI->boxsub[0][ii] - * StdI->boxsub[1][(ii + 1) % 3] - * StdI->boxsub[2][(ii + 2) % 3] - - StdI->boxsub[0][ii] - * StdI->boxsub[1][(ii + 2) % 3] - * StdI->boxsub[2][(ii + 1) % 3]; + * StdI->boxsub[1][(ii + 1) % 3] + * StdI->boxsub[2][(ii + 2) % 3] + - StdI->boxsub[0][ii] + * StdI->boxsub[1][(ii + 2) % 3] + * StdI->boxsub[2][(ii + 1) % 3]; } printf(" Number of Cell in the sublattice: %d\n", abs(StdI->NCellsub)); if (StdI->NCellsub == 0) { @@ -1427,7 +1427,7 @@ static void StdFace_InitSiteSub(struct StdIntList *StdI) for (ii = 0; ii < 3; ii++) { for (jj = 0; jj < 3; jj++) { StdI->rboxsub[ii][jj] = StdI->boxsub[(ii + 1) % 3][(jj + 1) % 3] * StdI->boxsub[(ii + 2) % 3][(jj + 2) % 3] - - StdI->boxsub[(ii + 1) % 3][(jj + 2) % 3] * StdI->boxsub[(ii + 2) % 3][(jj + 1) % 3]; + - StdI->boxsub[(ii + 1) % 3][(jj + 2) % 3] * StdI->boxsub[(ii + 2) % 3][(jj + 1) % 3]; } } if (StdI->NCellsub < 0) { diff --git a/src/StdFace/StdFace_main.c b/src/StdFace/StdFace_main.c index ed55d6df..d36c5816 100644 --- a/src/StdFace/StdFace_main.c +++ b/src/StdFace/StdFace_main.c @@ -333,13 +333,26 @@ static void PrintExcitation(struct StdIntList *StdI) { if (StdI->SpectrumBody == 1) { fp = fopen("single.def", "w"); fprintf(fp, "=============================================\n"); - fprintf(fp, "NSingle %d\n", StdI->nsite * NumOp); + if (strcmp(StdI->model, "kondo") == 0) { + fprintf(fp, "NSingle %d\n", StdI->nsite / 2 * NumOp); + } + else { + fprintf(fp, "NSingle %d\n", StdI->nsite * NumOp); + } fprintf(fp, "=============================================\n"); fprintf(fp, "============== Single Excitation ============\n"); fprintf(fp, "=============================================\n"); - for (isite = 0; isite < StdI->nsite; isite++) { - fprintf(fp, "%d %d 0 %25.15f %25.15f\n", isite, spin[0][0], - fourier_r[isite]*coef[0], fourier_i[isite] * coef[0]); + if (strcmp(StdI->model, "kondo") == 0) { + for (isite = StdI->nsite / 2; isite < StdI->nsite; isite++) { + fprintf(fp, "%d %d 0 %25.15f %25.15f\n", isite, spin[0][0], + fourier_r[isite] * coef[0], fourier_i[isite] * coef[0]); + }/*for (isite = 0; isite < StdI->nsite; isite++)*/ + }/*if (strcmp(StdI->model, "kondo") == 0)*/ + else { + for (isite = 0; isite < StdI->nsite; isite++) { + fprintf(fp, "%d %d 0 %25.15f %25.15f\n", isite, spin[0][0], + fourier_r[isite] * coef[0], fourier_i[isite] * coef[0]); + }/*for (isite = 0; isite < StdI->nsite; isite++)*/ } fprintf(stdout, " single.def is written.\n\n"); } @@ -1037,9 +1050,9 @@ static void PrintModPara(struct StdIntList *StdI) fprintf(fp, "NumAve %-5d\n", StdI->NumAve); fprintf(fp, "ExpecInterval %-5d\n", StdI->ExpecInterval); fprintf(fp, "NOmega %-5d\n", StdI->Nomega); - fprintf(fp, "OmegaMax %-25.15e\n", StdI->OmegaMax); - fprintf(fp, "OmegaMin %-25.15e\n", StdI->OmegaMin); - fprintf(fp, "OmegaIm %-25.15e\n", StdI->OmegaIm); + fprintf(fp, "OmegaMax %-25.15e %-25.15e\n", StdI->OmegaMax, StdI->OmegaIm); + fprintf(fp, "OmegaMin %-25.15e %-25.15e\n", StdI->OmegaMin, StdI->OmegaIm); + fprintf(fp, "OmegaOrg 0.0 0.0\n"); #elif defined(_mVMC) fprintf(fp, "VMC_Cal_Parameters\n"); fprintf(fp, "--------------------\n"); @@ -1806,12 +1819,14 @@ void StdFace_main( char *fname//!<[in] Input file name for the standard mode ) { - struct StdIntList StdI[1]; + struct StdIntList *StdI; FILE *fp; int ktrans, kintr; char ctmpline[256]; char *keyword, *value; + StdI = (struct StdIntList *)malloc(sizeof(struct StdIntList)); + fprintf(stdout, "\n###### Standard Intarface Mode STARTS ######\n"); if ((fp = fopen(fname, "r")) == NULL) { fprintf(stdout, "\n ERROR ! Cannot open input file %s !\n\n", fname); @@ -2105,7 +2120,7 @@ void StdFace_main( */ if (strcmp(StdI->lattice, "chain") == 0 || strcmp(StdI->lattice, "chainlattice") == 0) StdFace_Chain(StdI); - else if (strcmp(StdI->lattice, "facecenteredorthorhombic") == 0 + else if (strcmp(StdI->lattice, "face-centeredorthorhombic") == 0 || strcmp(StdI->lattice, "fcorthorhombic") == 0 || strcmp(StdI->lattice, "fco") == 0) StdFace_FCOrtho(StdI); else if (strcmp(StdI->lattice, "honeycomb") == 0 @@ -2189,7 +2204,7 @@ void StdFace_main( free(StdI->intr); fprintf(stdout, "\n###### Input files are generated. ######\n\n"); - + free(StdI); }/*void StdFace_main*/ /** @page page_addstandard Add new lattice model into Standard mode diff --git a/tool/gen_frmsf.sh b/tool/gen_frmsf.sh new file mode 100755 index 00000000..9fafea5a --- /dev/null +++ b/tool/gen_frmsf.sh @@ -0,0 +1,54 @@ +#!/bin/sh + +if test -z ${4} +then + echo "Usage:" + echo "$ gen_frmsf.sh filename nk1 nk2 nk3" + echo "In Standard mode, nk1=W, nk2=L, nk3=Height." + return +fi + +icor[1]=4 +icor[2]=6 +icor[3]=8 +icor[4]=14 + +cor[1]="up" +cor[2]="down" +cor[3]="density" +cor[4]="s2" + +for i in 1 2 3 4 +do + fname="${1}.${cor[i]}.frmsf" + echo -n "Writing ${fname} ... " + echo ${4} ${3} ${2} > ${fname} + + echo "1" >> ${fname} + echo "1" >> ${fname} + + awk 'NR==4+'${2}'*'${3}'+1{print '${4}'*$1, '${4}'*$2, '${4}'*$3}' ${1} >> ${fname} + awk 'NR==4+'${2}'+1 {print '${3}'*$1, '${3}'*$2, '${3}'*$3}' ${1} >> ${fname} + awk 'NR==4+1+1 {print '${2}'*$1, '${2}'*$2, '${2}'*$3}' ${1} >> ${fname} + + awk 'NR>4{print $'${icor[i]}'}' ${1} >> ${fname} + awk 'NR>4{print $'${icor[i]}'}' ${1} >> ${fname} + + #for i4 in `seq 1 ${4}` + #do + # ii4=`expr \( ${i4} - 1 + ${4} / 2 \) % ${4} - ${4} / 2` + # k4=`echo ${ii4} / ${4} | bc -l` + # for i3 in `seq 1 ${3}` + # do + # ii3=`expr \( $i3 - 1 + $3 / 2 \) % $3 - $3 / 2` + # k3=`echo ${ii3} / ${3} | bc -l` + # for i2 in `seq 1 ${2}` + # do + # ii2=`expr \( $i2 - 1 + $2 / 2 \) % $2 - $2 / 2` + # k2=`echo ${ii2} / ${2} | bc -l` + # echo `echo ${k2}^2 + ${k3}^2 + ${k4}^2 | bc -l` >> ${fname} + # done + # done + #done + echo "done" +done From 88aa5b0663f7d5528eeb50bebdd83bcc5bd07a0b Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Fri, 13 Oct 2017 09:42:17 +0900 Subject: [PATCH 08/34] Unify to HPhi --- tool/CMakeLists.txt | 10 +++++++++- tool/fourier.F90 | 2 +- 2 files changed, 10 insertions(+), 2 deletions(-) diff --git a/tool/CMakeLists.txt b/tool/CMakeLists.txt index 17ef0d7d..23f07813 100644 --- a/tool/CMakeLists.txt +++ b/tool/CMakeLists.txt @@ -13,4 +13,12 @@ target_link_libraries(fourier key2lower ${LAPACK_LIBRARIES}) install(TARGETS fourier RUNTIME DESTINATION bin) install(TARGETS corplot RUNTIME DESTINATION bin) - +# +# Scripts +# +configure_file(gen_frmsf.sh gen_frmsf.sh COPYONLY) +install(FILES ${CMAKE_CURRENT_BINARY_DIR}/gen_frmsf.sh DESTINATION bin + PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ GROUP_EXECUTE WORLD_READ WORLD_EXECUTE) +configure_file(wout2geom.sh wout2geom.sh COPYONLY) +install(FILES ${CMAKE_CURRENT_BINARY_DIR}/wout2geom.sh DESTINATION bin + PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ GROUP_EXECUTE WORLD_READ WORLD_EXECUTE) diff --git a/tool/fourier.F90 b/tool/fourier.F90 index d50c60e1..b9c40be0 100644 --- a/tool/fourier.F90 +++ b/tool/fourier.F90 @@ -813,7 +813,7 @@ SUBROUTINE output_cor() ELSE cor_err(1:nk,1:6) = CMPLX(SQRT( DBLE(cor_err(1:nk,1:6))), & & SQRT(AIMAG(cor_err(1:nk,1:6))), KIND(0d0)) & - & / (DBLE(nwfc - 1) * SQRT(DBLE(nwfc))) + & / SQRT(DBLE(nwfc * (nwfc - 1))) END IF ! filename = TRIM(filehead) // "_corr.dat" From 695be1c532d486534f1d6275dc03cf1533b0358d Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Tue, 14 Nov 2017 12:01:59 +0900 Subject: [PATCH 09/34] Add distribution tool --- dist.sh | 47 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 47 insertions(+) create mode 100755 dist.sh diff --git a/dist.sh b/dist.sh new file mode 100755 index 00000000..74b0f553 --- /dev/null +++ b/dist.sh @@ -0,0 +1,47 @@ +#!/bin/sh +# +# ############# Note ################################ +# Before packing, you should clean the GIT directory as +# $ git clean -f -d -x +# ##################################################### +# +# Version ID +# +major=`awk '$2=="VERSION_MAJOR"{print $3}' src/mVMC/include/version.h` +minor=`awk '$2=="VERSION_MINOR"{print $3}' src/mVMC/include/version.h` +patch=`awk '$2=="VERSION_PATCH"{print $3}' src/mVMC/include/version.h` +vid=`echo ${major}.${minor}.${patch}` +# +mkdir mVMC-${vid} +# +cp -rf * mVMC-${vid} +# +# Build docments +# +cd mVMC-${vid}/doc/jp +make -f makefile_doc_jp +cp userguide_jp.pdf ../../../ +cd ../en +make -f makefile_doc_en +cp userguide_en.pdf ../../../ +cd ../fourier/ja +sed -i -e "s/mathjax/pngmath/g" conf.py +make latexpdfja +make html +cd ../en +sed -i -e "s/mathjax/pngmath/g" conf.py +make latexpdfja +make html +cd ../../../ +# +# Remove some files +# +find ./ -name ".git*" -delete +rm dist.sh +rm -rf mVMC-${vid} +# +# Pack +# +cd ../ +tar czvf mVMC-${vid}.tar.gz mVMC-${vid} +rm -rf mVMC-${vid} From 90187164c1fd13a71a098029cc19813494274b97 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Tue, 16 Jan 2018 10:02:11 +0900 Subject: [PATCH 10/34] Unify to HPhi 20a96666f99f0a4df8d7ecfb9b034fda3a4c563f --- src/StdFace/ChainLattice.c | 11 +- src/StdFace/FCOrtho.c | 37 +-- src/StdFace/HoneycombLattice.c | 37 +-- src/StdFace/Kagome.c | 49 ++-- src/StdFace/Ladder.c | 21 +- src/StdFace/Orthorhombic.c | 53 ++-- src/StdFace/Pyrochlore.c | 49 ++-- src/StdFace/SquareLattice.c | 17 +- src/StdFace/StdFace_ModelUtil.c | 76 +++++- src/StdFace/StdFace_ModelUtil.h | 6 +- src/StdFace/StdFace_main.c | 448 ++++++++++++++++++++++++++------ src/StdFace/StdFace_vals.h | 31 ++- src/StdFace/TriangularLattice.c | 25 +- src/StdFace/Wannier90.c | 5 +- 14 files changed, 617 insertions(+), 248 deletions(-) diff --git a/src/StdFace/ChainLattice.c b/src/StdFace/ChainLattice.c index b6b75d67..73245215 100644 --- a/src/StdFace/ChainLattice.c +++ b/src/StdFace/ChainLattice.c @@ -38,7 +38,8 @@ void StdFace_Chain( int isite, jsite, ntransMax, nintrMax; int iL; double complex Cphase; - + double dR[3]; + fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); fprintf(stdout, "\n"); @@ -187,25 +188,25 @@ void StdFace_Chain( /* Nearest neighbor */ - StdFace_SetLabel(StdI, fp, 0, iL, 0, 1, 0, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, 0, iL, 0, 1, 0, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* Second nearest neighbor */ - StdFace_SetLabel(StdI, fp, 0, iL, 0, 2, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, 0, iL, 0, 2, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } }/*for (iL = 0; iL < StdI->L; iL++)*/ diff --git a/src/StdFace/FCOrtho.c b/src/StdFace/FCOrtho.c index 2981be37..a4627e32 100644 --- a/src/StdFace/FCOrtho.c +++ b/src/StdFace/FCOrtho.c @@ -38,6 +38,7 @@ void StdFace_FCOrtho( int iL, iW, iH, kCell; FILE *fp; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -207,109 +208,109 @@ void StdFace_FCOrtho( /* (2) Nearest neighbor along W */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 0, 0, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 0, 0, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* (3) Nearest neighbor along W */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 1, -1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 1, -1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* (4) Nearest neighbor along L */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 1, 0, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 1, 0, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* (5) Nearest neighbor along L */ - StdFace_FindSite(StdI, iW, iL, iH, -1, 0, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, -1, 0, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* (6) Nearest neighbor along H */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); } /* (7) Nearest neighbor along H */ - StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 0, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 0, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); } /* (8) Second nearest neighbor along -W+L+H */ - StdFace_FindSite(StdI, iW, iL, iH, -1, 1, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, -1, 1, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0p, isite, jsite); } /* (9) Second nearest neighbor along -L+H+W */ - StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1p, isite, jsite); } /* (10) Second nearest neighbor along -H+W+L */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 1, -1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 1, -1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2p, isite, jsite); } }/*for (kCell = 0; kCell < StdI->NCell; kCell++)*/ diff --git a/src/StdFace/HoneycombLattice.c b/src/StdFace/HoneycombLattice.c index ded6f609..baf0f1f7 100644 --- a/src/StdFace/HoneycombLattice.c +++ b/src/StdFace/HoneycombLattice.c @@ -36,6 +36,7 @@ void StdFace_Honeycomb(struct StdIntList *StdI) int iL, iW; FILE *fp; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -198,109 +199,109 @@ void StdFace_Honeycomb(struct StdIntList *StdI) /* Nearest neighbor intra cell 0 -> 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 0, 0, 1, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 0, 0, 1, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* Nearest neighbor along W 1 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 1, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 1, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* Nearest neighbor along L 1 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 1, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 1, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); } /* Second nearest neighbor along W 0 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along W 1 -> 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 1, 1, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 1, 1, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along L 0 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along L 1 -> 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 1, 1, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 1, 1, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along W-L 0 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, - 1, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, - 1, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along W - L 1 -> 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, -1, 1, 1, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, -1, 1, 1, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } }/*for (kCell = 0; kCell < StdI->NCell; kCell++)*/ diff --git a/src/StdFace/Kagome.c b/src/StdFace/Kagome.c index dc43ad73..28b0aa5c 100644 --- a/src/StdFace/Kagome.c +++ b/src/StdFace/Kagome.c @@ -38,6 +38,7 @@ void StdFace_Kagome( int iL, iW; FILE *fp; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -201,145 +202,145 @@ void StdFace_Kagome( /*>> Nearest neighbor intra cell 0 -> 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 0, 0, 1, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 0, 0, 1, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); }//<< /* Nearest neighbor intra cell 0 -> 2 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 0, 0, 2, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 0, 0, 2, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* Nearest neighbor intra cell 1 -> 2 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 0, 1, 2, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 0, 1, 2, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* Nearest neighbor along W 1 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 1, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 1, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); } /* Nearest neighbor along L 2 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 2, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 2, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* Nearest neighbor along W-L 1 -> 2 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, - 1, 1, 2, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, - 1, 1, 2, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* Second nearest neighbor along W 2 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 2, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 2, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along W 1 -> 2 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 1, 2, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 1, 2, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along L 1 -> 0 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 1, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 1, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along L 2 -> 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 2, 1, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 2, 1, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along W-L 0 -> 2 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, - 1, 0, 2, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, - 1, 0, 2, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor along L-W 0 -> 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, - 1, 1, 0, 1, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, - 1, 1, 0, 1, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } }/*for (kCell = 0; kCell < StdI->NCell; kCell++)*/ diff --git a/src/StdFace/Ladder.c b/src/StdFace/Ladder.c index ddbb23f5..8cab651a 100644 --- a/src/StdFace/Ladder.c +++ b/src/StdFace/Ladder.c @@ -38,6 +38,7 @@ void StdFace_Ladder( int isite, jsite, ntransMax, nintrMax; int iL, isiteUC; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -211,25 +212,25 @@ void StdFace_Ladder( /* Nearest neighbor along the ladder */ - StdFace_SetLabel(StdI, fp, 0, iL, 0, 1, isiteUC, isiteUC, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, 0, iL, 0, 1, isiteUC, isiteUC, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); }/*if (model != "spin")*/ /* Second nearest neighbor along the ladder */ - StdFace_SetLabel(StdI, fp, 0, iL, 0, 2, isiteUC, isiteUC, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, 0, iL, 0, 2, isiteUC, isiteUC, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J1p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1p, isite, jsite); }/*if (model != "spin")*/ /* @@ -239,37 +240,37 @@ void StdFace_Ladder( /* Vertical */ - StdFace_SetLabel(StdI, fp, 0, iL, 0, 0, isiteUC, isiteUC + 1, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, 0, iL, 0, 0, isiteUC, isiteUC + 1, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); }/*if (model != "spin")*/ /* Diagonal 1 */ - StdFace_SetLabel(StdI, fp, 0, iL, 0, 1, isiteUC, isiteUC + 1, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, 0, iL, 0, 1, isiteUC, isiteUC + 1, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); }/*if (model != "spin")*/ /* Diagonal 2 */ - StdFace_SetLabel(StdI, fp, 0, iL, 0, -1, isiteUC, isiteUC + 1, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, 0, iL, 0, -1, isiteUC, isiteUC + 1, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J2p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2p, isite, jsite); }/*if (model != "spin")*/ diff --git a/src/StdFace/Orthorhombic.c b/src/StdFace/Orthorhombic.c index 63aa60ab..dd79c52d 100644 --- a/src/StdFace/Orthorhombic.c +++ b/src/StdFace/Orthorhombic.c @@ -38,6 +38,7 @@ void StdFace_Orthorhombic( int iL, iW, iH, kCell; FILE *fp; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -207,157 +208,157 @@ void StdFace_Orthorhombic( /* (2) Nearest neighbor along W */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 0, 0, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 0, 0, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* (3) Nearest neighbor along L */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 1, 0, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 1, 0, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* (4) Nearest neighbor along H */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); } /* (5) Second nearest neighbor along +L+H */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 1, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 1, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0p, isite, jsite); } /* (6) Second nearest neighbor along +L-H */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 1, -1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 1, -1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J0p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0p, isite, jsite); } /* (7) Second nearest neighbor along +H+W */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 0, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 0, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1p, isite, jsite); } /* (8) Second nearest neighbor along +H-W */ - StdFace_FindSite(StdI, iW, iL, iH, -1, 0, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, -1, 0, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1p, isite, jsite); } /* (9) Second nearest neighbor along +W+L */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 1, 0, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 1, 0, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2p, isite, jsite); } /* (10) Second nearest neighbor along +W-L */ - StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 0, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 0, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2p, isite, jsite); } /* (11) Third nearest neighbor along +W+L+H */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 1, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 1, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->Jpp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tpp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tpp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vpp, isite, jsite); } /* (12) Third nearest neighbor along -W+L+H */ - StdFace_FindSite(StdI, iW, iL, iH, -1, 1, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, -1, 1, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->Jpp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tpp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tpp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vpp, isite, jsite); } /* (13) Third nearest neighbor along +W-L+H */ - StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, -1, 1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->Jpp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tpp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tpp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vpp, isite, jsite); } /* (14) Third nearest neighbor along +W+L-H */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 1, -1, 0, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 1, -1, 0, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->Jpp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tpp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tpp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vpp, isite, jsite); } }/*for (kCell = 0; kCell < StdI->NCell; kCell++)*/ diff --git a/src/StdFace/Pyrochlore.c b/src/StdFace/Pyrochlore.c index 24f7b17e..94681e5c 100644 --- a/src/StdFace/Pyrochlore.c +++ b/src/StdFace/Pyrochlore.c @@ -38,6 +38,7 @@ void StdFace_Pyrochlore( int iL, iW, iH, kCell; FILE *fp; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -217,145 +218,145 @@ void StdFace_Pyrochlore( /* (2) Intra-Cell along W */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 0, 1, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 0, 1, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* (3) Intra-Cell along L */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 0, 2, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 0, 2, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* (4) Intra-Cell along H */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 0, 3, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 0, 3, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); } /* (5) Intra-Cell along L-H */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 2, 3, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 2, 3, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J0p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0p, isite, jsite); } /* (6) Intra-Cell along H-W */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 3, 1, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 3, 1, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1p, isite, jsite); } /* (7) Intra-Cell along W-L */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 1, 2, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 0, 1, 2, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2p, isite, jsite); } /* (8) Inter-Cell along W */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 0, 0, 1, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 0, 0, 1, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* (9) Inter-Cell along L */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 1, 0, 2, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 1, 0, 2, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* (10) Inter-Cell along H */ - StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 1, 3, 0, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, 0, 1, 3, 0, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); } /* (11) Inter-Cell along L-H */ - StdFace_FindSite(StdI, iW, iL, iH, 0, -1, 1, 3, 2, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 0, -1, 1, 3, 2, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J0p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0p, isite, jsite); } /* (12) Intra-Cell along H-W */ - StdFace_FindSite(StdI, iW, iL, iH, 1, 0, -1, 1, 3, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, 1, 0, -1, 1, 3, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J1p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1p, isite, jsite); } /* (13) Intra-Cell along W-L */ - StdFace_FindSite(StdI, iW, iL, iH, -1, 1, 0, 2, 1, &isite, &jsite, &Cphase); + StdFace_FindSite(StdI, iW, iL, iH, -1, 1, 0, 2, 1, &isite, &jsite, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0) { StdFace_GeneralJ(StdI, StdI->J2p, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2p, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2p, isite, jsite); } }/*for (kCell = 0; kCell < StdI->NCell; kCell++)*/ diff --git a/src/StdFace/SquareLattice.c b/src/StdFace/SquareLattice.c index 92ea2c6d..88404ad3 100644 --- a/src/StdFace/SquareLattice.c +++ b/src/StdFace/SquareLattice.c @@ -36,6 +36,7 @@ void StdFace_Tetragonal(struct StdIntList *StdI) int iL, iW, kCell; FILE *fp; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -187,49 +188,49 @@ void StdFace_Tetragonal(struct StdIntList *StdI) /* Nearest neighbor along W */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 0, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 0, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* Nearest neighbor along L */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 0, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 0, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* Second nearest neighbor 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 1, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 1, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor 2 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, -1, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, -1, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); }/*if (model != "spin")*/ }/*for (kCell = 0; kCell < StdI->NCell; kCell++)*/ diff --git a/src/StdFace/StdFace_ModelUtil.c b/src/StdFace/StdFace_ModelUtil.c index 59bfcf7c..c3728c23 100644 --- a/src/StdFace/StdFace_ModelUtil.c +++ b/src/StdFace/StdFace_ModelUtil.c @@ -76,19 +76,46 @@ void StdFace_Hopping( struct StdIntList *StdI,//!<[inout] double complex trans0,//!<[in] Hopping integral @f$t@f$ int isite,//!<[in] @f$i@f$ for @f$c_{i \sigma}^\dagger@f$ - int jsite//!<[in] @f$j@f$ for @f$c_{j \sigma}@f$ + int jsite,//!<[in] @f$j@f$ for @f$c_{j \sigma}@f$ + double *dR//!<[in] R_i - R_j ) { - int ispin; + int ispin, it, ii; + double complex Cphase, coef; /**@brief Both @f$c_{i \sigma}^\dagger c_{j \sigma}@f$ and @f$c_{j \sigma}^\dagger c_{i \sigma}@f$ for every spin channel (@f$\sigma@f$) is specified */ - for (ispin = 0; ispin < 2; ispin++) { - StdFace_trans(StdI, trans0, jsite, ispin, isite, ispin); - StdFace_trans(StdI, conj(trans0), isite, ispin, jsite, ispin); - }/*for (ispin = 0; ispin < 2; ispin++)*/ +#if defined(_HPhi) + if (strcmp(StdI->method, "timeevolution") == 0 && StdI->PumpBody == 1) { + for (it = 0; it < StdI->Lanczos_max; it++) { + Cphase = 0.0f; + for (ii = 0; ii < 3; ii++) Cphase += /*2.0*StdI->pi */ StdI->At[it][ii] * dR[ii]; + coef = cos(Cphase) + I * sin(-Cphase); + for (ispin = 0; ispin < 2; ispin++) { + StdI->pump[it][StdI->npump[it]] = coef * trans0; + StdI->pumpindx[it][StdI->npump[it]][0] = isite; + StdI->pumpindx[it][StdI->npump[it]][1] = ispin; + StdI->pumpindx[it][StdI->npump[it]][2] = jsite; + StdI->pumpindx[it][StdI->npump[it]][3] = ispin; + StdI->npump[it] = StdI->npump[it] + 1; + + StdI->pump[it][StdI->npump[it]] = conj(coef * trans0); + StdI->pumpindx[it][StdI->npump[it]][0] = jsite; + StdI->pumpindx[it][StdI->npump[it]][1] = ispin; + StdI->pumpindx[it][StdI->npump[it]][2] = isite; + StdI->pumpindx[it][StdI->npump[it]][3] = ispin; + StdI->npump[it] = StdI->npump[it] + 1; + }/*for (ispin = 0; ispin < 2; ispin++)*/ + }/*for (it = 0; it < StdI->Lanczos_max; it++)*/ + }/*if (strcmp(StdI->method, "timeevolution") == 0)*/ + else +#endif + for (ispin = 0; ispin < 2; ispin++) { + StdFace_trans(StdI, trans0, jsite, ispin, isite, ispin); + StdFace_trans(StdI, conj(trans0), isite, ispin, jsite, ispin); + }/*for (ispin = 0; ispin < 2; ispin++)*/ }/*void StdFace_Hopping*/ /** @brief Add intra-Coulomb, magnetic field, chemical potential for the @@ -805,12 +832,17 @@ void StdFace_FindSite( int jsiteUC,//!<[in] Intrinsic site index of final site int *isite,//!<[out] initial site int *jsite,//!<[out] final site - double complex *Cphase//!<[out] Boundary phase, if it across boundary + double complex *Cphase,//!<[out] Boundary phase, if it across boundary + double *dR//!<[out] R_i - R_j in the fractional coordinate ) { int iCell, jCell, kCell, ii; int nBox[3], jCellV[3]; /**/ + dR[0] = - (double)diW + StdI->tau[isiteUC][0] - StdI->tau[jsiteUC][0]; + dR[1] = - (double)diL + StdI->tau[isiteUC][1] - StdI->tau[jsiteUC][1]; + dR[2] = - (double)diH + StdI->tau[isiteUC][2] - StdI->tau[jsiteUC][2]; + /**/ jCellV[0] = iW + diW; jCellV[1] = iL + diL; jCellV[2] = iH + diH; @@ -854,14 +886,15 @@ void StdFace_SetLabel( int *isite,//!<[out] initial site int *jsite,//!<[out] final site int connect,//!<[in] 1 for nearest neighbor, 2 for 2nd nearest - double complex *Cphase//!<[out] Boundary phase, if it across boundary + double complex *Cphase,//!<[out] Boundary phase, if it across boundary + double *dR//!<[out] R_i - R_j ) { double xi, yi, xj, yj; /**@brief First print the reversed one */ - StdFace_FindSite(StdI, iW, iL, 0, -diW, -diL, 0, jsiteUC, isiteUC, isite, jsite, Cphase); + StdFace_FindSite(StdI, iW, iL, 0, -diW, -diL, 0, jsiteUC, isiteUC, isite, jsite, Cphase, dR); xi = StdI->direct[0][0] * ((double)iW + StdI->tau[jsiteUC][0]) + StdI->direct[1][0] * ((double)iL + StdI->tau[jsiteUC][1]); @@ -881,7 +914,7 @@ void StdFace_SetLabel( /**@brief Then print the normal one, these are different when they cross boundary. */ - StdFace_FindSite(StdI, iW, iL, 0, diW, diL, 0, isiteUC, jsiteUC, isite, jsite, Cphase); + StdFace_FindSite(StdI, iW, iL, 0, diW, diL, 0, isiteUC, jsiteUC, isite, jsite, Cphase, dR); xi = StdI->direct[1][0] * ((double)iL + StdI->tau[isiteUC][1]) + StdI->direct[0][0] * ((double)iW + StdI->tau[isiteUC][0]); @@ -1165,6 +1198,9 @@ void StdFace_MallocInteractions( int nintrMax//!<[in] upper limit of the number of interaction ) { int ii; +#if defined(_HPhi) + int it; +#endif /**@brief (1) Transfer StdIntList::trans, StdIntList::transindx */ @@ -1174,6 +1210,21 @@ void StdFace_MallocInteractions( StdI->transindx[ii] = (int *)malloc(sizeof(int) * 4); } StdI->ntrans = 0; +#if defined(_HPhi) + if (strcmp(StdI->method, "timeevolution") == 0 && StdI->PumpBody == 1) { + StdI->npump = (int *)malloc(sizeof(int) * StdI->Lanczos_max); + StdI->pumpindx = (int ***)malloc(sizeof(int**) * StdI->Lanczos_max); + StdI->pump = (double complex **)malloc(sizeof(double complex*) * StdI->Lanczos_max); + for (it = 0; it < StdI->Lanczos_max; it++) { + StdI->npump[it] = 0; + StdI->pumpindx[it] = (int **)malloc(sizeof(int*) * ntransMax); + StdI->pump[it] = (double complex *)malloc(sizeof(double complex) * ntransMax); + for (ii = 0; ii < ntransMax; ii++) { + StdI->pumpindx[it][ii] = (int *)malloc(sizeof(int) * 4); + } + }/*for (it = 0; it < StdI->Lanczos_max;)*/ + }/*if (strcmp(StdI->method, "timeevolution") == 0*/ +#endif /**@brief (2) InterAll StdIntList::intr, StdIntList::intrindx */ @@ -1588,6 +1639,7 @@ void PrintJastrow(struct StdIntList *StdI) { int dCell, iCell;//, jCell, dCellv[3]; int **Jastrow; double complex Cphase; + double dR[3]; Jastrow = (int **)malloc(sizeof(int*) * StdI->nsite); for (isite = 0; isite < StdI->nsite; isite++) @@ -1683,7 +1735,7 @@ void PrintJastrow(struct StdIntList *StdI) { StdFace_FindSite(StdI, 0, 0, 0, -StdI->Cell[dCell][0], -StdI->Cell[dCell][1], -StdI->Cell[dCell][2], - 0, 0, &isite, &jsite, &Cphase); + 0, 0, &isite, &jsite, &Cphase, dR); if (strcmp(StdI->model, "kondo") == 0) jsite += -StdI->NCell * StdI->NsiteUC; iCell = jsite / StdI->NsiteUC; if (iCell < dCell) { @@ -1712,7 +1764,7 @@ void PrintJastrow(struct StdIntList *StdI) { StdFace_FindSite(StdI, StdI->Cell[iCell][0], StdI->Cell[iCell][1], StdI->Cell[iCell][2], StdI->Cell[dCell][0], StdI->Cell[dCell][1], StdI->Cell[dCell][2], - isiteUC, jsiteUC, &isite, &jsite, &Cphase); + isiteUC, jsiteUC, &isite, &jsite, &Cphase, dR); Jastrow[isite][jsite] = NJastrow; Jastrow[jsite][isite] = NJastrow; diff --git a/src/StdFace/StdFace_ModelUtil.h b/src/StdFace/StdFace_ModelUtil.h index e063b6bf..907d0a61 100644 --- a/src/StdFace/StdFace_ModelUtil.h +++ b/src/StdFace/StdFace_ModelUtil.h @@ -24,7 +24,7 @@ void StdFace_intr(struct StdIntList *StdI, double complex intr0, int site1, int spin1, int site2, int spin2, int site3, int spin3, int site4, int spin4); -void StdFace_Hopping(struct StdIntList *StdI, double complex trans0, int isite, int jsite); +void StdFace_Hopping(struct StdIntList *StdI, double complex trans0, int isite, int jsite, double *dR); void StdFace_HubbardLocal(struct StdIntList *StdI, double mu0, double h0, double Gamma0, double U0, int isite); void StdFace_MagField(struct StdIntList *StdI, int S2, double h, double Gamma, int isite); @@ -54,13 +54,13 @@ void StdFace_InputHopp(struct StdIntList *StdI, double complex *t0, char *t0name void StdFace_InitSite(struct StdIntList *StdI, FILE *fp, int dim); void StdFace_SetLabel(struct StdIntList *StdI, FILE *fp, int iW, int iL, int diW, int diL, int isiteUC, int jsiteUC, - int *isite, int *jsite, int connect, double complex *Cphase); + int *isite, int *jsite, int connect, double complex *Cphase, double *dR); void StdFace_PrintGeometry(struct StdIntList *StdI); void StdFace_MallocInteractions(struct StdIntList *StdI, int ntransMax, int nintrMax); void StdFace_FindSite(struct StdIntList *StdI, int iW, int iL, int iH, int diW, int diL, int diH, int isiteUC, int jsiteUC, - int *isite, int *jsite, double complex *Cphase); + int *isite, int *jsite, double complex *Cphase, double *dR); void StdFace_PrintXSF(struct StdIntList *StdI); void StdFace_Tetragonal(struct StdIntList *StdI); diff --git a/src/StdFace/StdFace_main.c b/src/StdFace/StdFace_main.c index d36c5816..30d10f05 100644 --- a/src/StdFace/StdFace_main.c +++ b/src/StdFace/StdFace_main.c @@ -102,14 +102,14 @@ static void PrintCalcMod(struct StdIntList *StdI) iCalcEigenvec = 1; } else if (strcmp(StdI->method, "tpq") == 0) iCalcType = 1; - else if (strcmp(StdI->method, "fulldiag") == 0 || - strcmp(StdI->method, "alldiag") == 0 || - strcmp(StdI->method, "direct") == 0 ) iCalcType = 2; + else if (strcmp(StdI->method, "fulldiag") == 0 ) iCalcType = 2; else if (strcmp(StdI->method, "cg") == 0) iCalcType = 3; + else if (strcmp(StdI->method, "timeevolution") == 0) iCalcType = 4; else{ fprintf(stdout, "\n ERROR ! Unsupported Solver : %s\n", StdI->method); StdFace_exit(-1); }/*if (strcmp(StdI->method, METHODS) != 0*/ + if (iCalcType != 4) StdI->PumpBody = 0; /* Model */ @@ -136,9 +136,11 @@ static void PrintCalcMod(struct StdIntList *StdI) else { fprintf(stdout, " Restart = %s\n", StdI->Restart); if (strcmp(StdI->Restart, "none") == 0) iRestart = 0; - else if (strcmp(StdI->Restart, "save") == 0) iRestart = 1; - else if (strcmp(StdI->Restart, "restartsave") == 0) iRestart = 2; - else if (strcmp(StdI->Restart, "restart") == 0) iRestart = 3; + else if (strcmp(StdI->Restart, "restart_out") == 0 || + strcmp(StdI->Restart, "save") == 0) iRestart = 1; + else if (strcmp(StdI->Restart, "restartsave") == 0 || + strcmp(StdI->Restart, "restart") == 0) iRestart = 2; + else if (strcmp(StdI->Restart, "restart_in") == 0) iRestart = 3; else { fprintf(stdout, "\n ERROR ! Restart Mode : %s\n", StdI->Restart); StdFace_exit(-1); @@ -184,6 +186,7 @@ static void PrintCalcMod(struct StdIntList *StdI) StdFace_exit(-1); } }/*if (strcmp(StdI->EigenVecIO, "****") != 0)*/ + if (strcmp(StdI->method, "timeevolution") == 0) InputEigenVec = 1; /* CalcSpec */ @@ -197,9 +200,10 @@ static void PrintCalcMod(struct StdIntList *StdI) if (strcmp(StdI->CalcSpec, "none") == 0) iCalcSpec = 0; else if (strcmp(StdI->CalcSpec, "normal") == 0) iCalcSpec = 1; else if (strcmp(StdI->CalcSpec, "noiteration") == 0) iCalcSpec = 2; - else if (strcmp(StdI->CalcSpec, "save") == 0) iCalcSpec = 3; - else if (strcmp(StdI->CalcSpec, "restart") == 0) iCalcSpec = 4; - else if (strcmp(StdI->CalcSpec, "restartsave") == 0) iCalcSpec = 5; + else if (strcmp(StdI->CalcSpec, "restart_out") == 0) iCalcSpec = 3; + else if (strcmp(StdI->CalcSpec, "restart_in") == 0) iCalcSpec = 4; + else if (strcmp(StdI->CalcSpec, "restartsave") == 0 || + strcmp(StdI->CalcSpec, "restart") == 0) iCalcSpec = 5; else { fprintf(stdout, "\n ERROR ! CalcSpec : %s\n", StdI->CalcSpec); StdFace_exit(-1); @@ -207,7 +211,7 @@ static void PrintCalcMod(struct StdIntList *StdI) }/*if (strcmp(StdI->CalcSpec, "****") != 0)*/ fp = fopen("calcmod.def", "w"); - fprintf(fp, "#CalcType = 0:Lanczos, 1:TPQCalc, 2:FullDiag, 3:CG\n"); + fprintf(fp, "#CalcType = 0:Lanczos, 1:TPQCalc, 2:FullDiag, 3:CG, 4:Time-evolution\n"); fprintf(fp, "#CalcModel = 0:Hubbard, 1:Spin, 2:Kondo, 3:HubbardGC, 4:SpinGC, 5:KondoGC\n"); fprintf(fp, "#Restart = 0:None, 1:Save, 2:Restart&Save, 3:Restart\n"); fprintf(fp, "#CalcSpec = 0:None, 1:Normal, 2:No H*Phi, 3:Save, 4:Restart, 5:Restart&Save\n"); @@ -229,35 +233,43 @@ static void PrintCalcMod(struct StdIntList *StdI) */ static void PrintExcitation(struct StdIntList *StdI) { FILE *fp; - int NumOp, spin[2][2], isite, ispin, icell, itau; - double coef[2], pi, Cphase; + int NumOp, **spin, isite, ispin, icell, itau; + double *coef, pi, Cphase, S, Sz; double *fourier_r, *fourier_i; + if (strcmp(StdI->model, "spin") == 0 && StdI->S2 > 1) { + coef = (double *)malloc(sizeof(double) * (StdI->S2 + 1)); + spin = (int **)malloc(sizeof(int*) * (StdI->S2 + 1)); + for (ispin = 0; ispin < StdI->S2 + 1; ispin++) spin[ispin] = (int *)malloc(sizeof(int) * 2); + } + else { + coef = (double *)malloc(sizeof(double) * 2); + spin = (int **)malloc(sizeof(int*) * 2); + for (ispin = 0; ispin < 2; ispin++) spin[ispin] = (int *)malloc(sizeof(int) * 2); + } + fourier_r = (double *)malloc(sizeof(double) * StdI->nsite); fourier_i = (double *)malloc(sizeof(double) * StdI->nsite); - pi = acos(-1.0); - + fprintf(stdout, "\n @ Spectrum\n\n"); - StdFace_PrintVal_d("SpectrumQW", &StdI->SpectrumQW, 0.0); - StdFace_PrintVal_d("SpectrumQL", &StdI->SpectrumQL, 0.0); - StdFace_PrintVal_d("SpectrumQH", &StdI->SpectrumQH, 0.0); + StdFace_PrintVal_d("SpectrumQW", &StdI->SpectrumQ[0], 0.0); + StdFace_PrintVal_d("SpectrumQL", &StdI->SpectrumQ[1], 0.0); + StdFace_PrintVal_d("SpectrumQH", &StdI->SpectrumQ[2], 0.0); if (strcmp(StdI->SpectrumType, "****") == 0) { strcpy(StdI->SpectrumType, "szsz\0"); fprintf(stdout, " SpectrumType = szsz ###### DEFAULT VALUE IS USED ######\n"); - NumOp = 2; - coef[0] = 0.5; - coef[1] = -0.5; - spin[0][0] = 0; - spin[0][1] = 0; - spin[1][0] = 1; - spin[1][1] = 1; - StdI->SpectrumBody = 2; - } - else { - fprintf(stdout, " SpectrumType = %s\n", StdI->SpectrumType); - if (strcmp(StdI->SpectrumType, "szsz") == 0) { + if (strcmp(StdI->model, "spin") == 0) { + NumOp = StdI->S2 + 1; + for (ispin = 0; ispin <= StdI->S2; ispin++) { + Sz = (double)ispin - (double)StdI->S2 * 0.5; + coef[ispin] = Sz; + spin[ispin][0] = ispin; + spin[ispin][1] = ispin; + } + } + else { NumOp = 2; coef[0] = 0.5; coef[1] = -0.5; @@ -265,13 +277,49 @@ static void PrintExcitation(struct StdIntList *StdI) { spin[0][1] = 0; spin[1][0] = 1; spin[1][1] = 1; + } + StdI->SpectrumBody = 2; + } + else { + fprintf(stdout, " SpectrumType = %s\n", StdI->SpectrumType); + if (strcmp(StdI->SpectrumType, "szsz") == 0) { + if (strcmp(StdI->model, "spin") == 0) { + NumOp = StdI->S2 + 1; + for (ispin = 0; ispin <= StdI->S2; ispin++) { + Sz = (double)ispin - (double)StdI->S2 * 0.5; + coef[ispin] = Sz; + spin[ispin][0] = ispin; + spin[ispin][1] = ispin; + } + } + else { + NumOp = 2; + coef[0] = 0.5; + coef[1] = -0.5; + spin[0][0] = 0; + spin[0][1] = 0; + spin[1][0] = 1; + spin[1][1] = 1; + } StdI->SpectrumBody = 2; } else if (strcmp(StdI->SpectrumType, "s+s-") == 0) { - NumOp = 1; - coef[0] = 1.0; - spin[0][0] = 0; - spin[0][1] = 1; + if (strcmp(StdI->model, "spin") == 0 && StdI->S2 > 1) { + NumOp = StdI->S2; + S = (double)StdI->S2 * 0.5; + for (ispin = 0; ispin < StdI->S2; ispin++) { + Sz = (double)ispin - (double)StdI->S2 * 0.5; + coef[ispin] = sqrt(S*(S + 1.0) - Sz*(Sz + 1.0)); + spin[ispin][0] = ispin; + spin[ispin][1] = ispin + 1; + } + } + else { + NumOp = 1; + coef[0] = 1.0; + spin[0][0] = 0; + spin[0][1] = 1; + } StdI->SpectrumBody = 2; } else if (strcmp(StdI->SpectrumType, "density") == 0) { @@ -302,24 +350,14 @@ static void PrintExcitation(struct StdIntList *StdI) { } } - if ((strcmp(StdI->model, "spin") == 0 && StdI->S2 > 1) - || strcmp(StdI->model, "kondo") == 0) { - printf("####################################\n"); - printf("########### CAUTION ##############\n"); - printf("####################################\n"); - printf("\n"); - printf(" For Kondo or S>1 system, excitation parameter file is NOT generated automatically.\n"); - printf(" Please write it by hand.\n"); - }/*if (StdI->S2 > 1 || strcmp(StdI->model, "kondo") == 0)*/ - isite = 0; for (icell = 0; icell < StdI->NCell; icell++) { for (itau = 0; itau < StdI->NsiteUC; itau++) { - Cphase = (StdI->Cell[icell][0] + StdI->tau[itau][0])*StdI->SpectrumQW - + (StdI->Cell[icell][1] + StdI->tau[itau][1])*StdI->SpectrumQL - + (StdI->Cell[icell][2] + StdI->tau[itau][2])*StdI->SpectrumQH; - fourier_r[isite] = cos(2.0*pi*Cphase); - fourier_i[isite] = sin(2.0*pi*Cphase); + Cphase = (StdI->Cell[icell][0] + StdI->tau[itau][0])*StdI->SpectrumQ[0] + + (StdI->Cell[icell][1] + StdI->tau[itau][1])*StdI->SpectrumQ[1] + + (StdI->Cell[icell][2] + StdI->tau[itau][2])*StdI->SpectrumQ[2]; + fourier_r[isite] = cos(2.0*StdI->pi*Cphase); + fourier_i[isite] = sin(2.0*StdI->pi*Cphase); isite += 1; } } @@ -377,8 +415,180 @@ static void PrintExcitation(struct StdIntList *StdI) { free(fourier_r); free(fourier_i); + if (strcmp(StdI->model, "spin") == 0) + for (ispin = 0; ispin < StdI->S2 + 1; ispin++) free(spin[ispin]); + else + for (ispin = 0; ispin < 2; ispin++) free(spin[ispin]); + free(spin); + free(coef); }/*static void PrintExcitation()*/ +/* +@brief Compute vectorpotential +*/ +static void VectorPotential(struct StdIntList *StdI) { + FILE *fp; + int it, ii, isite, icell, itau, itrans, jsite, jcell, jtau, ntrans0; + double Cphase, time, dR[3]; + double **Et; + double complex coef; + + fprintf(stdout, "\n @ Time-evolution\n\n"); + + StdFace_PrintVal_d("VecPotW", &StdI->VecPot[0], 0.0); + StdFace_PrintVal_d("VecPotL", &StdI->VecPot[1], 0.0); + StdFace_PrintVal_d("VecPotH", &StdI->VecPot[2], 0.0); + StdFace_PrintVal_i("Lanczos_max", &StdI->Lanczos_max, 1000); + StdFace_PrintVal_d("dt", &StdI->dt, 0.1); + StdFace_PrintVal_d("freq", &StdI->freq, 0.1); + StdFace_PrintVal_d("tshift", &StdI->tshift, 0.0); + StdFace_PrintVal_d("tdump", &StdI->tdump, 0.1); + StdFace_PrintVal_d("Uquench", &StdI->Uquench, 0.0); + StdFace_PrintVal_i("ExpandCoef", &StdI->ExpandCoef, 10); + StdI->At = (double **)malloc(sizeof(double*) * StdI->Lanczos_max); + Et = (double **)malloc(sizeof(double*) * StdI->Lanczos_max); + for (it = 0; it < StdI->Lanczos_max; it++) { + StdI->At[it] = (double *)malloc(sizeof(double) * 3); + Et[it] = (double *)malloc(sizeof(double) * 3); + } + + if (strcmp(StdI->PumpType, "****") == 0) { + strcpy(StdI->PumpType, "quench\0"); + fprintf(stdout, " PumpType = quench ###### DEFAULT VALUE IS USED ######\n"); + StdI->PumpBody = 2; + }/*if (strcmp(StdI->PumpType, "****")*/ + else { + fprintf(stdout, " PumpType = %s\n", StdI->PumpType); + if (strcmp(StdI->PumpType, "quench") == 0) { + StdI->PumpBody = 2; + }/*if (strcmp(StdI->PumpType, "quench")*/ + else if (strcmp(StdI->PumpType, "pulselaser") == 0) { + for (it = 0; it < StdI->Lanczos_max; it++) { + time = StdI->dt*(double)it; + for (ii = 0; ii < 3; ii++) { + StdI->At[it][ii] = StdI->VecPot[ii] * cos(StdI->freq*(time - StdI->tshift)) + * exp(-0.5* (time - StdI->tshift)*(time - StdI->tshift) / StdI->tdump*StdI->tdump); + Et[it][ii] = -StdI->VecPot[ii] + * ( + (StdI->tshift - time) / (StdI->tdump*StdI->tdump) * cos(StdI->freq*(time - StdI->tshift)) + - StdI->freq* sin(StdI->freq*(time - StdI->tshift)) + ) + * exp(-0.5* (time - StdI->tshift)*(time - StdI->tshift) / StdI->tdump*StdI->tdump); + } + }/*for (it = 0; it < StdI->Lanczos_max; it++)*/ + StdI->PumpBody = 1; + }/*if (strcmp(StdI->PumpType, "pulselaser") == 0)*/ + else if (strcmp(StdI->PumpType, "aclaser") == 0) { + for (it = 0; it < StdI->Lanczos_max; it++) { + time = StdI->dt*(double)it; + for (ii = 0; ii < 3; ii++) { + StdI->At[it][ii] = StdI->VecPot[ii] * sin(StdI->freq*(time - StdI->tshift)); + Et[it][ii] = StdI->VecPot[ii] * cos(StdI->freq*(time - StdI->tshift)) * StdI->freq; + } + }/*for (it = 0; it < StdI->Lanczos_max; it++)*/ + StdI->PumpBody = 1; + }/*if (strcmp(StdI->PumpType, "aclaser") == 0)*/ + else if (strcmp(StdI->PumpType, "dclaser") == 0) { + for (it = 0; it < StdI->Lanczos_max; it++) { + time = StdI->dt*(double)it; + for (ii = 0; ii < 3; ii++) { + StdI->At[it][ii] = StdI->VecPot[ii] * time; + Et[it][ii] = -StdI->VecPot[ii]; + } + }/*for (it = 0; it < StdI->Lanczos_max; it++)*/ + StdI->PumpBody = 1; + }/* if (strcmp(StdI->PumpType, "dclaser") == 0)*/ + else { + fprintf(stdout, "\n ERROR ! PumpType : %s\n", StdI->PumpType); + StdFace_exit(-1); + } + }/*if (! strcmp(StdI->PumpType, "****"))*/ + + if (StdI->PumpBody == 1) { + fp = fopen("potential.dat", "w"); + fprintf(fp, "# Time A_W A_L A_H E_W E_L E_H\n"); + for (it = 0; it < StdI->Lanczos_max; it++) { + time = StdI->dt*(double)it; + fprintf(fp, "%f %f %f %f %f %f %f\n", + time, StdI->At[it][0], StdI->At[it][1], StdI->At[it][2], Et[it][0], Et[it][1], Et[it][2]); + } + fflush(fp); + fclose(fp); + }/*if (StdI->PumpBody == 1)*/ + + for (it = 0; it < StdI->Lanczos_max; it++) free(Et[it]); + free(Et); +}/*static void VectorPotential(struct StdIntList *StdI)*/ +/** +@brief Print single.def or pair.def +@author Mitsuaki Kawamura (The University of Tokyo) +*/ +static void PrintPump(struct StdIntList *StdI) { + FILE *fp; + int it, ii, isite, ipump, jpump, npump0; + + if (StdI->PumpBody == 1) { + + fp = fopen("teone.def", "w"); + fprintf(fp, "=============================================\n"); + fprintf(fp, "AllTimeStep %d\n", StdI->Lanczos_max); + fprintf(fp, "=============================================\n"); + fprintf(fp, "========= OneBody Time Evolution ==========\n"); + fprintf(fp, "=============================================\n"); + for (it = 0; it < StdI->Lanczos_max; it++) { + /* + Sum equivalent pumping + */ + for (ipump = 0; ipump < StdI->npump[it]; ipump++) { + for (jpump = ipump + 1; jpump < StdI->npump[it]; jpump++) { + if (StdI->pumpindx[it][ipump][0] == StdI->pumpindx[it][jpump][0] + && StdI->pumpindx[it][ipump][1] == StdI->pumpindx[it][jpump][1] + && StdI->pumpindx[it][ipump][2] == StdI->pumpindx[it][jpump][2] + && StdI->pumpindx[it][ipump][3] == StdI->pumpindx[it][jpump][3]) { + StdI->pump[it][ipump] = StdI->pump[it][ipump] + StdI->pump[it][jpump]; + StdI->pump[it][jpump] = 0.0; + } + }/*for (ktrans = jtrans + 1; ktrans < StdI->ntrans; ktrans++)*/ + }/*for (jtrans = 0; jtrans < StdI->ntrans; jtrans++)*/ + /* + Count the number of finite pumping + */ + npump0 = 0; + for (ipump = 0; ipump < StdI->npump[it]; ipump++) + if (cabs(StdI->pump[it][ipump]) > 0.000001) npump0 += 1; + + fprintf(fp, "%f %d\n", StdI->dt*(double)it, npump0); + for (ipump = 0; ipump < StdI->npump[it]; ipump++) { + + if (cabs(StdI->pump[it][ipump]) <= 0.000001) continue; + + fprintf(fp, "%5d %5d %5d %5d %25.15f %25.15f\n", + StdI->pumpindx[it][ipump][0], StdI->pumpindx[it][ipump][1], + StdI->pumpindx[it][ipump][2], StdI->pumpindx[it][ipump][3], + creal(StdI->pump[it][ipump]), cimag(StdI->pump[it][ipump])); + }/*for (itrans = 0; itrans < StdI->ntrans; itrans++)*/ + }/*for (it = 0; it < StdI->Lanczos_max; it++)*/ + fprintf(stdout, " teone.def is written.\n\n"); + } + else { + fp = fopen("tetwo.def", "w"); + fprintf(fp, "=============================================\n"); + fprintf(fp, "AllTimeStep %d\n", StdI->Lanczos_max); + fprintf(fp, "=============================================\n"); + fprintf(fp, "========== TwoBody Time Evolution ===========\n"); + fprintf(fp, "=============================================\n"); + for (it = 0; it < StdI->Lanczos_max; it++) { + fprintf(fp, "%f %d\n", StdI->dt*(double)it, StdI->nsite); + for (isite = 0; isite < StdI->nsite; isite++) { + fprintf(fp, "%5d %5d %5d %5d %5d %5d %5d %5d %25.15f %25.15f\n", + isite, 0, isite, 0, isite, 1, isite, 1, StdI->Uquench, 0.0); + }/*for (isite = 0; isite < StdI->nsite; isite++)*/ + }/*for (it = 0; it < StdI->Lanczos_max; it++)*/ + fprintf(stdout, " tetwo.def is written.\n\n"); + } + fflush(fp); + fclose(fp); +}/*tatic void PrintPump*/ #elif defined(_mVMC) /** @brief Output Anti-parallel orbital index @@ -600,6 +810,7 @@ static void StdFace_ResetVals(struct StdIntList *StdI) { */ NaN_d = 0.0 / 0.0; StdI->NaN_i = 2147483647; + StdI->pi = acos(-1.0); /**/ StdI->a = NaN_d; for (i = 0; i < 3; i++) StdI->length[i] = NaN_d; @@ -660,10 +871,8 @@ static void StdFace_ResetVals(struct StdIntList *StdI) { StdI->V2 = NaN_d; StdI->V2p = NaN_d; StdI->W = StdI->NaN_i; - StdI->phase[0] = NaN_d; - StdI->phase[1] = NaN_d; - StdI->phase[2] = NaN_d; - StdI->pi180 = 0.01745329251994329576;/*Pi/180*/ + for (i = 0; i < 3; i++)StdI->phase[i] = NaN_d; + StdI->pi180 = StdI->pi / 180.0; StdI->nelec = StdI->NaN_i; StdI->Sz2 = StdI->NaN_i; @@ -680,9 +889,7 @@ static void StdFace_ResetVals(struct StdIntList *StdI) { StdI->OmegaMin = NaN_d; StdI->OmegaIm = NaN_d; StdI->Nomega = StdI->NaN_i; - StdI->SpectrumQW = NaN_d; - StdI->SpectrumQL = NaN_d; - StdI->SpectrumQH = NaN_d; + for (i = 0; i < 3; i++)StdI->SpectrumQ[i] = NaN_d; strcpy(StdI->method, "****\0"); strcpy(StdI->Restart, "****\0"); strcpy(StdI->EigenVecIO, "****\0"); @@ -698,6 +905,14 @@ static void StdFace_ResetVals(struct StdIntList *StdI) { StdI->LanczosTarget = StdI->NaN_i; StdI->NumAve = StdI->NaN_i; StdI->ExpecInterval = StdI->NaN_i; + StdI->dt = NaN_d; + StdI->tdump = NaN_d; + StdI->tshift = NaN_d; + StdI->freq = NaN_d; + StdI->Uquench = NaN_d; + for (i = 0; i < 3; i++)StdI->VecPot[i] = NaN_d;; + strcpy(StdI->PumpType, "****\0"); + StdI->ExpandCoef = StdI->NaN_i; #elif defined(_mVMC) strcpy(StdI->CParaFileHead, "****\0"); StdI->NVMCCalMode = StdI->NaN_i; @@ -952,30 +1167,26 @@ static void PrintTrans(struct StdIntList *StdI){ for (ktrans = 0; ktrans < StdI->ntrans; ktrans++){ if (cabs(StdI->trans[ktrans]) > 0.000001) ntrans0 = ntrans0 + 1; } - if (ntrans0 != 0 || StdI->lBoost == 1) StdI->Ltrans = 1; - else StdI->Ltrans = 0; - if(StdI->Ltrans == 1){ - fp = fopen("trans.def", "w"); - fprintf(fp, "======================== \n"); - fprintf(fp, "NTransfer %7d \n", ntrans0); - fprintf(fp, "======================== \n"); - fprintf(fp, "========i_j_s_tijs====== \n"); - fprintf(fp, "======================== \n"); + fp = fopen("trans.def", "w"); + fprintf(fp, "======================== \n"); + fprintf(fp, "NTransfer %7d \n", ntrans0); + fprintf(fp, "======================== \n"); + fprintf(fp, "========i_j_s_tijs====== \n"); + fprintf(fp, "======================== \n"); - ntrans0 = 0; - for (ktrans = 0; ktrans < StdI->ntrans; ktrans++) { - if (cabs(StdI->trans[ktrans]) > 0.000001) - fprintf(fp, "%5d %5d %5d %5d %25.15f %25.15f\n", - StdI->transindx[ktrans][0], StdI->transindx[ktrans][1], - StdI->transindx[ktrans][2], StdI->transindx[ktrans][3], - creal(StdI->trans[ktrans]), cimag(StdI->trans[ktrans])); - } + ntrans0 = 0; + for (ktrans = 0; ktrans < StdI->ntrans; ktrans++) { + if (cabs(StdI->trans[ktrans]) > 0.000001) + fprintf(fp, "%5d %5d %5d %5d %25.15f %25.15f\n", + StdI->transindx[ktrans][0], StdI->transindx[ktrans][1], + StdI->transindx[ktrans][2], StdI->transindx[ktrans][3], + creal(StdI->trans[ktrans]), cimag(StdI->trans[ktrans])); + } - fflush(fp); - fclose(fp); - fprintf(stdout, " trans.def is written.\n"); - }/*if (StdI->Ltrans == 1)*/ + fflush(fp); + fclose(fp); + fprintf(stdout, " trans.def is written.\n"); }/*static void PrintTrans*/ /** @brief Print namelist.def @@ -987,7 +1198,7 @@ static void PrintNamelist(struct StdIntList *StdI){ fp = fopen("namelist.def", "w"); fprintf( fp, " ModPara modpara.def\n"); fprintf( fp, " LocSpin locspn.def\n"); - if (StdI->Ltrans == 1) fprintf( fp, " Trans trans.def\n"); + fprintf( fp, " Trans trans.def\n"); if (StdI->LCintra == 1) fprintf( fp, " CoulombIntra coulombintra.def\n"); if (StdI->LCinter == 1) fprintf( fp, " CoulombInter coulombinter.def\n"); if (StdI->LHund == 1)fprintf( fp, " Hund hund.def\n"); @@ -1003,6 +1214,12 @@ static void PrintNamelist(struct StdIntList *StdI){ if(StdI->SpectrumBody == 1) fprintf( fp, "SingleExcitation single.def\n"); else fprintf( fp, " PairExcitation pair.def\n"); + if (strcmp(StdI->method, "timeevolution") == 0) { + if (StdI->PumpBody == 1) + fprintf(fp, " TEOneBody teone.def\n"); + else if (StdI->PumpBody == 2) + fprintf(fp, " TETwoBody tetwo.def\n"); + }/*if (strcmp(StdI->method, "timeevolution") == 0)*/ fprintf( fp, " SpectrumVec %s_eigenvec_0\n", StdI->CDataFileHead); if (StdI->lBoost == 1) fprintf( fp, " Boost boost.def\n"); @@ -1053,6 +1270,8 @@ static void PrintModPara(struct StdIntList *StdI) fprintf(fp, "OmegaMax %-25.15e %-25.15e\n", StdI->OmegaMax, StdI->OmegaIm); fprintf(fp, "OmegaMin %-25.15e %-25.15e\n", StdI->OmegaMin, StdI->OmegaIm); fprintf(fp, "OmegaOrg 0.0 0.0\n"); + if (strcmp(StdI->method, "timeevolution") == 0) + fprintf(fp, "ExpandCoef %-5d\n", StdI->ExpandCoef); #elif defined(_mVMC) fprintf(fp, "VMC_Cal_Parameters\n"); fprintf(fp, "--------------------\n"); @@ -2013,9 +2232,12 @@ void StdFace_main( else if (strcmp(keyword, "calcspec") == 0) StoreWithCheckDup_sl(keyword, value, StdI->CalcSpec); else if (strcmp(keyword, "exct") == 0) StoreWithCheckDup_i(keyword, value, &StdI->exct); else if (strcmp(keyword, "eigenvecio") == 0) StoreWithCheckDup_sl(keyword, value, StdI->EigenVecIO); + else if (strcmp(keyword, "expandcoef") == 0) StoreWithCheckDup_i(keyword, value, &StdI->ExpandCoef); else if (strcmp(keyword, "expecinterval") == 0) StoreWithCheckDup_i(keyword, value, &StdI->ExpecInterval); else if (strcmp(keyword, "cdatafilehead") == 0) StoreWithCheckDup_s(keyword, value, StdI->CDataFileHead); + else if (strcmp(keyword, "dt") == 0) StoreWithCheckDup_d(keyword, value, &StdI->dt); else if (strcmp(keyword, "flgtemp") == 0) StoreWithCheckDup_i(keyword, value, &StdI->FlgTemp); + else if (strcmp(keyword, "freq") == 0) StoreWithCheckDup_d(keyword, value, &StdI->freq); else if (strcmp(keyword, "initialvectype") == 0) StoreWithCheckDup_sl(keyword, value, StdI->InitialVecType); else if (strcmp(keyword, "initial_iv") == 0) StoreWithCheckDup_i(keyword, value, &StdI->initial_iv); else if (strcmp(keyword, "lanczoseps") == 0) StoreWithCheckDup_i(keyword, value, &StdI->LanczosEps); @@ -2029,11 +2251,18 @@ void StdFace_main( else if (strcmp(keyword, "omegamax") == 0) StoreWithCheckDup_d(keyword, value, &StdI->OmegaMax); else if (strcmp(keyword, "omegamin") == 0) StoreWithCheckDup_d(keyword, value, &StdI->OmegaMin); else if (strcmp(keyword, "omegaim") == 0) StoreWithCheckDup_d(keyword, value, &StdI->OmegaIm); + else if (strcmp(keyword, "pumptype") == 0) StoreWithCheckDup_sl(keyword, value, StdI->PumpType); else if (strcmp(keyword, "restart") == 0) StoreWithCheckDup_sl(keyword, value, StdI->Restart); - else if (strcmp(keyword, "spectrumqh") == 0) StoreWithCheckDup_d(keyword, value, &StdI->SpectrumQH); - else if (strcmp(keyword, "spectrumql") == 0) StoreWithCheckDup_d(keyword, value, &StdI->SpectrumQL); - else if (strcmp(keyword, "spectrumqw") == 0) StoreWithCheckDup_d(keyword, value, &StdI->SpectrumQW); + else if (strcmp(keyword, "spectrumqh") == 0) StoreWithCheckDup_d(keyword, value, &StdI->SpectrumQ[2]); + else if (strcmp(keyword, "spectrumql") == 0) StoreWithCheckDup_d(keyword, value, &StdI->SpectrumQ[1]); + else if (strcmp(keyword, "spectrumqw") == 0) StoreWithCheckDup_d(keyword, value, &StdI->SpectrumQ[0]); else if (strcmp(keyword, "spectrumtype") == 0) StoreWithCheckDup_sl(keyword, value, StdI->SpectrumType); + else if (strcmp(keyword, "tdump") == 0) StoreWithCheckDup_d(keyword, value, &StdI->tdump); + else if (strcmp(keyword, "tshift") == 0) StoreWithCheckDup_d(keyword, value, &StdI->tshift); + else if (strcmp(keyword, "uquench") == 0) StoreWithCheckDup_d(keyword, value, &StdI->Uquench); + else if (strcmp(keyword, "vecpoth") == 0) StoreWithCheckDup_d(keyword, value, &StdI->VecPot[2]); + else if (strcmp(keyword, "vecpotl") == 0) StoreWithCheckDup_d(keyword, value, &StdI->VecPot[1]); + else if (strcmp(keyword, "vecpotw") == 0) StoreWithCheckDup_d(keyword, value, &StdI->VecPot[0]); else if (strcmp(keyword, "2s") == 0) StoreWithCheckDup_i(keyword, value, &StdI->S2); #elif defined(_mVMC) else if (strcmp(keyword, "a0hsub") == 0) StoreWithCheckDup_i(keyword, value, &StdI->boxsub[0][2]); @@ -2114,7 +2343,22 @@ void StdFace_main( StdI->lGC = 1; } else UnsupportedSystem(StdI->model, StdI->lattice); - +#if defined(_HPhi) + /* + Check the method + */ + if (strcmp(StdI->method, "direct") == 0 + || strcmp(StdI->method, "alldiag") == 0) + strcpy(StdI->method, "fulldiag\0"); + else if (strcmp(StdI->method, "te") == 0 + || strcmp(StdI->method, "time-evolution") == 0) { + strcpy(StdI->method, "timeevolution\0"); + } + /* + Compute vector potential and electrical field + */ + if (strcmp(StdI->method, "timeevolution") == 0) VectorPotential(StdI); +#endif /*>> Generate Hamiltonian definition files */ @@ -2169,6 +2413,7 @@ void StdFace_main( PrintModPara(StdI); #if defined(_HPhi) PrintExcitation(StdI); + if (strcmp(StdI->method, "timeevolution") == 0) PrintPump(StdI); PrintCalcMod(StdI); #elif defined(_mVMC) @@ -2266,4 +2511,45 @@ The non-local term is as follows: For more details, please see each functions. StdFace_Kagome_Boost()? Forget!! + +@page page_addstandardval Add new input variable into Standard mode + +We add new input variable in Standard mode through the following procedure: + +@section sec_parse_standard Parse the input file + +The input file for Standared mode is read in StdFace_main(). +In that function, the keyword value pair is found as follows: + +@dontinclude StdFace_main.c +@skip (fgets(ctmpline +@until fclose + +We have to add new variable (new_val in this case) as +@code{C} +else if (strcmp(keyword, "new_val") == 0) StoreWithCheckDup_i(keyword, value, &StdI->new_val); +@endcode +where StoreWithCheckDup_i() is for the integer variable; +for other type, please refer the above link. + +@section sec_share_standard If it should be shared + +If the inputted variable should be shared among routines in Standard mode, +we have to add it to the list in StdFace_vals.h. + +Also, the variable should be intialized before it is read. +This initiallization is performed in the function StdFace_ResetVals(). +We have to initialize new variable in this function as: +@code{C} +StdI->new_val = NaN_d; +\endcode +for the float, +@code{C} +StdI->new_val = NaN_i; +\endcode +for the integer, and +@code{C} +strcpy(StdI->new_val, "****\0"); +\endcode +for the string. */ diff --git a/src/StdFace/StdFace_vals.h b/src/StdFace/StdFace_vals.h index ae5dd08a..9339bdea 100644 --- a/src/StdFace/StdFace_vals.h +++ b/src/StdFace/StdFace_vals.h @@ -28,6 +28,7 @@ struct StdIntList { int NaN_i;/**<@brief It is used for initializing input parameter. This means that a parameter wich is not specified in input file. Set in StdFace_ResetVals().*/ + double pi;/**<@brief @f$\pi=3.14...@f$*/ /* Parameters for LATTICE */ @@ -140,7 +141,6 @@ struct StdIntList { int *locspinflag;/**<@brief [StdIntList::nsite] LocSpin in Expert mode, malloc and set in each lattice file.*/ int ntrans;/**<@brief Number of transfer, counted in each lattice file.*/ - int Ltrans;/**<@brief Print trans.def or not, set in PrintTrans().*/ int **transindx;/**<@brief [StdIntList::ntrans][4] Site/spin indices of one-body term, malloc in StdFace_MallocInteractions() and set in StdFace_trans().*/ @@ -250,18 +250,39 @@ struct StdIntList { int **list_6spin_star;/**<@brief */ int num_pivot;/**<@brief */ int ishift_nspin;/**<@brief */ - /*Spectrum*/ + /* + Spectrum + */ char CalcSpec[256];/**<@brief The name of mode for spectrum, input from file.*/ char SpectrumType[256];/**<@brief The type of mode for spectrum, input from file.*/ int Nomega;/**<@brief Number of frequencies, input from file.*/ double OmegaMax;/**<@brief Maximum of frequency for spectrum, input from file.*/ double OmegaMin;/**<@brief Minimum of frequency for spectrum, input from file.*/ double OmegaIm;/**<@brief Imaginary part of frequency.*/ - double SpectrumQL;/**<@brief wavenumver (q-vector) in fractional coordinate*/ - double SpectrumQW;/**<@brief wavenumver (q-vector) in fractional coordinate*/ - double SpectrumQH;/**<@brief wavenumver (q-vector) in fractional coordinate*/ + double SpectrumQ[3];/**<@brief wavenumver (q-vector) in fractional coordinate*/ int SpectrumBody;/**<@brief one- or two-body excitation, defined from StdIntList::SpectrumType*/ + /* + Time evolution + */ + double dt;/**<@brief Time step*/ + double tshift;/**<@brief Shift of time-step of laser*/ + double tdump;/**<@brief Time scale of dumping*/ + double freq;/**<@brief Frequency of laser*/ + double Uquench;/**<@brief Quenched on-site potential*/ + double VecPot[3];/**<@brief Vector potential*/ + char PumpType[256];/**<@brief The type of pump*/ + int PumpBody;/**<@brief one- or two-body pumping, defined from + StdIntList::PumpType*/ + int *npump;/**<@brief [StdIntList::nt] Number of transfer, counted in each lattice file.*/ + int ***pumpindx;/**<@brief [StdIntList::nt][StdIntList::npump][4] Site/spin indices of + one-body term, malloc in StdFace_MallocInteractions() + and set in StdFace_trans().*/ + double complex **pump;/**<@brief [StdIntList::nt][StdIntList::npump] Coefficient of + one-body term, malloc in StdFace_MallocInteractions() + and set in StdFace_trans().*/ + double **At;/**<@brief [StdIntList::nt][3] Vector potential.*/ + int ExpandCoef;/**<@brief The number of Hamiltonian-vector operation for the time-evolution*/ #elif defined(_mVMC) /*mVMC modpara*/ char CParaFileHead[256];/**<@brief Header of the optimized wavefunction, diff --git a/src/StdFace/TriangularLattice.c b/src/StdFace/TriangularLattice.c index 3c621080..ef118a05 100644 --- a/src/StdFace/TriangularLattice.c +++ b/src/StdFace/TriangularLattice.c @@ -36,6 +36,7 @@ void StdFace_Triangular(struct StdIntList *StdI) int iL, iW; FILE *fp; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -190,73 +191,73 @@ void StdFace_Triangular(struct StdIntList *StdI) /* Nearest neighbor along W */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 0, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 0, 0, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J0, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t0, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V0, isite, jsite); } /* Nearest neighbor along L */ - StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 0, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 0, 1, 0, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J1, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t1, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V1, isite, jsite); } /* Nearest neighbor along W - L */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, - 1, 0, 0, &isite, &jsite, 1, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, - 1, 0, 0, &isite, &jsite, 1, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->J2, StdI->S2, StdI->S2, isite, jsite); } else { - StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->t2, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->V2, isite, jsite); } /* Second nearest neighbor 1 */ - StdFace_SetLabel(StdI, fp, iW, iL, 2, - 1, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 2, - 1, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); } /* Second nearest neighbor 2 */ - StdFace_SetLabel(StdI, fp, iW, iL, 1, 1, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, 1, 1, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); }/*if (model != "spin")*/ /* Second nearest neighbor 3 */ - StdFace_SetLabel(StdI, fp, iW, iL, - 1, 2, 0, 0, &isite, &jsite, 2, &Cphase); + StdFace_SetLabel(StdI, fp, iW, iL, - 1, 2, 0, 0, &isite, &jsite, 2, &Cphase, dR); /**/ if (strcmp(StdI->model, "spin") == 0 ) { StdFace_GeneralJ(StdI, StdI->Jp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->tp, isite, jsite, dR); StdFace_Coulomb(StdI, StdI->Vp, isite, jsite); }/*if (model != "spin")*/ }/*for (kCell = 0; kCell < StdI->NCell; kCell++)*/ diff --git a/src/StdFace/Wannier90.c b/src/StdFace/Wannier90.c index 60e465a6..41143bac 100644 --- a/src/StdFace/Wannier90.c +++ b/src/StdFace/Wannier90.c @@ -237,6 +237,7 @@ void StdFace_Wannier90( double Jtmp[3][3] = { {0.0} }; FILE *fp; double complex Cphase; + double dR[3]; fprintf(stdout, "\n"); fprintf(stdout, "####### Parameter Summary #######\n"); @@ -347,13 +348,13 @@ void StdFace_Wannier90( */ StdFace_FindSite(StdI, iW, iL, iH, StdI->W90_indx[it][0], StdI->W90_indx[it][1], StdI->W90_indx[it][2], - StdI->W90_indx[it][3], StdI->W90_indx[it][4], &isite, &jsite, &Cphase); + StdI->W90_indx[it][3], StdI->W90_indx[it][4], &isite, &jsite, &Cphase, dR); if (strcmp(StdI->model, "spin") == 0) { for (ii = 0; ii < 3; ii++) Jtmp[ii][ii] = StdI->W90_t[it] * conj(StdI->W90_t[it]) / StdI->U; StdFace_GeneralJ(StdI, Jtmp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->W90_t[it], isite, jsite); + StdFace_Hopping(StdI, Cphase * StdI->W90_t[it], isite, jsite, dR); } }/*Non-local term*/ }/*for (it = 0; it < StdI->W90_nt; it++)*/ From a6ee17f359c696b0d7bb4729bffc3cd926d2f4bc Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Fri, 19 Jan 2018 19:55:23 +0900 Subject: [PATCH 11/34] Unify to 26079a9e8c368aa1fdfd7013744e4389302e99c4 --- src/StdFace/ChainLattice.c | 3 - src/StdFace/FCOrtho.c | 3 - src/StdFace/HoneycombLattice.c | 3 - src/StdFace/Kagome.c | 3 - src/StdFace/Ladder.c | 3 - src/StdFace/Orthorhombic.c | 3 - src/StdFace/Pyrochlore.c | 3 - src/StdFace/SquareLattice.c | 3 - src/StdFace/StdFace_ModelUtil.c | 11 +- src/StdFace/StdFace_ModelUtil.h | 1 + src/StdFace/StdFace_main.c | 140 +++++++++-- src/StdFace/StdFace_vals.h | 25 +- src/StdFace/TriangularLattice.c | 3 - src/StdFace/Wannier90.c | 432 +++++++++++++++++++++++--------- tool/CMakeLists.txt | 3 + tool/respack2wan90.py | 139 ++++++++++ 16 files changed, 600 insertions(+), 178 deletions(-) create mode 100644 tool/respack2wan90.py diff --git a/src/StdFace/ChainLattice.c b/src/StdFace/ChainLattice.c index 73245215..1acece1e 100644 --- a/src/StdFace/ChainLattice.c +++ b/src/StdFace/ChainLattice.c @@ -40,9 +40,6 @@ void StdFace_Chain( double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/FCOrtho.c b/src/StdFace/FCOrtho.c index a4627e32..9a6b5367 100644 --- a/src/StdFace/FCOrtho.c +++ b/src/StdFace/FCOrtho.c @@ -40,9 +40,6 @@ void StdFace_FCOrtho( double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/HoneycombLattice.c b/src/StdFace/HoneycombLattice.c index baf0f1f7..ddf1dca9 100644 --- a/src/StdFace/HoneycombLattice.c +++ b/src/StdFace/HoneycombLattice.c @@ -38,9 +38,6 @@ void StdFace_Honeycomb(struct StdIntList *StdI) double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/Kagome.c b/src/StdFace/Kagome.c index 28b0aa5c..a2ebacf6 100644 --- a/src/StdFace/Kagome.c +++ b/src/StdFace/Kagome.c @@ -40,9 +40,6 @@ void StdFace_Kagome( double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/Ladder.c b/src/StdFace/Ladder.c index 8cab651a..8f41d804 100644 --- a/src/StdFace/Ladder.c +++ b/src/StdFace/Ladder.c @@ -40,9 +40,6 @@ void StdFace_Ladder( double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/Orthorhombic.c b/src/StdFace/Orthorhombic.c index dd79c52d..01c9a983 100644 --- a/src/StdFace/Orthorhombic.c +++ b/src/StdFace/Orthorhombic.c @@ -40,9 +40,6 @@ void StdFace_Orthorhombic( double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/Pyrochlore.c b/src/StdFace/Pyrochlore.c index 94681e5c..50aae2da 100644 --- a/src/StdFace/Pyrochlore.c +++ b/src/StdFace/Pyrochlore.c @@ -40,9 +40,6 @@ void StdFace_Pyrochlore( double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/SquareLattice.c b/src/StdFace/SquareLattice.c index 88404ad3..bec605ff 100644 --- a/src/StdFace/SquareLattice.c +++ b/src/StdFace/SquareLattice.c @@ -38,9 +38,6 @@ void StdFace_Tetragonal(struct StdIntList *StdI) double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/StdFace_ModelUtil.c b/src/StdFace/StdFace_ModelUtil.c index c3728c23..7483dace 100644 --- a/src/StdFace/StdFace_ModelUtil.c +++ b/src/StdFace/StdFace_ModelUtil.c @@ -718,7 +718,7 @@ void StdFace_InitSite( * StdI->box[1][(ii + 2) % 3] * StdI->box[2][(ii + 1) % 3]; } - printf(" Number of Cell = %d\n", abs(StdI->NCell)); + printf(" Number of Cell = %d\n", abs(StdI->NCell)); if (StdI->NCell == 0) { StdFace_exit(-1); } @@ -1279,6 +1279,15 @@ void StdFace_MallocInteractions( StdI->PLIndx[ii] = (int *)malloc(sizeof(int) * 2); } StdI->NPairLift = 0; + /**@brief + (7) PairHopp StdIntList::PairHopp, StdIntList::PHIndx + */ + StdI->PHIndx = (int **)malloc(sizeof(int*) * nintrMax); + StdI->PairHopp = (double *)malloc(sizeof(double) * nintrMax); + for (ii = 0; ii < nintrMax; ii++) { + StdI->PHIndx[ii] = (int *)malloc(sizeof(int) * 2); + } + StdI->NPairHopp = 0; }/*void StdFace_MallocInteractions*/ #if defined(_mVMC) /** diff --git a/src/StdFace/StdFace_ModelUtil.h b/src/StdFace/StdFace_ModelUtil.h index 907d0a61..a5537f8a 100644 --- a/src/StdFace/StdFace_ModelUtil.h +++ b/src/StdFace/StdFace_ModelUtil.h @@ -25,6 +25,7 @@ void StdFace_intr(struct StdIntList *StdI, double complex intr0, int site3, int spin3, int site4, int spin4); void StdFace_Hopping(struct StdIntList *StdI, double complex trans0, int isite, int jsite, double *dR); +void StdFace_trans(struct StdIntList *StdI,double complex trans0,int isite,int ispin,int jsite,int jspin); void StdFace_HubbardLocal(struct StdIntList *StdI, double mu0, double h0, double Gamma0, double U0, int isite); void StdFace_MagField(struct StdIntList *StdI, int S2, double h, double Gamma, int isite); diff --git a/src/StdFace/StdFace_main.c b/src/StdFace/StdFace_main.c index 30d10f05..b4ab6ce5 100644 --- a/src/StdFace/StdFace_main.c +++ b/src/StdFace/StdFace_main.c @@ -880,9 +880,9 @@ static void StdFace_ResetVals(struct StdIntList *StdI) { strcpy(StdI->lattice, "****\0"); strcpy(StdI->outputmode, "****\0"); strcpy(StdI->CDataFileHead, "****\0"); - strcpy(StdI->W90_geom, "****\0"); - strcpy(StdI->W90_hr, "****\0"); - StdI->W90_cutoff = NaN_d; + StdI->cutoff_t = NaN_d; + StdI->cutoff_u = NaN_d; + StdI->cutoff_j = NaN_d; #if defined(_HPhi) StdI->LargeValue = NaN_d; StdI->OmegaMax = NaN_d; @@ -1204,6 +1204,7 @@ static void PrintNamelist(struct StdIntList *StdI){ if (StdI->LHund == 1)fprintf( fp, " Hund hund.def\n"); if (StdI->LEx == 1)fprintf( fp, " Exchange exchange.def\n"); if (StdI->LPairLift == 1)fprintf(fp, " PairLift pairlift.def\n"); + if (StdI->LPairHopp == 1)fprintf(fp, " PairHop pairhopp.def\n"); if (StdI->Lintr == 1)fprintf( fp, " InterAll interall.def\n"); if (StdI->ioutputmode != 0) { fprintf( fp, " OneBodyG greenone.def\n"); @@ -1616,12 +1617,6 @@ static void CheckOutputMode(struct StdIntList *StdI) static void CheckModPara(struct StdIntList *StdI) { - if (strcmp(StdI->CDataFileHead, "****") == 0) { - strcpy(StdI->CDataFileHead, "zvo\0"); - fprintf(stdout, " CDataFileHead = %-12s###### DEFAULT VALUE IS USED ######\n", StdI->CDataFileHead); - } - else fprintf(stdout, " CDataFileHead = %-s\n", StdI->CDataFileHead); - /**/ #if defined(_HPhi) StdFace_PrintVal_i("Lanczos_max", &StdI->Lanczos_max, 2000); @@ -1739,6 +1734,14 @@ static void PrintInteractions(struct StdIntList *StdI) /* Coulomb INTRA */ + for (kintr = 0; kintr < StdI->NCintra; kintr++) { + for (jintr = kintr + 1; jintr < StdI->NCintra; jintr++) + if(StdI->CintraIndx[jintr][0] == StdI->CintraIndx[kintr][0]) + { + StdI->Cintra[kintr] += StdI->Cintra[jintr]; + StdI->Cintra[jintr] = 0.0; + } + } nintr0 = 0; for (kintr = 0; kintr < StdI->NCintra; kintr++) { if (fabs(StdI->Cintra[kintr]) > 0.000001) nintr0 = nintr0 + 1; @@ -1765,6 +1768,20 @@ static void PrintInteractions(struct StdIntList *StdI) /* Coulomb INTER */ + for (kintr = 0; kintr < StdI->NCinter; kintr++) { + for (jintr = kintr + 1; jintr < StdI->NCinter; jintr++) + if ( + ( StdI->CinterIndx[jintr][0] == StdI->CinterIndx[kintr][0] + && StdI->CinterIndx[jintr][1] == StdI->CinterIndx[kintr][1]) + || + ( StdI->CinterIndx[jintr][0] == StdI->CinterIndx[kintr][1] + && StdI->CinterIndx[jintr][1] == StdI->CinterIndx[kintr][0]) + ) + { + StdI->Cinter[kintr] += StdI->Cinter[jintr]; + StdI->Cinter[jintr] = 0.0; + } + }/*for (kintr = 0; kintr < StdI->NCinter; kintr++)*/ nintr0 = 0; for (kintr = 0; kintr < StdI->NCinter; kintr++) { if (fabs(StdI->Cinter[kintr]) > 0.000001) nintr0 = nintr0 + 1; @@ -1791,6 +1808,20 @@ static void PrintInteractions(struct StdIntList *StdI) /* Hund */ + for (kintr = 0; kintr < StdI->NHund; kintr++) { + for (jintr = kintr + 1; jintr < StdI->NHund; jintr++) + if ( + (StdI->HundIndx[jintr][0] == StdI->HundIndx[kintr][0] + && StdI->HundIndx[jintr][1] == StdI->HundIndx[kintr][1]) + || + (StdI->HundIndx[jintr][0] == StdI->HundIndx[kintr][1] + && StdI->HundIndx[jintr][1] == StdI->HundIndx[kintr][0]) + ) + { + StdI->Hund[kintr] += StdI->Hund[jintr]; + StdI->Hund[jintr] = 0.0; + } + }/*for (kintr = 0; kintr < StdI->NHund; kintr++)*/ nintr0 = 0; for (kintr = 0; kintr < StdI->NHund; kintr++) { if (fabs(StdI->Hund[kintr]) > 0.000001) nintr0 = nintr0 + 1; @@ -1817,6 +1848,20 @@ static void PrintInteractions(struct StdIntList *StdI) /* Exchange */ + for (kintr = 0; kintr < StdI->NEx; kintr++) { + for (jintr = kintr + 1; jintr < StdI->NEx; jintr++) + if ( + (StdI->ExIndx[jintr][0] == StdI->ExIndx[kintr][0] + && StdI->ExIndx[jintr][1] == StdI->ExIndx[kintr][1]) + || + (StdI->ExIndx[jintr][0] == StdI->ExIndx[kintr][1] + && StdI->ExIndx[jintr][1] == StdI->ExIndx[kintr][0]) + ) + { + StdI->Ex[kintr] += StdI->Ex[jintr]; + StdI->Ex[jintr] = 0.0; + } + }/*for (kintr = 0; kintr < StdI->NEx; kintr++)*/ nintr0 = 0; for (kintr = 0; kintr < StdI->NEx; kintr++) { if (fabs(StdI->Ex[kintr]) > 0.000001) nintr0 = nintr0 + 1; @@ -1843,6 +1888,20 @@ static void PrintInteractions(struct StdIntList *StdI) /* PairLift */ + for (kintr = 0; kintr < StdI->NPairLift; kintr++) { + for (jintr = kintr + 1; jintr < StdI->NPairLift; jintr++) + if ( + (StdI->PLIndx[jintr][0] == StdI->PLIndx[kintr][0] + && StdI->PLIndx[jintr][1] == StdI->PLIndx[kintr][1]) + || + (StdI->PLIndx[jintr][0] == StdI->PLIndx[kintr][1] + && StdI->PLIndx[jintr][1] == StdI->PLIndx[kintr][0]) + ) + { + StdI->PairLift[kintr] += StdI->PairLift[jintr]; + StdI->PairLift[jintr] = 0.0; + } + }/*for (kintr = 0; kintr < StdI->NPairLift; kintr++)*/ nintr0 = 0; for (kintr = 0; kintr < StdI->NPairLift; kintr++) { if (fabs(StdI->PairLift[kintr]) > 0.000001) nintr0 = nintr0 + 1; @@ -1853,9 +1912,9 @@ static void PrintInteractions(struct StdIntList *StdI) if (StdI->LPairLift == 1) { fp = fopen("pairlift.def", "w"); fprintf(fp, "=============================================\n"); - fprintf(fp, "NExchange %10d\n", nintr0); + fprintf(fp, "NPairLift %10d\n", nintr0); fprintf(fp, "=============================================\n"); - fprintf(fp, "====== ExchangeCoupling coupling ============\n"); + fprintf(fp, "====== Pair-Lift term ============\n"); fprintf(fp, "=============================================\n"); for (kintr = 0; kintr < StdI->NPairLift; kintr++) { if (fabs(StdI->PairLift[kintr]) > 0.000001) @@ -1864,7 +1923,47 @@ static void PrintInteractions(struct StdIntList *StdI) } fflush(fp); fclose(fp); - fprintf(stdout, " exchange.def is written.\n"); + fprintf(stdout, " pairlift.def is written.\n"); + } + /* + PairHopp + */ + for (kintr = 0; kintr < StdI->NPairHopp; kintr++) { + for (jintr = kintr + 1; jintr < StdI->NPairHopp; jintr++) + if ( + (StdI->PHIndx[jintr][0] == StdI->PHIndx[kintr][0] + && StdI->PHIndx[jintr][1] == StdI->PHIndx[kintr][1]) + || + (StdI->PHIndx[jintr][0] == StdI->PHIndx[kintr][1] + && StdI->PHIndx[jintr][1] == StdI->PHIndx[kintr][0]) + ) + { + StdI->PairHopp[kintr] += StdI->PairHopp[jintr]; + StdI->PairHopp[jintr] = 0.0; + } + }/*for (kintr = 0; kintr < StdI->NPairHopp; kintr++)*/ + nintr0 = 0; + for (kintr = 0; kintr < StdI->NPairHopp; kintr++) { + if (fabs(StdI->PairHopp[kintr]) > 0.000001) nintr0 = nintr0 + 1; + } + if (nintr0 == 0 || StdI->lBoost == 1) StdI->LPairHopp = 0; + else StdI->LPairHopp = 1; + + if (StdI->LPairHopp == 1) { + fp = fopen("pairhopp.def", "w"); + fprintf(fp, "=============================================\n"); + fprintf(fp, "NPairHopp %10d\n", nintr0); + fprintf(fp, "=============================================\n"); + fprintf(fp, "====== Pair-Hopping term ============\n"); + fprintf(fp, "=============================================\n"); + for (kintr = 0; kintr < StdI->NPairHopp; kintr++) { + if (fabs(StdI->PairHopp[kintr]) > 0.000001) + fprintf(fp, "%5d %5d %25.15f\n", + StdI->PHIndx[kintr][0], StdI->PHIndx[kintr][1], StdI->PairHopp[kintr]); + } + fflush(fp); + fclose(fp); + fprintf(stdout, " pairhopp.def is written.\n"); } /* InterAll @@ -2046,7 +2145,7 @@ void StdFace_main( StdI = (struct StdIntList *)malloc(sizeof(struct StdIntList)); - fprintf(stdout, "\n###### Standard Intarface Mode STARTS ######\n"); + fprintf(stdout, "\n###### Input Parameter of Standard Intarface ######\n"); if ((fp = fopen(fname, "r")) == NULL) { fprintf(stdout, "\n ERROR ! Cannot open input file %s !\n\n", fname); StdFace_exit(-1); @@ -2087,6 +2186,9 @@ void StdFace_main( else if (strcmp(keyword, "a2h") == 0) StoreWithCheckDup_i(keyword, value, &StdI->box[2][2]); else if (strcmp(keyword, "a2l") == 0) StoreWithCheckDup_i(keyword, value, &StdI->box[2][1]); else if (strcmp(keyword, "a2w") == 0) StoreWithCheckDup_i(keyword, value, &StdI->box[2][0]); + else if (strcmp(keyword, "cutoff_j") == 0) StoreWithCheckDup_d(keyword, value, &StdI->cutoff_j); + else if (strcmp(keyword, "cutoff_t") == 0) StoreWithCheckDup_d(keyword, value, &StdI->cutoff_t); + else if (strcmp(keyword, "cutoff_u") == 0) StoreWithCheckDup_d(keyword, value, &StdI->cutoff_u); else if (strcmp(keyword, "d") == 0) StoreWithCheckDup_d(keyword, value, &StdI->D[2][2]); else if (strcmp(keyword, "gamma") == 0) StoreWithCheckDup_d(keyword, value, &StdI->Gamma); else if (strcmp(keyword, "h") == 0) StoreWithCheckDup_d(keyword, value, &StdI->h); @@ -2223,9 +2325,6 @@ void StdFace_main( else if (strcmp(keyword, "wx") == 0) StoreWithCheckDup_d(keyword, value, &StdI->direct[0][0]); else if (strcmp(keyword, "wy") == 0) StoreWithCheckDup_d(keyword, value, &StdI->direct[0][1]); else if (strcmp(keyword, "wz") == 0) StoreWithCheckDup_d(keyword, value, &StdI->direct[0][2]); - else if (strcmp(keyword, "w90_cutoff") == 0) StoreWithCheckDup_d(keyword, value, &StdI->W90_cutoff); - else if (strcmp(keyword, "w90_geom") == 0) StoreWithCheckDup_s(keyword, value, StdI->W90_geom); - else if (strcmp(keyword, "w90_hr") == 0) StoreWithCheckDup_s(keyword, value, StdI->W90_hr); else if (strcmp(keyword, "2sz") == 0) StoreWithCheckDup_i(keyword, value, &StdI->Sz2); #if defined(_HPhi) @@ -2306,9 +2405,18 @@ void StdFace_main( } fflush(fp); fclose(fp); + fprintf(stdout, "\n"); + fprintf(stdout, "####### Construct Model #######\n"); + fprintf(stdout, "\n"); /* Check the model */ + if (strcmp(StdI->CDataFileHead, "****") == 0) { + strcpy(StdI->CDataFileHead, "zvo\0"); + fprintf(stdout, " CDataFileHead = %-12s###### DEFAULT VALUE IS USED ######\n", StdI->CDataFileHead); + } + else fprintf(stdout, " CDataFileHead = %-s\n", StdI->CDataFileHead); + /**/ StdI->lGC = 0; StdI->lBoost = 0; if (strcmp(StdI->model, "fermionhubbard") == 0 diff --git a/src/StdFace/StdFace_vals.h b/src/StdFace/StdFace_vals.h index 9339bdea..cbc774b4 100644 --- a/src/StdFace/StdFace_vals.h +++ b/src/StdFace/StdFace_vals.h @@ -197,6 +197,14 @@ struct StdIntList { double *PairLift;/**<@brief [StdIntList::NPairLift] Coefficient of pair-lift term, malloc in StdFace_MallocInteractions() and set in StdFace_intr().*/ + int NPairHopp;/**<@brief Number of pair-hopping term, counted in each lattice file.*/ + int LPairHopp;/**<@brief Print pairhopp.def or not, set in PrintInteractions().*/ + int **PHIndx;/**<@brief [StdIntList::NPairLift][2] Site indices of + pair-hopping term, malloc in StdFace_MallocInteractions() + and set in StdFace_intr().*/ + double *PairHopp;/**<@brief [StdIntList::NPairLift] Coefficient of + pair-hopping term, malloc in StdFace_MallocInteractions() + and set in StdFace_intr().*/ int lBoost; /* Calculation conditions @@ -207,23 +215,16 @@ struct StdIntList { int S2;/**<@brief Total spin |S| of a local spin, input from file.*/ char outputmode[256];/**<@brief Select amount of correlation function, input from file.*/ - char CDataFileHead[256];/**<@brief String fron tof the output files, - input from file*/ + char CDataFileHead[256];/**<@brief Header of the output files. + Input from file*/ int Sz2;/**<@brief Total Sz, input from file.*/ int ioutputmode;/**<@brief Switch associated to StdIntList::outputmode*/ /* Wannier90 mode */ - char W90_hr[256];/**<@brief Name of hopping parameter file from wannier90, - input from file.*/ - char W90_geom[256];/**<@brief Name of geometry file from wannier90 converter, - input from file.*/ - int W90_nt;/**<@brief Number of transfer in wannier90 HR file.*/ - int **W90_indx;/**<@brief [StdIntList::W90_nt][5] Hopping index, - malloc in read_W90().*/ - double complex *W90_t;/**<@brief [StdIntList::W90_nt] Hopping parameter, - malloc in read_W90().*/ - double W90_cutoff;/**<@brief Cutoof for the hopping in wannier90, input from file*/ + double cutoff_t;/**<@brief Cutoof for the hopping in wannier90, input from file*/ + double cutoff_u;/**<@brief Cutoof for the Coulomb in wannier90, input from file*/ + double cutoff_j;/**<@brief Cutoof for the Hund in wannier90, input from file*/ #if defined(_HPhi) /* HPhi modpara diff --git a/src/StdFace/TriangularLattice.c b/src/StdFace/TriangularLattice.c index ef118a05..9b2a37c6 100644 --- a/src/StdFace/TriangularLattice.c +++ b/src/StdFace/TriangularLattice.c @@ -38,9 +38,6 @@ void StdFace_Triangular(struct StdIntList *StdI) double complex Cphase; double dR[3]; - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ diff --git a/src/StdFace/Wannier90.c b/src/StdFace/Wannier90.c index 41143bac..a0eec352 100644 --- a/src/StdFace/Wannier90.c +++ b/src/StdFace/Wannier90.c @@ -30,104 +30,101 @@ along with this program. If not, see . @author Mitsuaki Kawamura (The University of Tokyo) */ static void geometry_W90( - struct StdIntList *StdI,//!<[inout] - int *wan_num//!<[out] -) { + struct StdIntList *StdI//!<[inout] +) +{ int isite, ii, ierr; + char filename[256]; FILE *fp; - fprintf(stdout, " Wannier90 Geometry file = %s\n", StdI->W90_geom); + sprintf(filename, "%s_geom.dat", StdI->CDataFileHead); + fprintf(stdout, " Wannier90 Geometry file = %s\n", filename); - fp = fopen(StdI->W90_geom, "r"); + fp = fopen(filename, "r"); /**@brief Direct lattice vector StdIntList::direct */ for (ii = 0; ii < 3; ii++) ierr = fscanf(fp, "%lf%lf%lf", &StdI->direct[ii][0], &StdI->direct[ii][1], &StdI->direct[ii][2]); - if(ierr != 0) printf("%d\n", ierr); + if(ierr == EOF) printf("%d\n", ierr); /**@brief Intrinsic site position StdIntList::tau and its number StdIntList::NsiteUC */ for (isite = 0; isite < StdI->NsiteUC; isite++) free(StdI->tau[isite]); free(StdI->tau); ierr = fscanf(fp, "%d", &StdI->NsiteUC); - fprintf(stdout, " Number of EFFECTIVE Sites = %d\n", StdI->NsiteUC); + fprintf(stdout, " Number of Correlated Sites = %d\n", StdI->NsiteUC); StdI->tau = (double **)malloc(sizeof(double*) * StdI->NsiteUC); for (ii = 0; ii < StdI->NsiteUC; ii++) StdI->tau[ii] = (double *)malloc(sizeof(double) * 3); for (isite = 0; isite < StdI->NsiteUC; isite++) - ierr = fscanf(fp, "%d%lf%lf%lf", &wan_num[isite], - &StdI->tau[isite][0], &StdI->tau[isite][1], &StdI->tau[isite][2]); + ierr = fscanf(fp, "%lf%lf%lf", &StdI->tau[isite][0], &StdI->tau[isite][1], &StdI->tau[isite][2]); fclose(fp); - printf(" Direct lattice vectors:\n"); + printf(" Direct lattice vectors:\n"); for (ii = 0; ii < 3; ii++) printf(" %10.5f %10.5f %10.5f\n", StdI->direct[ii][0], StdI->direct[ii][1], StdI->direct[ii][2]); - printf(" Wannier centres:\n"); + printf(" Wannier centres:\n"); for (isite = 0; isite < StdI->NsiteUC; isite++) printf(" %10.5f %10.5f %10.5f\n", StdI->tau[isite][0], StdI->tau[isite][1], StdI->tau[isite][2]); }/*static void geometry_W90(struct StdIntList *StdI) */ /** -@brief Read Wannier90 hamiltonian file (*_hr) +@brief Read Wannier90 hamiltonian file (*_hr) and compute the number of effective term @author Mitsuaki Kawamura (The University of Tokyo) */ -static void read_W90(struct StdIntList *StdI) +static int read_W90_query( + struct StdIntList *StdI,//!<[inout] + char *filename,//!<[in] Input file name + double cutoff//!<[in] Threshold for the Hamiltonian +) { FILE *fp; + int nMat; int ierr, nWan, nWSC, iWSC, jWSC, iWan, jWan, iWan0, jWan0, ii; - double dtmp[2], tmax, tabs; + double dtmp[2]; char ctmp[256], *ctmp2; - double complex ***t_tot, **t0; - int **indx_tot, *wan_num; - - fprintf(stdout, "\n @ Wannier90 Mode\n\n"); + double complex ***Mat_tot; + int **indx_tot; - StdFace_PrintVal_d("W90_thr", &StdI->W90_cutoff, 0.1); - - fprintf(stdout, " Wannier90 file = %s\n", StdI->W90_hr); - - fp = fopen(StdI->W90_hr, "r"); + fprintf(stdout, " Wannier90 file = %s\n", filename); + /* + Header part + */ + fp = fopen(filename, "r"); ctmp2 = fgets(ctmp, 256, fp); ierr = fscanf(fp, "%d", &nWan); - if(ierr != 0) printf("%d %s\n", ierr, ctmp2); + if(ierr == EOF) printf("%d %s\n", ierr, ctmp2); ierr = fscanf(fp, "%d", &nWSC); for (iWSC = 0; iWSC < nWSC; iWSC++) { ierr = fscanf(fp, "%d", &ii); } - fprintf(stdout, " Number of Wannier = %d\n", nWan); - fprintf(stdout, " Number of Wigner-Seitz Cell = %d\n", nWSC); - - t_tot = (double complex ***)malloc(sizeof(double complex **) * nWSC); + fprintf(stdout, " Number of Wannier = %d\n", nWan); + fprintf(stdout, " Number of Wigner-Seitz Cell = %d\n", nWSC); + /* + Allocation of matgrix element and its index + */ + Mat_tot = (double complex ***)malloc(sizeof(double complex **) * nWSC); indx_tot = (int **)malloc(sizeof(int*) * nWSC); for (iWSC = 0; iWSC < nWSC; iWSC++) { - t_tot[iWSC] = (double complex **)malloc(sizeof(double complex *) * nWan); + Mat_tot[iWSC] = (double complex **)malloc(sizeof(double complex *) * nWan); indx_tot[iWSC] = (int *)malloc(sizeof(int) * 3); for (iWan = 0; iWan < nWan; iWan++) { - t_tot[iWSC][iWan] = (double complex *)malloc(sizeof(double complex) * nWan); + Mat_tot[iWSC][iWan] = (double complex *)malloc(sizeof(double complex) * nWan); } } - t0 = (double complex **)malloc(sizeof(double complex *) * nWan); - for (iWan = 0; iWan < nWan; iWan++) - t0[iWan] = (double complex *)malloc(sizeof(double complex) * nWan); - wan_num = (int *)malloc(sizeof(int) * nWan); - - geometry_W90(StdI, wan_num); - - tmax = 0.0; + /* + Read body + */ for (iWSC = 0; iWSC < nWSC; iWSC++) { for (iWan = 0; iWan < nWan; iWan++) { for (jWan = 0; jWan < nWan; jWan++) { ierr = fscanf(fp, "%d%d%d%d%d%lf%lf", &indx_tot[iWSC][0], &indx_tot[iWSC][1], &indx_tot[iWSC][2], &iWan0, &jWan0, &dtmp[0], &dtmp[1]); - t0[iWan0 - 1][jWan0 - 1] = dtmp[0] + I * dtmp[1]; - } - } - for (iWan = 0; iWan < StdI->NsiteUC; iWan++) { - for (jWan = 0; jWan < StdI->NsiteUC; jWan++) { - t_tot[iWSC][iWan][jWan] = t0[wan_num[iWan]][wan_num[jWan]]; + if(iWan0 <= StdI->NsiteUC && jWan0 <= StdI->NsiteUC) + Mat_tot[iWSC][iWan0 - 1][jWan0 - 1] = dtmp[0] + I * dtmp[1]; } } /**@brief @@ -141,7 +138,7 @@ static void read_W90(struct StdIntList *StdI) ) for (iWan = 0; iWan < StdI->NsiteUC; iWan++) { for (jWan = 0; jWan < StdI->NsiteUC; jWan++) { - t_tot[iWSC][iWan][jWan] = 0.0; + Mat_tot[iWSC][iWan][jWan] = 0.0; } } }/*for (jWSC = 0; jWSC < iWSC; jWSC++)*/ @@ -150,62 +147,138 @@ static void read_W90(struct StdIntList *StdI) indx_tot[iWSC][2] == 0) for (iWan = 0; iWan < StdI->NsiteUC; iWan++) { for (jWan = 0; jWan < iWan; jWan++) { - t_tot[iWSC][iWan][jWan] = 0.0; + Mat_tot[iWSC][iWan][jWan] = 0.0; } } - /**@brief - (2) Search maximum transfer for appling cutoff later - */ - for (iWan = 0; iWan < StdI->NsiteUC; iWan++) { - for (jWan = 0; jWan < StdI->NsiteUC; jWan++) { - tabs = cabs(t_tot[iWSC][iWan][jWan]); - if (tmax < tabs) tmax = tabs; - } - } }/*for (iWSC = 0; iWSC < nWSC; iWSC++)*/ fclose(fp); - - fprintf(stdout, " Maximum Hopping = %f\n", tmax); - fprintf(stdout, " Threshold for Hopping = %f\n", tmax * StdI->W90_cutoff); - /**@brief - (3) Apply cut-off of Hopping - */ /**@brief - (3-1) Set the number of t with cut-off (StdIntList::W90_nt) - with the inputted cut-off StdIntList::W90_cutoff + (3-1) Compute the number of terms lerger than cut-off. */ - StdI->W90_nt = 0; + fprintf(stdout, "\n EFFECTIVE terms:\n"); + fprintf(stdout, " R0 R1 R2 band_i band_f Hamiltonian\n"); + nMat = 0; for (iWSC = 0; iWSC < nWSC; iWSC++) { for (iWan = 0; iWan < StdI->NsiteUC; iWan++) { for (jWan = 0; jWan < StdI->NsiteUC; jWan++) { - if (tmax * StdI->W90_cutoff < cabs(t_tot[iWSC][iWan][jWan])) StdI->W90_nt += 1; + if (cutoff < cabs(Mat_tot[iWSC][iWan][jWan])) { + fprintf(stdout, " %5d%5d%5d%5d%5d%12.6f%12.6f\n", + indx_tot[iWSC][0], indx_tot[iWSC][1], indx_tot[iWSC][2], iWan, jWan, + creal(Mat_tot[iWSC][iWan][jWan]), cimag(Mat_tot[iWSC][iWan][jWan])); + nMat += 1; + } } } } - fprintf(stdout, " Total number of EFFECTIVE Hopping = %d\n", StdI->W90_nt); + fprintf(stdout, " Total number of EFFECTIVE term = %d\n", nMat); + + for (iWSC = 0; iWSC < nWSC; iWSC++) { + for (iWan = 0; iWan < nWan; iWan++) { + free(Mat_tot[iWSC][iWan]); + } + free(Mat_tot[iWSC]); + free(indx_tot[iWSC]); + } + free(Mat_tot); + free(indx_tot); + + return nMat; +}/*static int read_W90_query(struct StdIntList *StdI, char *model)*/ + /** + @brief Read Wannier90 hamiltonian file (*_hr) + @author Mitsuaki Kawamura (The University of Tokyo) + */ +static void read_W90( + struct StdIntList *StdI,//!<[inout] + char *filename,//!<[in] Input file name + double cutoff,//!<[in] Threshold for the Hamiltonian + double complex *Mat,//!<[out] Matrix element + int **Matindx//!<[out] R, band index of matrix element +) +{ + FILE *fp; + int nMat; + int ierr, nWan, nWSC, iWSC, jWSC, iWan, jWan, iWan0, jWan0, ii; + double dtmp[2]; + char ctmp[256], *ctmp2; + double complex ***Mat_tot; + int **indx_tot; + /* + Header part + */ + fp = fopen(filename, "r"); + ctmp2 = fgets(ctmp, 256, fp); + ierr = fscanf(fp, "%d", &nWan); + if (ierr == EOF) printf("%d %s\n", ierr, ctmp2); + ierr = fscanf(fp, "%d", &nWSC); + for (iWSC = 0; iWSC < nWSC; iWSC++) { + ierr = fscanf(fp, "%d", &ii); + } + /* + Malloc Matrix elements and their indices + */ + Mat_tot = (double complex ***)malloc(sizeof(double complex **) * nWSC); + indx_tot = (int **)malloc(sizeof(int*) * nWSC); + for (iWSC = 0; iWSC < nWSC; iWSC++) { + Mat_tot[iWSC] = (double complex **)malloc(sizeof(double complex *) * nWan); + indx_tot[iWSC] = (int *)malloc(sizeof(int) * 3); + for (iWan = 0; iWan < nWan; iWan++) { + Mat_tot[iWSC][iWan] = (double complex *)malloc(sizeof(double complex) * nWan); + } + } + /* + Read body + */ + for (iWSC = 0; iWSC < nWSC; iWSC++) { + for (iWan = 0; iWan < nWan; iWan++) { + for (jWan = 0; jWan < nWan; jWan++) { + ierr = fscanf(fp, "%d%d%d%d%d%lf%lf", + &indx_tot[iWSC][0], &indx_tot[iWSC][1], &indx_tot[iWSC][2], + &iWan0, &jWan0, + &dtmp[0], &dtmp[1]); + if (iWan0 <= StdI->NsiteUC && jWan0 <= StdI->NsiteUC) + Mat_tot[iWSC][iWan0 - 1][jWan0 - 1] = dtmp[0] + I * dtmp[1]; + } + } + /**@brief + (1) Apply inversion symmetry and delete duplication + */ + for (jWSC = 0; jWSC < iWSC; jWSC++) { + if ( + indx_tot[iWSC][0] == -indx_tot[jWSC][0] && + indx_tot[iWSC][1] == -indx_tot[jWSC][1] && + indx_tot[iWSC][2] == -indx_tot[jWSC][2] + ) + for (iWan = 0; iWan < StdI->NsiteUC; iWan++) { + for (jWan = 0; jWan < StdI->NsiteUC; jWan++) { + Mat_tot[iWSC][iWan][jWan] = 0.0; + } + } + }/*for (jWSC = 0; jWSC < iWSC; jWSC++)*/ + if (indx_tot[iWSC][0] == 0 && + indx_tot[iWSC][1] == 0 && + indx_tot[iWSC][2] == 0) + for (iWan = 0; iWan < StdI->NsiteUC; iWan++) { + for (jWan = 0; jWan < iWan; jWan++) { + Mat_tot[iWSC][iWan][jWan] = 0.0; + } + } + }/*for (iWSC = 0; iWSC < nWSC; iWSC++)*/ + fclose(fp); /**@brief - Then malloc and store to the hopping Integeral StdIntList::W90_t and - its site index StdIntList::W90_indx + Then Store to the hopping Integeral and + its site index. */ - StdI->W90_t = (double complex *)malloc(sizeof(double complex) * StdI->W90_nt); - StdI->W90_indx = (int **)malloc(sizeof(int*) * StdI->W90_nt); - for (ii = 0; ii < StdI->W90_nt; ii++) StdI->W90_indx[ii] = (int *)malloc(sizeof(int) * 5); - - fprintf(stdout, " EFFECTIVE Hoppings:\n"); - StdI->W90_nt = 0; + nMat = 0; for (iWSC = 0; iWSC < nWSC; iWSC++) { for (iWan = 0; iWan < StdI->NsiteUC; iWan++) { for (jWan = 0; jWan < StdI->NsiteUC; jWan++) { - if (tmax * StdI->W90_cutoff < cabs(t_tot[iWSC][iWan][jWan])) { - for (ii = 0; ii < 3; ii++) StdI->W90_indx[StdI->W90_nt][ii] = indx_tot[iWSC][ii]; - StdI->W90_indx[StdI->W90_nt][3] = iWan; - StdI->W90_indx[StdI->W90_nt][4] = jWan; - StdI->W90_t[StdI->W90_nt] = t_tot[iWSC][iWan][jWan]; - fprintf(stdout, " %5d%5d%5d%5d%5d%12.6f%12.6f\n", - StdI->W90_indx[StdI->W90_nt][0], StdI->W90_indx[StdI->W90_nt][1], StdI->W90_indx[StdI->W90_nt][2], - StdI->W90_indx[StdI->W90_nt][3], StdI->W90_indx[StdI->W90_nt][4], - creal(StdI->W90_t[StdI->W90_nt]), cimag(StdI->W90_t[StdI->W90_nt])); - StdI->W90_nt += 1; + if (cutoff < cabs(Mat_tot[iWSC][iWan][jWan])) { + for (ii = 0; ii < 3; ii++) Matindx[nMat][ii] = indx_tot[iWSC][ii]; + Matindx[nMat][3] = iWan; + Matindx[nMat][4] = jWan; + Mat[nMat] = Mat_tot[iWSC][iWan][jWan]; + nMat += 1; } }/*for (jWan = 0; jWan < StdI->NsiteUC; jWan++)*/ }/*for (iWan = 0; iWan < StdI->NsiteUC; iWan++)*/ @@ -213,18 +286,14 @@ static void read_W90(struct StdIntList *StdI) for (iWSC = 0; iWSC < nWSC; iWSC++) { for (iWan = 0; iWan < nWan; iWan++) { - free(t_tot[iWSC][iWan]); + free(Mat_tot[iWSC][iWan]); } - free(t_tot[iWSC]); + free(Mat_tot[iWSC]); free(indx_tot[iWSC]); } - free(t_tot); + free(Mat_tot); free(indx_tot); - for (iWan = 0; iWan < nWan; iWan++) free(t0[iWan]); - free(t0); - free(wan_num); -}/*static void read_W90(struct StdIntList *StdI, char *model)*/ -/** +}/*static int read_W90(struct StdIntList *StdI, char *model)*//** @brief Setup a Hamiltonian for the Wannier90 *_hr.dat @author Mitsuaki Kawamura (The University of Tokyo) */ @@ -237,23 +306,57 @@ void StdFace_Wannier90( double Jtmp[3][3] = { {0.0} }; FILE *fp; double complex Cphase; - double dR[3]; + double dR[3], *Uspin; + int n_t, n_u, n_j; + double complex *W90_t, *W90_j, *W90_u; + int **t_indx, **u_indx, **j_indx; + char filename[256]; + + fprintf(stdout, "\n @ Wannier90 Geometry \n\n"); + geometry_W90(StdI); - fprintf(stdout, "\n"); - fprintf(stdout, "####### Parameter Summary #######\n"); - fprintf(stdout, "\n"); /**@brief (1) Compute the shape of the super-cell and sites in the super-cell */ fp = fopen("lattice.xsf", "w"); /**/ - StdI->NsiteUC = 1; - StdFace_InitSite(StdI, fp, 3); StdFace_PrintVal_d("phase0", &StdI->phase[0], 0.0); StdFace_PrintVal_d("phase1", &StdI->phase[1], 0.0); StdFace_PrintVal_d("phase2", &StdI->phase[2], 0.0); - /**/ - read_W90(StdI); + StdFace_InitSite(StdI, fp, 3); + /* + Read Hopping + */ + fprintf(stdout, "\n @ Wannier90 hopping \n\n"); + StdFace_PrintVal_d("cutoff_t", &StdI->cutoff_t, 1.0e-8); + sprintf(filename, "%s_hr.dat", StdI->CDataFileHead); + n_t = read_W90_query(StdI, filename, StdI->cutoff_t); + W90_t = (double complex *)malloc(sizeof(double complex) * n_t); + t_indx = (int **)malloc(sizeof(int*) * n_t); + for (ii = 0; ii < n_t; ii++) t_indx[ii] = (int *)malloc(sizeof(int) * 5); + read_W90(StdI, filename, StdI->cutoff_t, W90_t, t_indx); + /* + Read Coulomb + */ + fprintf(stdout, "\n @ Wannier90 Coulomb \n\n"); + StdFace_PrintVal_d("cutoff_u", &StdI->cutoff_u, 1.0e-8); + sprintf(filename, "%s_ur.dat", StdI->CDataFileHead); + n_u = read_W90_query(StdI, filename, StdI->cutoff_u); + W90_u = (double complex *)malloc(sizeof(double complex) * n_u); + u_indx = (int **)malloc(sizeof(int*) * n_u); + for (ii = 0; ii < n_u; ii++) u_indx[ii] = (int *)malloc(sizeof(int) * 5); + read_W90(StdI, filename, StdI->cutoff_u, W90_u, u_indx); + /* + Read Hund + */ + fprintf(stdout, "\n @ Wannier90 Hund \n\n"); + StdFace_PrintVal_d("cutoff_j", &StdI->cutoff_j, 1.0e-8); + sprintf(filename, "%s_jr.dat", StdI->CDataFileHead); + n_j = read_W90_query(StdI, filename, StdI->cutoff_j); + W90_j = (double complex *)malloc(sizeof(double complex) * n_j); + j_indx = (int **)malloc(sizeof(int*) * n_j); + for (ii = 0; ii < n_j; ii++) j_indx[ii] = (int *)malloc(sizeof(int) * 5); + read_W90(StdI, filename, StdI->cutoff_j, W90_j, j_indx); /**@brief (2) check & store parameters of Hamiltonian */ @@ -261,16 +364,16 @@ void StdFace_Wannier90( StdFace_NotUsed_d("K", StdI->K); StdFace_PrintVal_d("h", &StdI->h, 0.0); StdFace_PrintVal_d("Gamma", &StdI->Gamma, 0.0); + StdFace_NotUsed_d("U", StdI->U); /**/ if (strcmp(StdI->model, "spin") == 0 ) { - StdFace_NotUsed_i("2S", StdI->S2); - StdFace_PrintVal_d("U", &StdI->U, 1.0); + StdFace_PrintVal_i("2S", &StdI->S2, 1); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else if (strcmp(StdI->model, "hubbard") == 0) { StdFace_PrintVal_d("mu", &StdI->mu, 0.0); - StdFace_PrintVal_d("U", &StdI->U, 0.0); } else{ + printf("wannier + Kondo is not available !\n"); StdFace_exit(-1); }/*if (model != "spin")*/ fprintf(stdout, "\n @ Numerical conditions\n\n"); @@ -290,16 +393,26 @@ void StdFace_Wannier90( */ if (strcmp(StdI->model, "spin") == 0 ) { ntransMax = StdI->nsite * (StdI->S2 + 1/*h*/ + 2 * StdI->S2/*Gamma*/); - nintrMax = StdI->NCell * (StdI->NsiteUC/*D*/ + StdI->W90_nt/*J*/) + nintrMax = StdI->NCell * (StdI->NsiteUC/*D*/ + n_t/*J*/ + n_u + n_j) * (3 * StdI->S2 + 1) * (3 * StdI->S2 + 1); } else if (strcmp(StdI->model, "hubbard") == 0) { - ntransMax = StdI->NCell * 2/*spin*/ * (2 * StdI->NsiteUC/*mu+h+Gamma*/ + StdI->W90_nt * 2/*t*/); - nintrMax = StdI->NCell * StdI->NsiteUC/*U*/; + ntransMax = StdI->NCell * 2/*spin*/ * (2 * StdI->NsiteUC/*mu+h+Gamma*/ + n_t * 2/*t*/); + nintrMax = StdI->NCell * (n_u + n_j + 1); } /**/ StdFace_MallocInteractions(StdI, ntransMax, nintrMax); /**@brief + (4.5) For spin system, compute super exchange interaction. + */ + if (strcmp(StdI->model, "spin") == 0) { + Uspin = (double *)malloc(sizeof(double) * StdI->NsiteUC); + for (it = 0; it < n_u; it++) + if (u_indx[it][0] == 0 && u_indx[it][1] == 0 && u_indx[it][2] == 0 + && u_indx[it][3] == u_indx[it][4]) + Uspin[u_indx[it][3]] = creal(W90_u[it]); + }/*if (strcmp(StdI->model, "spin") == 0)*/ + /**@brief (5) Set Transfer & Interaction */ for (kCell = 0; kCell < StdI->NCell; kCell++){ @@ -317,23 +430,23 @@ void StdFace_Wannier90( }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { for (isite = StdI->NsiteUC*kCell; isite < StdI->NsiteUC*(kCell + 1); isite++) { - StdFace_HubbardLocal(StdI, StdI->mu, -StdI->h, -StdI->Gamma, StdI->U, isite); + StdFace_HubbardLocal(StdI, StdI->mu, -StdI->h, -StdI->Gamma, 0.0, isite); } }/*if (strcmp(StdI->model, "spin") != 0 )*/ /* - Hopping from Wannier90 + Hopping */ - for (it = 0; it < StdI->W90_nt; it++) { + for (it = 0; it < n_t; it++) { /* Local term */ - if (StdI->W90_indx[it][0] == 0 && StdI->W90_indx[it][1] == 0 && StdI->W90_indx[it][2] == 0 - && StdI->W90_indx[it][3] == StdI->W90_indx[it][4]) + if (t_indx[it][0] == 0 && t_indx[it][1] == 0 && t_indx[it][2] == 0 + && t_indx[it][3] == t_indx[it][4]) { if (strcmp(StdI->model, "hubbard") == 0) { - isite = StdI->NsiteUC*kCell + StdI->W90_indx[it][3]; + isite = StdI->NsiteUC*kCell + t_indx[it][3]; for (ispin = 0; ispin < 2; ispin++) { - StdI->trans[StdI->ntrans] = StdI->W90_t[it]; + StdI->trans[StdI->ntrans] = -W90_t[it]; StdI->transindx[StdI->ntrans][0] = isite; StdI->transindx[StdI->ntrans][1] = ispin; StdI->transindx[StdI->ntrans][2] = isite; @@ -347,25 +460,100 @@ void StdFace_Wannier90( Non-local term */ StdFace_FindSite(StdI, iW, iL, iH, - StdI->W90_indx[it][0], StdI->W90_indx[it][1], StdI->W90_indx[it][2], - StdI->W90_indx[it][3], StdI->W90_indx[it][4], &isite, &jsite, &Cphase, dR); + t_indx[it][0], t_indx[it][1], t_indx[it][2], + t_indx[it][3], t_indx[it][4], &isite, &jsite, &Cphase, dR); if (strcmp(StdI->model, "spin") == 0) { - for (ii = 0; ii < 3; ii++) Jtmp[ii][ii] = StdI->W90_t[it] * conj(StdI->W90_t[it]) / StdI->U; + for (ii = 0; ii < 3; ii++) + Jtmp[ii][ii] = 2.0 * W90_t[it] * conj(W90_t[it]) + * (1.0 / Uspin[t_indx[it][3]] + 1.0 / Uspin[t_indx[it][4]]); StdFace_GeneralJ(StdI, Jtmp, StdI->S2, StdI->S2, isite, jsite); }/*if (strcmp(StdI->model, "spin") == 0 )*/ else { - StdFace_Hopping(StdI, Cphase * StdI->W90_t[it], isite, jsite, dR); + StdFace_Hopping(StdI, - Cphase * W90_t[it], isite, jsite, dR); + } + }/*Non-local term*/ + }/*for (it = 0; it < n_t; it++)*/ + /* + Coulomb integral (U) + */ + for (it = 0; it < n_u; it++) { + /* + Local term + */ + if (u_indx[it][0] == 0 && u_indx[it][1] == 0 && u_indx[it][2] == 0 + && u_indx[it][3] == u_indx[it][4]) + { + StdI->Cintra[StdI->NCintra] = creal(W90_u[it]); + StdI->CintraIndx[StdI->NCintra][0] = StdI->NsiteUC*kCell + u_indx[it][3]; + StdI->NCintra += 1; + }/*Local term*/ + else { + /* + Non-local term + */ + StdFace_FindSite(StdI, iW, iL, iH, + u_indx[it][0], u_indx[it][1], u_indx[it][2], + u_indx[it][3], u_indx[it][4], &isite, &jsite, &Cphase, dR); + StdFace_Coulomb(StdI, creal(W90_u[it]), isite, jsite); + }/*Non-local term*/ + }/*for (it = 0; it < n_t; it++)*/ + /* + Hund coupling (J) + */ + for (it = 0; it < n_j; it++) { + /* + Local term should not be computed + */ + if (j_indx[it][0] != 0 || j_indx[it][1] != 0 || j_indx[it][2] != 0 + || j_indx[it][3] != j_indx[it][4]) + { + StdFace_FindSite(StdI, iW, iL, iH, + j_indx[it][0], j_indx[it][1], j_indx[it][2], + j_indx[it][3], j_indx[it][4], &isite, &jsite, &Cphase, dR); + + StdI->Hund[StdI->NHund] = creal(W90_j[it]); + StdI->HundIndx[StdI->NHund][0] = isite; + StdI->HundIndx[StdI->NHund][1] = jsite; + StdI->NHund += 1; + + if (strcmp(StdI->model, "hubbard") == 0) { + StdI->Ex[StdI->NEx] = creal(W90_j[it]); + StdI->ExIndx[StdI->NEx][0] = isite; + StdI->ExIndx[StdI->NEx][1] = jsite; + StdI->NEx += 1; + + StdI->PairHopp[StdI->NPairHopp] = creal(W90_j[it]); + StdI->PHIndx[StdI->NPairHopp][0] = isite; + StdI->PHIndx[StdI->NPairHopp][1] = jsite; + StdI->NPairHopp += 1; + } + else { +#if defined(_mVMC) + StdI->Ex[StdI->NEx] = creal(W90_j[it]); +#else + StdI->Ex[StdI->NEx] = -creal(W90_j[it]); +#endif + StdI->ExIndx[StdI->NEx][0] = isite; + StdI->ExIndx[StdI->NEx][1] = jsite; + StdI->NEx += 1; } }/*Non-local term*/ - }/*for (it = 0; it < StdI->W90_nt; it++)*/ + }/*for (it = 0; it < n_t; it++)*/ }/*for (kCell = 0; kCell < StdI->NCell; kCell++)*/ fclose(fp); StdFace_PrintXSF(StdI); StdFace_PrintGeometry(StdI); - for (it = 0; it < StdI->W90_nt; it++) free(StdI->W90_indx[it]); - free(StdI->W90_indx); - free(StdI->W90_t); + for (it = 0; it < n_t; it++) free(t_indx[it]); + free(t_indx); + free(W90_t); + for (it = 0; it < n_u; it++) free(u_indx[it]); + free(u_indx); + free(W90_u); + for (it = 0; it < n_j; it++) free(j_indx[it]); + free(j_indx); + free(W90_j); + if (strcmp(StdI->model, "spin") == 0) free(Uspin); -}/*void StdFace_Pyrochlore*/ +}/*void StdFace_Wannier90*/ diff --git a/tool/CMakeLists.txt b/tool/CMakeLists.txt index 23f07813..18b55a25 100644 --- a/tool/CMakeLists.txt +++ b/tool/CMakeLists.txt @@ -22,3 +22,6 @@ install(FILES ${CMAKE_CURRENT_BINARY_DIR}/gen_frmsf.sh DESTINATION bin configure_file(wout2geom.sh wout2geom.sh COPYONLY) install(FILES ${CMAKE_CURRENT_BINARY_DIR}/wout2geom.sh DESTINATION bin PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ GROUP_EXECUTE WORLD_READ WORLD_EXECUTE) +configure_file(respack2wan90.py respack2wan90.py COPYONLY) +install(FILES ${CMAKE_CURRENT_BINARY_DIR}/respack2wan90.py DESTINATION bin + PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ GROUP_EXECUTE WORLD_READ WORLD_EXECUTE) diff --git a/tool/respack2wan90.py b/tool/respack2wan90.py new file mode 100644 index 00000000..f2246ab3 --- /dev/null +++ b/tool/respack2wan90.py @@ -0,0 +1,139 @@ +#!/usr/bin/python +# +# DCore -- Integrated DMFT software for correlated electrons +# Copyright (C) 2017 The University of Tokyo +# +# This program is free software: you can redistribute it and/or modify +# it under the terms of the GNU General Public License as published by +# the Free Software Foundation, either version 3 of the License, or +# (at your option) any later version. +# +# This program is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU General Public License for more details. +# +# You should have received a copy of the GNU General Public License +# along with this program. If not, see . +# +from __future__ import print_function +import sys +import numpy + + +def res2wan(name_in, name_out): + # + print(" Convert from \"{0}\" to \"{1}\"".format(name_in, name_out)) + # + # Input + # + with open(name_in, 'r') as f: + for ii in range(3): + line = f.readline() # Skip + print(" "+line, end="") + line = f.readlines() + # + # Parse from RESPACK format + # + temp1 = [[]] + nr = 0 + for iline in range(len(line)): + if line[iline] == "\n": + temp1.append([]) + nr += 1 + else: + temp1[nr].append(line[iline].split()) + # + print(" Number of R : ", nr) + norb = int(numpy.sqrt(len(temp1[0])-1)+0.1) + print(" Number of bands : ", norb) + + irvec = numpy.zeros((nr, 3), numpy.int_) + hopping = numpy.zeros((nr, norb, norb), numpy.complex_) + + for ir in range(nr): + for ii in range(3): + irvec[ir, ii] = int(temp1[ir][0][ii]) + + ii = 0 + for iorb in range(norb): + for jorb in range(norb): + ii += 1 + hopping[ir, int(int(temp1[ir][ii][0]))-1, int(int(temp1[ir][ii][1]))-1] = \ + float(temp1[ir][ii][2]) + 1.0j * float(temp1[ir][ii][3]) + # + # Output to wannier90 format + # + with open(name_out, 'w') as f: + + print("Converted from RESPACK", file=f) + print(norb, file=f) + print(nr, file=f) + for ir in range(nr): + print(" 1", end="", file=f) + if ir % 15 == 14: + print("", file=f) + if nr % 15 != 0: + print("", file=f) + for ir in range(nr): + for iorb in range(norb): + for jorb in range(norb): + print("%5d%5d%5d%5d%5d%12.6f%12.6f" % + (irvec[ir, 0], irvec[ir, 1], irvec[ir, 2], jorb+1, iorb+1, + hopping[ir, jorb, iorb].real, hopping[ir, jorb, iorb].imag), file=f) + + +def ref2geom(filename): + # + print(" Convert from \"./dir-wfn/dat.lattice\" and \"./dir-wan/dat.wan-center\" to \"{0}\"".format(filename)) + # + # Geometry (for HPhi and mVMC) + # + avec = numpy.zeros((3, 3), numpy.float_) + with open("./dir-wfn/dat.lattice", 'r') as fi: + for ii in range(3): + line = fi.readline() + itemlist = line.split() + for jj in range(3): + avec[ii, jj] = float(itemlist[jj]) + # + bvec = numpy.linalg.inv(avec) + # + # + with open("./dir-wan/dat.wan-center", 'r') as fi: + for ii in range(2): + line = fi.readline() # skip + print(" " + line, end="") + line = fi.readlines() + nwan = len(line) + centre = numpy.zeros((nwan, 3), numpy.float_) + for iwan in range(nwan): + itemlist = line[iwan].split() + for ii in range(3): + centre[iwan, ii] = float(itemlist[ii]) + centre = numpy.dot(centre, bvec) + # + # Bohr -> Angstrom + # + avec[:, :] *= 0.529177249 + # + with open(filename, 'w') as fo: + for ii in range(3): + print("%f %f %f" % (avec[ii, 0], avec[ii, 1], avec[ii, 2]), file=fo) + print("%d" % nwan, file=fo) + for iwan in range(nwan): + print("%f %f %f" % (centre[iwan, 0], centre[iwan, 1], centre[iwan, 2]), file=fo) + + +args = sys.argv + +if len(args) != 2: + print("\nUsage:\n") + print(" $ respack2wan90.py seedname\n") + exit(-1) + +res2wan("./dir-wan/dat.h_mat_r", args[1] + "_hr.dat") +res2wan("./dir-intW/dat.Wmat", args[1] + "_ur.dat") +res2wan("./dir-intJ/dat.Jmat", args[1] + "_jr.dat") + +ref2geom(args[1] + "_geom.dat") From a048591fa69a2418102efba3c5bb049702db3082 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Wed, 24 Jan 2018 11:20:46 +0900 Subject: [PATCH 12/34] (BugFix) Incorrect copy of non-periodic function. --- doc/fourier/en/conf.py | 2 +- doc/fourier/ja/conf.py | 2 +- tool/corplot.F90 | 54 ++++++-------------- tool/fourier.F90 | 113 +++++++++++++---------------------------- 4 files changed, 53 insertions(+), 118 deletions(-) diff --git a/doc/fourier/en/conf.py b/doc/fourier/en/conf.py index 73f2fe82..923fbe37 100644 --- a/doc/fourier/en/conf.py +++ b/doc/fourier/en/conf.py @@ -56,7 +56,7 @@ # The short X.Y version. version = '0.1' # The full version, including alpha/beta/rc tags. -release = '0.1' +release = '0.1.1' # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. diff --git a/doc/fourier/ja/conf.py b/doc/fourier/ja/conf.py index d0bdfe9a..aa6da3d6 100644 --- a/doc/fourier/ja/conf.py +++ b/doc/fourier/ja/conf.py @@ -56,7 +56,7 @@ # The short X.Y version. version = '0.1' # The full version, including alpha/beta/rc tags. -release = '0.1' +release = '0.1.1' # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. diff --git a/tool/corplot.F90 b/tool/corplot.F90 index 20350e70..87460198 100644 --- a/tool/corplot.F90 +++ b/tool/corplot.F90 @@ -6,7 +6,6 @@ MODULE corplot_val & nline, & & itarget, & & nwfc, & ! Number of state - & nktot, & ! Total number of k & nk_row, & ! number row of total k & nk ! Number of k to be computed ! @@ -21,9 +20,6 @@ MODULE corplot_val & errbar, & & rpart ! - INTEGER,ALLOCATABLE,SAVE :: & - & equiv(:) ! (nktot) Equivalent k point in the 1st BZ - ! REAL(8),ALLOCATABLE,SAVE :: & & kvec(:,:) ! (2,nk) k-vector in the 1st BZ ! @@ -57,8 +53,8 @@ SUBROUTINE read_cor() #if defined(FUJITSU) USE service_routines, ONLY : IARGC #endif - USE corplot_val, ONLY : nwfc, nktot, nk_row, recipr, koff, & - & cor_k, cor_err, equiv, kvec, nk + USE corplot_val, ONLY : nwfc, nk_row, recipr, koff, & + & cor_k, cor_err, kvec, nk IMPLICIT NONE ! INTEGER :: fi = 10, ik, iwfc, nk0, idim @@ -81,7 +77,10 @@ SUBROUTINE read_cor() ! OPEN(fi, file = TRIM(filename)) ! - READ(fi,*) ctmp1, nk0 + READ(fi,*) ctmp1, nk0, nk_row + DO idim = 1, 3 + READ(fi,*) ctmp2, recipr(1:3,idim) + END DO READ(fi,*) ctmp2 READ(fi,*) ctmp2 READ(fi,*) ctmp2, koff(1:3) @@ -89,7 +88,7 @@ SUBROUTINE read_cor() IF(iwfc == 1) THEN ! nk = nk0 - ALLOCATE(cor_k(1:nk,1:6,1:nwfc), cor_err(1:nk,1:6,1:nwfc)) + ALLOCATE(cor_k(1:nk,1:6,1:nwfc), cor_err(1:nk,1:6,1:nwfc), kvec(3,nk)) cor_k(1:nk,1:6,1:nwfc) = CMPLX(0d0, 0d0, KIND(0d0)) cor_err(1:nk,1:6,1:nwfc) = 0d0 ! @@ -102,12 +101,12 @@ SUBROUTINE read_cor() IF(TRIM(ctmp1) == "#HPhi") THEN WRITE(*,'(a,a,a)') " Read ", TRIM(filename), " as HPhi Correlation File" DO ik = 1, nk - READ(fi,'(15e15.5)') rtmp(1:3), cor_k(ik,1:6,iwfc) + READ(fi,'(15e15.5)') kvec(1:3, ik), cor_k(ik,1:6,iwfc) END DO ELSE ! mVMC WRITE(*,'(a,a,a)') " Read ", TRIM(filename), " as mVMC Correlation File" DO ik = 1, nk - READ(fi,'(27e15.5)') rtmp(1:3), cor_k(ik,1:6,iwfc), cor_err(ik,1:6,iwfc) + READ(fi,'(27e15.5)') kvec(1:3, ik), cor_k(ik,1:6,iwfc), cor_err(ik,1:6,iwfc) END DO END IF ! @@ -115,27 +114,6 @@ SUBROUTINE read_cor() ! END DO ! iwfc = 1, nwfc ! - ! k-points in the larger area - ! - OPEN(fi, file = "kpoints.dat") - ! - READ(fi,*) nktot, nk_row - DO idim = 1, 3 - READ(fi,*) recipr(1:3,idim) - END DO - ! - ALLOCATE(kvec(3,nktot), equiv(nktot)) - WRITE(*,*) " Total Number of k : ", nktot - WRITE(*,*) " Row for k : ", nk_row - WRITE(*,*) " Reciplocal lattice vector :" - WRITE(*,'(4x3f15.10)') recipr(1:3, 1:3) - ! - DO ik = 1, nktot - READ(fi,*) kvec(1:3,ik), equiv(ik) - END DO - ! - CLOSE(fi) - ! END SUBROUTINE read_cor ! ! Set vectors to difine Bragg's plane @@ -475,8 +453,8 @@ END SUBROUTINE write_gnuplot ! SUBROUTINE write_data() ! - USE corplot_val, ONLY : itarget, rpart, nwfc, nktot, nk_row, & - & cor_k, cor_err, equiv, kvec, koff + USE corplot_val, ONLY : itarget, rpart, nwfc, nk_row, & + & cor_k, cor_err, kvec, koff, nk IMPLICIT NONE ! INTEGER :: fo = 20, ik @@ -492,16 +470,16 @@ SUBROUTINE write_data() koff2(1:2) = 0d0 END IF ! - DO ik = 1, nktot + DO ik = 1, nk ! IF(rpart) THEN WRITE(fo,TRIM(form)) kvec(1:2,ik) + koff2(1:2), & - & DBLE(cor_k( equiv(ik), itarget, 1:nwfc)), & - & DBLE(cor_err(equiv(ik), itarget, 1:nwfc)) + & DBLE(cor_k( ik, itarget, 1:nwfc)), & + & DBLE(cor_err(ik, itarget, 1:nwfc)) ELSE WRITE(fo,TRIM(form)) kvec(1:2,ik) + koff2(1:2), & - & AIMAG(cor_k( equiv(ik), itarget, 1:nwfc)), & - & AIMAG(cor_err(equiv(ik), itarget, 1:nwfc)) + & AIMAG(cor_k( ik, itarget, 1:nwfc)), & + & AIMAG(cor_err(ik, itarget, 1:nwfc)) END IF ! IF(MOD(ik, nk_row) == 0) WRITE(fo,*) diff --git a/tool/fourier.F90 b/tool/fourier.F90 index b9c40be0..46a0148b 100644 --- a/tool/fourier.F90 +++ b/tool/fourier.F90 @@ -11,8 +11,8 @@ MODULE fourier_val & ncor1, & ! Nomber of One-body Correlation function & ncor2, & ! Number of Two-body Correlation function & ncor(8), & ! Number of Correlation function for each index(See below) - & nktot, & ! Total number of k & nk_row, & ! number row of total k + & ncell, & ! number of unit cell & nk ! Number of k to be computed ! REAL(8),SAVE :: & @@ -26,12 +26,10 @@ MODULE fourier_val & file_two ! Filename for Two-body Correlation ! INTEGER,ALLOCATABLE,SAVE :: & - & indx(:,:,:), & ! (nsite:nsite,8) Mapping index for each Correlation function - & equiv(:) ! (nktot) Equivalent k point in the 1st BZ + & indx(:,:,:) ! (nsite:nsite,8) Mapping index for each Correlation function ! REAL(8),ALLOCATABLE,SAVE :: & & kvec(:,:), & ! (3,nk) k-vector in the 1st BZ - & kvec_tot(:,:), & ! (3,nktot) k-vector in the lerger area & site(:,:) ! (3,nsite) Site geometry in the fractional coordinate ! COMPLEX(8),ALLOCATABLE,SAVE :: & @@ -280,7 +278,7 @@ END SUBROUTINE read_filename ! SUBROUTINE read_geometry() ! - USE fourier_val, ONLY : direct, recipr, box, rbox, nsite, site, nk, koff + USE fourier_val, ONLY : direct, recipr, box, rbox, nsite, site, ncell, koff IMPLICIT NONE ! INTEGER :: fi = 10, isite, ii, jj @@ -328,11 +326,11 @@ SUBROUTINE read_geometry() ! CLOSE(fi) ! - ! The number of k in the 1st BZ + ! The number of unit cell ! - nk = 0 + ncell = 0 DO ii = 1, 3 - nk = nk & + ncell = ncell & & + box(ii,1) * box(MOD(ii, 3) + 1, 2) * box(MOD(ii + 1, 3) + 1, 3) & & - box(ii,1) * box(MOD(ii + 1, 3) + 1, 2) * box(MOD(ii, 3) + 1, 3) END DO @@ -347,12 +345,12 @@ SUBROUTINE read_geometry() END DO END DO ! - IF(nk < 0) THEN - nk = -nk + IF(ncell < 0) THEN + ncell = -ncell rbox(1:3,1:3) = - rbox(1:3,1:3) END IF - WRITE(*,*) " Number of k point : ", nk - WRITE(*,*) " Reciprocal superlattice vector (times nk) :" + WRITE(*,*) " Number of Unit Cell : ", ncell + WRITE(*,*) " Reciprocal superlattice vector (times ncell) :" WRITE(*,'(3i8)') rbox(1:3, 1:3) ! ! Compute Reciprocal Lattice Vector @@ -364,7 +362,7 @@ SUBROUTINE read_geometry() & - direct(ii,1) * direct(MOD(ii + 1, 3) + 1, 2) * direct(MOD(ii, 3) + 1, 3) END DO ! - ! Compute reciprocal SuperLattice Vector + ! ! DO ii = 1, 3 DO jj = 1, 3 @@ -381,7 +379,7 @@ SUBROUTINE read_geometry() ! phase(1:3) = phase(1:3) * pi180 koff(1:3) = MATMUL(DBLE(rbox(1:3,1:3)), phase(1:3)) - koff(1:3) = koff(1:3) / DBLE(nk) + koff(1:3) = koff(1:3) / DBLE(ncell) koff(1:3) = MATMUL(recipr(1:3,1:3), koff(1:3)) WRITE(*,*) " k-point offset :" WRITE(*,'(4x3f15.10)') koff(1:3) @@ -392,13 +390,11 @@ END SUBROUTINE read_geometry ! SUBROUTINE set_kpoints() ! - USE fourier_val, ONLY : box, rbox, nk, nktot, kvec, kvec_tot, equiv, nk_row + USE fourier_val, ONLY : box, rbox, nk, kvec, nk_row, ncell ! IMPLICIT NONE ! - INTEGER :: imax(3), imin(3), i1, i2, i3, ii, edge(3,8), nk0, ik, jk, idim, ikvec0(3) - INTEGER,ALLOCATABLE :: ikvec(:,:), ikvec_tot(:,:) - REAL(8) :: kvec0(3) + INTEGER :: imax(3), imin(3), i1, i2, i3, ii, edge(3,8), ik, jk, idim, ikvec(3) ! ! Define range of k-grid index spanning [-1:1] in fractional BZ ! @@ -417,53 +413,23 @@ SUBROUTINE set_kpoints() imax(idim) = MAXVAL(edge(idim,1:8)) END DO ! - nktot = PRODUCT(imax(1:3) - imin(1:3) + 1) + nk = PRODUCT(imax(1:3) - imin(1:3) + 1) nk_row = imax(1) - imin(1) + 1 - ALLOCATE(kvec(3,nk), ikvec(3,nk)) - ALLOCATE(kvec_tot(3,nktot), ikvec_tot(3,nktot), equiv(nktot)) + ALLOCATE(kvec(3,nk)) ! - nk0 = 0 - nktot = 0 + nk = 0 DO i3 = imin(3), imax(3) DO i2 = imin(2), imax(2) DO i1 = imin(1), imax(1) ! - ikvec0(1:3) = MATMUL(rbox(1:3,1:3), (/i1, i2, i3/)) - kvec0(1:3) = DBLE(ikvec0(1:3)) / DBLE(nk) - ! - ! Only k-vectors in the 1st BZ is used in the fourier trans. - ! - IF(ALL(0 <= ikvec0(1:3)) .AND. ALL(ikvec0(1:3) < nk)) THEN - nk0 = nk0 + 1 - ikvec(1:3,nk0) = ikvec0(1:3) - kvec( 1:3,nk0) = kvec0(1:3) - END IF - ! - IF(i3 == 0) THEN - nktot = nktot + 1 - ikvec_tot(1:3,nktot) = ikvec0(1:3) - kvec_tot( 1:3,nktot) = kvec0(1:3) - END IF + ikvec(1:3) = MATMUL(rbox(1:3,1:3), (/i1, i2, i3/)) + nk = nk + 1 + kvec(1:3, nk) = DBLE(ikvec(1:3)) / DBLE(ncell) ! END DO END DO END DO - WRITE(*,*) " Number of k : ", nk0 ! Must be the same as nk - ! - ! Search equivalent k-point - ! - DO ik = 1, nktot - ! - DO jk = 1, nk - ! - IF(ALL(MODULO(ikvec_tot(1:3,ik), nk) == ikvec(1:3,jk))) THEN - equiv(ik) = jk - EXIT - END IF - ! - END DO ! jk = 1, nk - ! - END DO ! ik = 1, nktot + WRITE(*,*) " Number of k : ", nk ! END SUBROUTINE set_kpoints ! @@ -735,7 +701,7 @@ END SUBROUTINE read_corrfile ! SUBROUTINE fourier_cor() ! - USE fourier_val, ONLY : nsite, cor, cor_k, site, kvec, nwfc, nk + USE fourier_val, ONLY : nsite, cor, cor_k, site, kvec, nwfc, nk, ncell IMPLICIT NONE ! INTEGER :: isite, jsite, ik @@ -758,8 +724,8 @@ SUBROUTINE fourier_cor() CALL zgemm('N', 'N', nk, 6*nwfc, nsite*nsite, CMPLX(1d0, 0d0, KIND(1d0)), fmat, nk, & & cor, nsite*nsite, CMPLX(0d0,0d0,KIND(1d0)), cor_k, nk) ! - cor_k(1:nk,1:2,1:nwfc) = cor_k(1:nk,1:2,1:nwfc) / dble(nk) - cor_k(1:nk,3:6,1:nwfc) = cor_k(1:nk,3:6,1:nwfc) / dble(nk*nk) + cor_k(1:nk,1:2,1:nwfc) = cor_k(1:nk,1:2,1:nwfc) / dble(ncell) + cor_k(1:nk,3:6,1:nwfc) = cor_k(1:nk,3:6,1:nwfc) / dble(ncell*ncell) ! DEALLOCATE(fmat, cor, site) ! @@ -769,8 +735,8 @@ END SUBROUTINE fourier_cor ! SUBROUTINE output_cor() ! - USE fourier_val, ONLY : cor_k, nk, nktot, nk_row, kvec, kvec_tot, koff, & - & equiv, nwfc, recipr, filehead, filetail, calctype + USE fourier_val, ONLY : cor_k, nk, nk_row, kvec, koff, & + & nwfc, recipr, filehead, filetail, calctype IMPLICIT NONE ! INTEGER :: fo = 20, ik, iwfc, idim @@ -819,7 +785,10 @@ SUBROUTINE output_cor() filename = TRIM(filehead) // "_corr.dat" OPEN(fo, file = TRIM(filename)) ! - WRITE(fo,*) "#mVMC", nk + WRITE(fo,*) "#mVMC", nk, nk_row + DO idim = 1, 3 + WRITE(fo,*) "# ", tpi * recipr(1:3, idim) + END DO WRITE(fo,*) "# kx[1] ky[2] kz[3](Cart.) UpUp[4,5,16,17] (Re. Im. Err.) DownDown[6,7,18,19]" WRITE(fo,*) "# Density[8,9,20,21] SzSz[10,11,22,23] S+S-[12,13,24,25] S.S[14,15,26.27]" WRITE(fo,'(a,3f15.7)') " #k-offset", koff(1:3) @@ -842,7 +811,10 @@ SUBROUTINE output_cor() filename = TRIM(filehead) // "_corr" // TRIM(filetail(iwfc)) OPEN(fo, file = TRIM(filename)) ! - WRITE(fo,*) "#HPhi", nk + WRITE(fo,*) "#HPhi", nk, nk_row + DO idim = 1, 3 + WRITE(fo,*) "# ", tpi * recipr(1:3, idim) + END DO WRITE(fo,*) "# kx[1] ky[2] kz[3](Cart.) UpUp[4,5] (Re. Im.) DownDown[6,7]" WRITE(fo,*) "# Density[8,9] SzSz[10,11] S+S-[12,13] S.S[14,15]" WRITE(fo,'(a,3f15.7)') " #k-offset", koff(1:3) @@ -857,22 +829,7 @@ SUBROUTINE output_cor() ! END IF ! IF(calctype == 4) ! - ! k-points in the larger area - ! - OPEN(fo, file = "kpoints.dat") - ! - WRITE(fo,*) nktot, nk_row - DO idim = 1, 3 - WRITE(fo,'(3e15.5)') tpi * recipr(1:3,idim) - END DO - ! - DO ik = 1, nktot - WRITE(fo,'(3e15.5,i7)') tpi * MATMUL(recipr(1:3,1:3), kvec_tot(1:3,ik)), equiv(ik) - END DO - ! - CLOSE(fo) - ! - DEALLOCATE(cor_k,kvec,kvec_tot,equiv) + DEALLOCATE(cor_k,kvec) ! END SUBROUTINE output_cor ! From e5d04946fcf44f2e7f1da4df5a1264dda857e081 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Wed, 31 Jan 2018 13:41:03 +0900 Subject: [PATCH 13/34] Introduce sphinx --- doc/bib/ref.txt | 9 + doc/figs/chap04_1_honeycomb.png | Bin 0 -> 260307 bytes doc/figs/chap04_1_lattice.png | Bin 0 -> 160239 bytes doc/figs/chap04_1_unitlattice.png | Bin 0 -> 161527 bytes doc/figs/corplot.png | Bin 0 -> 20340 bytes doc/figs/kagome.png | Bin 0 -> 400654 bytes doc/figs/ladder.png | Bin 0 -> 128987 bytes doc/figs/mVMC.png | Bin 0 -> 254099 bytes doc/jp/Makefile | 177 ++ doc/jp/acknowledge.rst | 13 + doc/jp/algorithm.rst | 340 ++++ doc/jp/appendix.rst | 199 ++ doc/jp/conf.py | 262 +++ doc/jp/expert.rst | 2504 ++++++++++++++++++++++++ doc/jp/fourier/fourier_contact_ja.rst | 14 + doc/jp/fourier/fourier_format_ja.rst | 250 +++ doc/jp/fourier/fourier_overview_ja.rst | 63 + doc/jp/fourier/fourier_tutorial_ja.rst | 115 ++ doc/jp/fourier/fourier_util_ja.rst | 94 + doc/jp/fourier/index.rst | 26 + doc/jp/index.rst | 29 + doc/jp/intro.rst | 140 ++ doc/jp/output.rst | 330 ++++ doc/jp/standard.rst | 673 +++++++ doc/jp/start.rst | 350 ++++ doc/jp/tutorial.rst | 332 ++++ 26 files changed, 5920 insertions(+) create mode 100644 doc/bib/ref.txt create mode 100644 doc/figs/chap04_1_honeycomb.png create mode 100644 doc/figs/chap04_1_lattice.png create mode 100644 doc/figs/chap04_1_unitlattice.png create mode 100644 doc/figs/corplot.png create mode 100644 doc/figs/kagome.png create mode 100644 doc/figs/ladder.png create mode 100644 doc/figs/mVMC.png create mode 100644 doc/jp/Makefile create mode 100644 doc/jp/acknowledge.rst create mode 100644 doc/jp/algorithm.rst create mode 100644 doc/jp/appendix.rst create mode 100644 doc/jp/conf.py create mode 100644 doc/jp/expert.rst create mode 100644 doc/jp/fourier/fourier_contact_ja.rst create mode 100644 doc/jp/fourier/fourier_format_ja.rst create mode 100644 doc/jp/fourier/fourier_overview_ja.rst create mode 100644 doc/jp/fourier/fourier_tutorial_ja.rst create mode 100644 doc/jp/fourier/fourier_util_ja.rst create mode 100644 doc/jp/fourier/index.rst create mode 100644 doc/jp/index.rst create mode 100644 doc/jp/intro.rst create mode 100644 doc/jp/output.rst create mode 100644 doc/jp/standard.rst create mode 100644 doc/jp/start.rst create mode 100644 doc/jp/tutorial.rst diff --git a/doc/bib/ref.txt b/doc/bib/ref.txt new file mode 100644 index 00000000..34e9fc1f --- /dev/null +++ b/doc/bib/ref.txt @@ -0,0 +1,9 @@ +.. _Tahara2008: http://dx.doi.org/10.1143/JPSJ.77.114701 +.. _Mutsuo2008: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT +.. _PFAPACK: https://dl.acm.org/citation.cfm?doid=2331130.2331138 +.. _HPhi: http://ma.cms-initiative.jp/ja/listapps/hphi +.. _Morita2015: http://journals.jps.jp/doi/abs/10.7566/JPSJ.84.024720 +.. _Misawa2014: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.115137 +.. _ImadaMiyake: http://journals.jps.jp/doi/abs/10.1143/JPSJ.79.112001 +.. _Gros: 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Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/) +endif + +# Internal variables. +PAPEROPT_a4 = -D latex_paper_size=a4 +PAPEROPT_letter = -D latex_paper_size=letter +ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . +# the i18n builder cannot share the environment and doctrees with the others +I18NSPHINXOPTS = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . + +.PHONY: help clean html dirhtml singlehtml pickle json htmlhelp qthelp devhelp epub latex latexpdf text man changes linkcheck doctest gettext + +help: + @echo "Please use \`make ' where is one of" + @echo " html to make standalone HTML files" + @echo " dirhtml to make HTML files named index.html in directories" + @echo " singlehtml to make a single large HTML file" + @echo " pickle to make pickle files" + @echo " json to make JSON files" + @echo " htmlhelp to make HTML files and a HTML help project" + @echo " qthelp to make HTML files and a qthelp project" + @echo " devhelp to make HTML files and a Devhelp project" + @echo " epub to make an epub" + @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter" + @echo " latexpdf to make LaTeX files and run them through pdflatex" + @echo " latexpdfja to make LaTeX files and run them through platex/dvipdfmx" + @echo " text to make text files" + @echo " man to make manual pages" + @echo " texinfo to make Texinfo files" + @echo " info to make Texinfo files and run them through makeinfo" + @echo " gettext to make PO message catalogs" + @echo " changes to make an overview of all changed/added/deprecated items" + @echo " xml to make Docutils-native XML files" + @echo " pseudoxml to make pseudoxml-XML files for display purposes" + @echo " linkcheck to check all external links for integrity" + @echo " doctest to run all doctests embedded in the documentation (if enabled)" + +clean: + rm -rf $(BUILDDIR)/* + +html: + $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html + @echo + @echo "Build finished. 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The pseudo-XML files are in $(BUILDDIR)/pseudoxml." diff --git a/doc/jp/acknowledge.rst b/doc/jp/acknowledge.rst new file mode 100644 index 00000000..7a86abdd --- /dev/null +++ b/doc/jp/acknowledge.rst @@ -0,0 +1,13 @@ +謝辞 +==== + +mVMCの開発は田原大資氏か開発された +変分モンテカルロ法のコードをもとに行いました。 +コードを提供していただいた田原大資氏に感謝します。 +また、田原大資氏のコードを改良していく段階で、 +品岡寛氏、山地洋平氏、栗田萌氏、金子隆威氏に協力して頂きました。 +この場を借りて、この方々に感謝します。 + +mVMC ver.0.1, ver. 0.2, ver. 1.0は、 東京大学物性研究所 +ソフトウェア高度化プロジェクト (2016 年度) +の支援を受け開発されました。この場を借りて感謝します。 diff --git a/doc/jp/algorithm.rst b/doc/jp/algorithm.rst new file mode 100644 index 00000000..ccb42a9f --- /dev/null +++ b/doc/jp/algorithm.rst @@ -0,0 +1,340 @@ +.. include:: ../bib/ref.txt + +アルゴリズム +============ + +変分モンテカルロ法 +------------------ + +変分モンテカルロ法では, 試行波動関数を用意して, +その試行波動関数が含むパラメータを +変分原理に従って最適化することで量子多体系の基底状態(または低励起エネルギー状態)の波動関数を +近似的に求めます。 試行波動関数に対する物理量の期待値を計算する部分で, +マルコフ連鎖モンテカルロ法を利用し, +効率よく重み付きサンプリングを行います。 + +本パッケージでは, +サンプリングに用いる完全系として電子の実空間配置 :math:`| x\rangle` をとっています: + +.. math:: + + | x\rangle = \prod_{n=1}^{N/2} c_{r_{n\uparrow}}^{\dagger} \prod_{n=1}^{N/2} + c_{r_{n\downarrow}}^{\dagger} |0 \rangle + +ここで, +:math:`r_{n\sigma}` は :math:`n` 番目の電子(スピン :math:`\sigma`)の位置, +:math:`c_{r_{n\sigma}}^{\dagger}` はその位置での +電子(スピン :math:`\sigma`)の生成演算子を表します。この基底を用いると, +演算子 :math:`A` の期待値は + +.. math:: + + \langle A \rangle =\frac{\langle \psi| A| \psi \rangle}{\langle \psi | \psi \rangle} + =\sum_x \frac{\langle \psi| A | x\rangle \langle x| \psi \rangle}{\langle \psi |\psi \rangle} + +となるため, マルコフ連鎖の重みを + +.. math:: \rho(x)=\frac{|\langle x| \psi \rangle|^2}{\langle \psi | \psi \rangle} \ge 0, \quad \sum_{x} \rho(x)=1 + + と定義して, + +.. math:: + + \langle A \rangle =\sum_x \rho(x) \frac{\langle \psi| A | x\rangle }{\langle \psi |x \rangle} + + +と書き直した後、:math:`x` に関する和をマルコフ連鎖モンテカルロ法により +評価しています。Local Green’s function +:math:`G_{ij\sigma\sigma'}(x)` は + +.. math:: + + G_{ij\sigma\sigma'}(x)=\frac{\langle \psi | c_{i\sigma}^{\dagger} c_{j\sigma'} + | \psi \rangle}{\langle \psi | x \rangle} + +と定義されますが, +これも演算子 :math:`A` を :math:`c_{i\sigma}^{\dagger} c_{j\sigma'}` ととることで, +同じ方法により重み付きサンプリングを行うことができます。 なお, +サンプリングに使用する乱数生成については, +メルセンヌツイスター法を使用しています[Mutsuo2008_ ]。 + +.. _BogoliubovRep: + +Bogoliubov表現 +-------------- + +スピン系の計算において一体項( ``transfer``), +``InterAll`` 形式での相互作用, +相関関数のインデックスの指定にはBogoliubov表現が使われています。 +一般に、スピンの演算子は次のようにフェルミオンの生成 :math:`\cdot` 消滅演算子 :math:`c_{i \sigma}`, +:math:`c_{i \sigma}^\dagger` によって書き換えることができます: + +.. math:: + + \begin{aligned} + S_{i z} &= \sum_{\sigma = -S}^{S} \sigma c_{i \sigma}^\dagger c_{i \sigma} + \\ + S_{i}^+ &= \sum_{\sigma = -S}^{S-1} + \sqrt{S(S+1) - \sigma(\sigma+1)} + c_{i \sigma+1}^\dagger c_{i \sigma} + \\ + S_{i}^- &= \sum_{\sigma = -S}^{S-1} + \sqrt{S(S+1) - \sigma(\sigma+1)} + c_{i \sigma}^\dagger c_{i \sigma+1} + \end{aligned} + +本パッケージでは、 :math:`S=1/2` のスピン系のみ取り扱っており、上記の式で +:math:`S=1/2` と置いたものを用いています。 + +.. _PuffAndSlater: + +パフィアン-スレーター行列式の性質 +--------------------------------- + +この節では, +パフィアン-スレーター行列式のもつ性質について簡単にまとめます。 +:ref:`次節 ` と :ref:`次々節 ` でパフィアン-スレーター行列式と単一スレーター行列式の間の関係を導出し、 +:ref:`最後 ` に :math:`f_{ij}` の特異値分解の意味について説明します。 + +.. _PfaffianAP: + +:math:`f_{ij}` と :math:`\Phi_{in\sigma}` の関係 (スピン反平行の場合) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +多変数変分モンテカルロ法で試行波動関数の一体部分として用いられるパフィアン-スレーター行列式は + +.. math:: + + |\phi_{\rm Pf}\rangle=\Big(\sum_{i,j=1}^{N_{s}}f_{ij} + c_{i\uparrow}^{\dagger}c_{j\downarrow}^{\dagger}\Big)^{N_{\rm e}/2}|0\rangle, + +のように定義されます。ここで, :math:`N_{s}` はサイト数, +:math:`N_{e}` は全電子数, :math:`f_{ij}` は変分パラメータです。 +簡単化のため, 以降 :math:`f_{ij}` は実数と仮定します。また, +単一スレーター行列式として + +.. math:: + + \begin{aligned} + |\phi_{\rm SL}\rangle&=\Big(\prod_{n=1}^{N_{e}/2}\psi_{n\uparrow}^{\dagger}\Big) + \Big(\prod_{m=1}^{N_{e}/2}\psi_{m\downarrow}^{\dagger}\Big)|0\rangle, \\ + \psi_{n\sigma}^{\dagger}&=\sum_{i=1}^{N_{s}}\Phi_{in\sigma}c^{\dagger}_{i\sigma}. + \end{aligned} + +を定義します。ただし, :math:`\Phi` は正規直交基底であり, +クロネッカーのデルタ :math:`\delta_{nm}` を用い + +.. math:: + + \sum_{i=1}^{N_{s}}\Phi_{in\sigma}\Phi_{im\sigma}=\delta_{nm}, + +で表されます。この直交性の関係から, 以下の関係式 + +.. math:: + + \begin{aligned} + [\psi^{\dagger}_{n\sigma},\psi_{m\sigma}]_{+}&=\delta_{nm},\\ + G_{ij\sigma}=\langle c_{i\sigma}^{\dagger}c_{j\sigma}\rangle + &=\frac{\langle \phi_{\rm SL}| c_{i\sigma}^{\dagger}c_{j\sigma} | \phi_{\rm SL}\rangle}{\langle \phi_{\rm SL}|\phi_{\rm SL}\rangle } \\ + &=\sum_{n} \Phi_{in\sigma} \Phi_{jn\sigma}. + \end{aligned} + +が導かれます。 + +次に, :math:`|\phi_{\rm SL}\rangle` を変形し, +:math:`f_{ij}` と :math:`\Phi_{in\sigma}` の間に成り立つ関係式を示します。 +:math:`\psi^{\dagger}_{n\sigma}` の交換関係を用いると, +:math:`|\phi_{\rm SL}\rangle` は + +.. math:: + + \begin{aligned} + |\phi_{\rm SL}\rangle \propto \prod_{n=1}^{N_{e}/2} + \Big(\psi_{n\uparrow}^{\dagger}\psi_{\mu(n)\downarrow}^{\dagger}\Big)|0\rangle, + \end{aligned} + +と書き換えられます。ここで, +:math:`\mu(n)` は :math:`n= 1, 2, \cdots, N_{e}/2` の置換を表します。 +議論を簡単にするため, +同一のペア :math:`n=\mu(n)` となる場合を考えましょう。 このとき, +:math:`K_{n}^{\dagger}=\psi_{n\uparrow}^{\dagger}\psi_{n\downarrow}^{\dagger}` として, +:math:`K_{n}^{\dagger}K_{m}^{\dagger}=K_{m}^{\dagger}K_{n}^{\dagger}` の関係を用いることで, + +.. math:: + + \begin{aligned} + |\phi_{\rm SL}\rangle &\propto \prod_{n=1}^{N_{e}/2}\Big(\psi_{n\uparrow}^{\dagger}\psi_{n\downarrow}^{\dagger}\Big)|0\rangle + =\prod_{n=1}^{N_{e}/2} K_{n}^{\dagger}|0\rangle \\ + &\propto\Big(\sum_{n=1}^{\frac{N_{e}}{2}}K_{n}^{\dagger}\Big)^{\frac{N_{e}}{2}} |0\rangle + =\Big(\sum_{i,j=1}^{N_{s}}\Big[\sum_{n=1}^{\frac{N_{e}}{2}}\Phi_{in\uparrow}\Phi_{jn\downarrow}\Big] + c_{i\uparrow}^{\dagger}c_{j\downarrow}^{\dagger}\Big)^{N_e/2}|0\rangle, + \end{aligned} + +の関係が得られます。これより :math:`f_{ij}` は単一スレーター行列式の係数により + +.. math:: + + \begin{aligned} + f_{ij}=\sum_{n=1}^{\frac{N_{e}}{2}}\Phi_{in\uparrow}\Phi_{jn\downarrow}. + \end{aligned} + +として表されることが分かります。なお, +この形式は単一スレーター行列式で与えられる :math:`f_{ij}` の表式の一つであり, +実際にはペアを組む自由度(どの :math:`\mu(n)` を選ぶか)およびゲージの自由度 +(すなわち :math:`\Phi_{in\sigma}` の符号の自由度)に依存します。 +この自由度の多さが :math:`f_{ij}` の冗長性につながっています。 + +.. _PfaffianP: + +:math:`F_{IJ}` と :math:`\Phi_{In\sigma}` の関係 (スピン平行も含めた場合) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +前節で考察したパフィアン-スレーター波動関数と単一スレーター波動関数の間の関係は、 +同種スピンのペアリングも考えた場合に拡張することができます。 +パフィアン-スレーター波動関数とスレーター波動関数をそれぞれ + +.. math:: + + \begin{aligned} + |\phi_{\rm Pf}\rangle&=\Big(\sum_{I,J=1}^{2N_{s}}F_{IJ}c_{I}^{\dagger}c_{J}^{\dagger}\Big)^{N_{\rm e}/2}|0\rangle, \\ + |\phi_{\rm SL}\rangle&=\Big(\prod_{n=1}^{N_{e}}\psi_{n}^{\dagger}\Big)|0\rangle,~~\psi_{n}^{\dagger}=\sum_{I=1}^{2N_{s}}\Phi_{In}c^{\dagger}_{I}.\end{aligned} + +と定義します。ここで :math:`I,J` はスピン自由度も含めたサイトのインデックスです。 +スピン反平行の場合とほぼ同様の議論を用いることで, + +.. math:: + + \begin{aligned} + F_{IJ}=\sum_{n=1}^{\frac{N_{e}}{2}}\Big(\Phi_{In}\Phi_{Jn+1}-\Phi_{Jn}\Phi_{In+1}\Big). + \end{aligned} + +の関係を示すことができます。これはスピン反平行のペアリングにもそのまま適用できるので, +mVMC ver1.0以降ではこの表式を使用しています。 + +.. _PfaffianSingular: + +:math:`f_{ij}` の特異値分解 +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +行列 :math:`F`, :math:`\Phi_{\uparrow}`, :math:`\Phi_{\downarrow}`, +:math:`\Sigma` を + +.. math:: + + \begin{aligned} + &(F)_{ij}=f_{ij},~~~ + (\Phi_{\uparrow})_{in}=\Phi_{in\uparrow},~~~ + (\Phi_{\downarrow})_{in}=\Phi_{in\downarrow}, \\ + &\Sigma={\rm diag}[\underbrace{1,\cdots,1}_{N_e/2},0,0,0],\end{aligned} + +として定義します。前節のように :math:`f_{ij}` (すなわち:math:`F`)が単一スレーター行列と関係づけられて +いるとき、 :math:`F` の特異値分解は + +.. math:: + + \begin{aligned} + F=\Phi_{\uparrow}\Sigma\Phi_{\downarrow}^{t}.\end{aligned} + +となることを示すことができます。 +この結果は、一般に :math:`F` を特異値分解したとき、非ゼロの特異値が :math:`N_{e}/2` 個存在し, +かつ全ての :math:`F` の非ゼロの特異値が :math:`1` であった場合, +:math:`f_{ij}` が単一スレーター波動関数を +記述すること(つまり平均場近似解として記述できること)を表しています。 +言い換えると, 特異値の非ゼロ成分の数とその値が, +シングルスレータ行列式からパフィアンスレーター行列式がどのようにしてずれるのか, +という点について定量的な基準を与えることを示しています。 + +Power-Lanczos法 +--------------- + +このセクションでは, +Power-Lanczos法での最適化パラメータ :math:`\alpha` の決定方法について述べます。 +また, +ここではシングルステップのLanczos法を適用した後の物理量の計算についても説明します。 + +:math:`\alpha` の決定 +~~~~~~~~~~~~~~~~~~~~~~ + +最初に, 変分モンテカルロ法のサンプリングに関して簡単に説明します。 +物理量 :math:`\hat{A}` は以下の手順で計算されます: + +.. math:: + + \begin{aligned} + &\langle \hat{A}\rangle = \frac{\langle \phi| \hat{A}|\phi \rangle}{\langle \phi| \phi \rangle} = \sum_{x} \rho(x) F(x, {\hat{A}}),\\ + & \rho(x)=\frac{|\langle \phi|x\rangle|^2}{\langle \phi | \phi \rangle}, ~~~~F(x, {\hat{A}}) = \frac{\langle x| \hat{A}|\phi \rangle}{\langle x| \phi \rangle}.\end{aligned} + +演算子の積 :math:`\hat{A}\hat{B}` を計算する場合には, +以下の二通りの方法があります。 + +.. math:: + + \begin{aligned} + &\langle \hat{A} \hat{B}\rangle = \sum_{x} \rho(x) F(x, {\hat{A}\hat{B}}),\\ + &\langle \hat{A} \hat{B}\rangle = \sum_{x} \rho(x) F^{\dagger}(x, {\hat{A})F(x, \hat{B}}).\end{aligned} + +後述するように, 後者の表記の方が数値的には安定します。 例えば, +エネルギーの期待値の分散 :math:`\sigma^2=\langle (\hat{H}-\langle \hat{H}\rangle)^2\rangle` を考えてみると, +分散は以下の2通りの方法で計算できます。 + +.. math:: + + \begin{aligned} + \sigma^2 &=\sum_{x} \rho(x) F(x, (\hat{H}-\langle \hat{H}\rangle)^2) = \sum_{x} \rho(x) F(x, \hat{H}^2) - \left[ \sum_{x} \rho(x) F(x, \hat{H})\right]^2 ,\\ + \sigma^2 &=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}-\langle \hat{H}\rangle)F(x, \hat{H}-\langle \hat{H}\rangle) \nonumber \\ + &= \sum_{x} \rho(x) F^{\dagger}(x, \hat{H}) F(x, \hat{H})- \left[ \sum_{x} \rho(x) F(x, \hat{H})\right]^2 + \end{aligned} + +この定義から, +後者の方法では常に正の値となることが保証されているのに対して, +前者の方法では分散が正の値になることが必ずしも保証されないことが分かります。次に, +シングルステップでのpower-Lanczos波動関数 :math:`|\phi\rangle =(1+\alpha \hat{H}) |\psi \rangle` +に対するエネルギーの期待値とその分散を考えます。エネルギーは以下の式で計算されます： + +.. math:: + + \begin{aligned} + E_{LS}(\alpha) =\frac{\langle \phi| \hat{H} |\phi\rangle}{\langle \phi|\phi\rangle}=\frac{h_1 + \alpha(h_{2(20)} + h_{2(11)}) + \alpha^2 h_{3(12)}}{1 + 2\alpha h_1 + \alpha^2 h_{2(11)}}, + \end{aligned} + +ここで, :math:`h_1`, :math:`h_{2(11)},~h_{2(20)},` and +:math:`h_{3(12)}` を以下のように定義しました： + +.. math:: + + \begin{aligned} + &h_1 =\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}),\\ + &h_{2(11)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}) F(x, \hat{H}),\\ + &h_{2(20)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}^2),\\ + &h_{3(12)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H})F(x, \hat{H}^2).\end{aligned} + +:math:`\frac{\partial E_{LS}(\alpha)}{\partial \alpha}=0` の条件から +:math:`\alpha` の二次方程式が導出され, +それを解くことで :math:`\alpha` が決定されます。 +分散に関しても同様の手法で計算することが可能です。 + +物理量の計算 +~~~~~~~~~~~~ + +最適化パラメータ :math:`\alpha` を用いることで, +演算子 :math:`\hat{A}` の期待値を以下の式から計算することが出来ます： + +.. math:: + + \begin{aligned} + A_{LS}(\alpha) =\frac{\langle \phi| \hat{A} |\phi\rangle}{\langle \phi|\phi\rangle}=\frac{A_0 + \alpha(A_{1(10)} + A_{1(01)}) + \alpha^2 A_{2(11)}}{1 + 2\alpha h_1 + \alpha^2 h_{2(11)}}, + \end{aligned} + +ここで, :math:`A_0`, :math:`A_{1(10)},~A_{1(01)},` and +:math:`A_{2(11)}` は + +.. math:: + + \begin{aligned} + &A_0 =\sum_{x} \rho(x) F(x, \hat{A}),\\ + &A_{1(10)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}) F(x, \hat{A}),\\ + &A_{1(01)}=\sum_{x} \rho(x) F(x, \hat{A}\hat{H}),\\ + &A_{2(11)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H})F(x, \hat{A}\hat{H}).\end{aligned} + +として定義される変数を表します。プログラムでは, +この表式に基づき一体グリーン関数および二体グリーン関数の計算を行っています。 diff --git a/doc/jp/appendix.rst b/doc/jp/appendix.rst new file mode 100644 index 00000000..66bc9978 --- /dev/null +++ b/doc/jp/appendix.rst @@ -0,0 +1,199 @@ +非制限Hartree-Fock近似プログラム +================================ + +mVMCでは補助プログラムとして、多変数変分モンテカルロ法のペア軌道 :math:`f_{ij}` の初期値を +非制限Hartree-Fock(UHF)近似から与えるためのプログラムを用意しています(対応関係は :ref:`PuffAndSlater` を参照)。 +なお、本プログラムは遍歴電子系を対象としており、スピン系、近藤系では正しく動作しません。 + +概要 +---- + +UHF近似では揺らぎ :math:`\delta A \equiv A-\langle A \rangle` の一次までを考慮することで、二体項を一体項へと近似します。 +たとえば、サイト間クーロン相互作用 + +.. math:: + + {\cal H}_V = \sum_{i,j, \sigma, \sigma'}V_{ij} n_ {i\sigma}n_{j\sigma'} + +について考えます。簡単化のため、 :math:`i\equiv (i, \sigma)`, +:math:`j\equiv (j, \sigma')` とすると相互作用の項は揺らぎの二次を落とすことで、 + +.. math:: + + \begin{aligned} + n_ {i}n_{j} &=& (\langle n_{i} \rangle +\delta n_i) (\langle n_{j} \rangle +\delta n_j) - \left[ \langle c_{i}^{\dag}c_j \rangle +\delta (c_{i}^{\dag}c_j ) \right] \left[ \langle c_{j}^{\dag}c_i \rangle +\delta (c_{j}^{\dag}c_i )\right] \nonumber\\ + &\sim&\langle n_{i} \rangle n_j+\langle n_{j} \rangle n_i - \langle c_{i}^{\dag}c_j \rangle c_{j}^{\dag}c_i - \langle c_{j}^{\dag}c_i \rangle c_{i}^{\dag}c_j + -\langle n_{i} \rangle \langle n_j \rangle + \langle c_{j}^{\dag}c_i \rangle \langle c_{i}^{\dag}c_j \rangle + \end{aligned} + +と近似されます。このような形式で、その他の相互作用についても近似を行うことで、一体問題に帰着させることができます。 +計算では、上記の各平均値がself-consistentになるまで計算を行います。 + +ソースコード +~~~~~~~~~~~~ + +ソースコード一式は ``src/ComplexUHF/src`` 以下に入っています。 + +コンパイル方法 +~~~~~~~~~~~~~~ + +コンパイルはmVMCのコンパイルと同様にmVMCのフォルダ直下で + +:: + + $ make mvmc + +を実行することで行われます。コンパイルが終了すると、 +``src/ComplexUHF/src`` に実行ファイル ``UHF`` が作成されます。 + +必要な入力ファイル +~~~~~~~~~~~~~~~~~~ + +入力ファイル指定用ファイル (namelsit.def) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +| UHFで指定するファイルは以下のファイルです。 + ``namelist.def`` は :ref:`InputFileList` で定義されているファイルと同じ様式です。 + +- ``ModPara`` + +- ``LocSpin`` + +- ``Trans`` + +- ``CoulombIntra`` + +- ``CoulombInter`` + +- ``Hund`` + +- ``PairHop`` + +- ``Exchange`` + +- ``Orbital`` / ``OrbitalAntiParallel`` + +- ``OrbitalParallel`` + +- ``OrbitalGeneral`` + +- ``Initial`` + +基本的にはmVMCと同じファイルとなりますが、 + +- ``ModPara`` ファイルで指定されるパラメータ + +- ``Initial`` ファイルの追加 + +がmVMCと異なります。以下、その詳細を記載します。 + +ModParaファイルで指定するパラメータ +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +UHFで指定するパラメータは以下のパラメータです。 + +- ``Nsite`` + +- ``Ne`` + +- ``Mix`` + +- ``EPS`` + +- ``IterationMax`` + +``Nsite``, +``Ne`` はmVMCと共通のパラメータで、以下の三つがUHF独特のパラメータです。 + +- | ``Mix`` + | linear + mixingをdouble型で指定します。mix=1とすると完全に新しいGreen関数に置き換えられます。 + +- | ``EPS`` + | 収束判定条件をint型で指定します。新しく計算されたGreen関数と一つ前のGreen関数の残差が :math:`10^{-\verb|eps|}` の場合に、計算が打ち切られます。 + +- | ``IterationMax`` + | ループの最大数をint型で指定します。 + +なお、mVMCで使用するその他パラメータが存在する場合はWarningが標準出力されます(計算は中断せずに実行されます)。 + +Initialファイル +^^^^^^^^^^^^^^^ + +グリーン関数 :math:`G_{ij\sigma_1\sigma_2}\equiv \langle c_{i\sigma_1}^\dag c_{j\sigma_2}\rangle` の初期値を与えます。 +ファイル様式は ``Trans`` ファイルと同じで、 :math:`t_{ij\sigma_1\sigma_2}` の代わりに :math:`G_{ij\sigma_1\sigma_2}` の値を記述します。 +なお、値を指定しないグリーン関数には０が入ります。 + +使用方法 +-------- + +UHF自体はmVMCと同じように + +:: + + $ UHF namelist.def + +で動きます。計算の流れは以下の通りです。 + +#. ファイル読み込み + +#. ハミルトニアンの作成 + +#. グリーン関数の計算 (self-consistentになるまで) + +#. :math:`f_{ij}` 、各種ファイルの出力 + +計算後に出力されるファイルおよび出力例は以下の通りです。 + +- | zvo\_result.dat: エネルギーと粒子数が出力されます。 + + :: + + energy -15.2265348135 + num 36.0000000000 + +- zvo\_check.dat: + イタレーションのステップ数、グリーン関数の残差の絶対値の平均、収束過程のエネルギー、粒子数を順に出力します。 + + :: + + 0 0.004925645652 -544.963484605164 36.000000 + 1 0.002481594941 -278.304285708488 36.000000 + 2 0.001274395448 -147.247026925130 36.000000 + 3 0.000681060599 -82.973664527606 36.000000 + ... + +- | zvo\_UHF\_cisajs.dat: + 収束した一体グリーン関数 :math:`G_{ij\sigma_1\sigma_2}\equiv\langle c_{i\sigma_1}^{\dag}c_{j\sigma_2}\rangle` 。 + | 全成分について :math:`i, \sigma_1, j, \sigma_2, {\rm Re}\left[G_{ij\sigma_1\sigma_2}\right], {\rm Im}\left[G_{ij\sigma_1\sigma_2}\right]` の順に出力されます。 + + :: + + 0 0 0 0 0.5037555283 0.0000000000 + 0 0 0 1 0.4610257618 0.0003115503 + 0 1 0 0 0.4610257618 -0.0003115503 + 0 1 0 1 0.4962444717 0.0000000000 + ... + +- | zvo\_eigen.dat: + 収束したハミルトニアンの固有値が低エネルギー順に出力されます。 + + :: + + 1 -2.9425069199 + 2 -2.9425069198 + 3 -1.5005359205 + ... + +- zvo\_gap.dat: + 全電子数を :math:`N_{\rm tot}` とした場合に、 :math:`\Delta E= E(N_{\rm tot}+1)-E(N_{\rm tot})` が出力されます。 + + :: + + 5.2208232631 + +- zvo\_orbital\_opt.dat: + スレータ行列式から生成した :math:`f_{ij}` 。 ``InOrbital``, ``InOrbitalAntiParallel``, + ``InOrbitalParallel``, ``InOrbitalAntiGeneral`` ファイルと同じ形式のファイルが出力されます。 + :math:`f_{ij}` が ``Orbital``, ``OrbitalAntiParallel``, + ``OrbitalParallel``, ``OrbitalAntiGeneral`` ファイルを参照し計算され、同種のパラメータについては平均化した値が採用されます。 diff --git a/doc/jp/conf.py b/doc/jp/conf.py new file mode 100644 index 00000000..e984163c --- /dev/null +++ b/doc/jp/conf.py @@ -0,0 +1,262 @@ +# -*- coding: utf-8 -*- +# +# mVMC documentation build configuration file, created by +# sphinx-quickstart on Sat Jan 7 22:10:04 2017. +# +# This file is execfile()d with the current directory set to its +# containing dir. +# +# Note that not all possible configuration values are present in this +# autogenerated file. +# +# All configuration values have a default; values that are commented out +# serve to show the default. + +import sys +import os + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +#sys.path.insert(0, os.path.abspath('.')) + +# -- General configuration ------------------------------------------------ + +# If your documentation needs a minimal Sphinx version, state it here. +#needs_sphinx = '1.0' + +# Add any Sphinx extension module names here, as strings. They can be +# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# ones. +extensions = [ + 'sphinx.ext.mathjax', + 'sphinx_numfig' +] + +# Add any paths that contain templates here, relative to this directory. +templates_path = ['_templates'] + +# The suffix of source filenames. +source_suffix = '.rst' + +# The encoding of source files. +#source_encoding = 'utf-8-sig' + +# The master toctree document. +master_doc = 'index' + +# General information about the project. +project = u'mVMC' +copyright = u'2017, mVMC team' + +# The version info for the project you're documenting, acts as replacement for +# |version| and |release|, also used in various other places throughout the +# built documents. +# +# The short X.Y version. +version = '1.0' +# The full version, including alpha/beta/rc tags. +release = '1.0.2' + +# The language for content autogenerated by Sphinx. Refer to documentation +# for a list of supported languages. +language = 'ja' + +# There are two options for replacing |today|: either, you set today to some +# non-false value, then it is used: +#today = '' +# Else, today_fmt is used as the format for a strftime call. +#today_fmt = '%B %d, %Y' + +# List of patterns, relative to source directory, that match files and +# directories to ignore when looking for source files. +exclude_patterns = ['_build'] + +# The reST default role (used for this markup: `text`) to use for all +# documents. +#default_role = None + +# If true, '()' will be appended to :func: etc. cross-reference text. +#add_function_parentheses = True + +# If true, the current module name will be prepended to all description +# unit titles (such as .. function::). +#add_module_names = True + +# If true, sectionauthor and moduleauthor directives will be shown in the +# output. They are ignored by default. +#show_authors = False + +# The name of the Pygments (syntax highlighting) style to use. +pygments_style = 'sphinx' + +# A list of ignored prefixes for module index sorting. +#modindex_common_prefix = [] + +# If true, keep warnings as "system message" paragraphs in the built documents. +#keep_warnings = False + + +# -- Options for HTML output ---------------------------------------------- + +# The theme to use for HTML and HTML Help pages. See the documentation for +# a list of builtin themes. +html_theme = 'default' + +# Theme options are theme-specific and customize the look and feel of a theme +# further. For a list of options available for each theme, see the +# documentation. +#html_theme_options = {} + +# Add any paths that contain custom themes here, relative to this directory. +#html_theme_path = [] + +# The name for this set of Sphinx documents. If None, it defaults to +# " v documentation". +#html_title = None + +# A shorter title for the navigation bar. Default is the same as html_title. +#html_short_title = None + +# The name of an image file (relative to this directory) to place at the top +# of the sidebar. +html_logo = '../figs/mVMC.png' + +# The name of an image file (within the static path) to use as favicon of the +# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 +# pixels large. +#html_favicon = None + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +html_static_path = ['_static'] + +# Add any extra paths that contain custom files (such as robots.txt or +# .htaccess) here, relative to this directory. These files are copied +# directly to the root of the documentation. +#html_extra_path = [] + +# If not '', a 'Last updated on:' timestamp is inserted at every page bottom, +# using the given strftime format. +#html_last_updated_fmt = '%b %d, %Y' + +# If true, SmartyPants will be used to convert quotes and dashes to +# typographically correct entities. +#html_use_smartypants = True + +# Custom sidebar templates, maps document names to template names. +#html_sidebars = {} + +# Additional templates that should be rendered to pages, maps page names to +# template names. +#html_additional_pages = {} + +# If false, no module index is generated. +#html_domain_indices = True + +# If false, no index is generated. +#html_use_index = True + +# If true, the index is split into individual pages for each letter. +#html_split_index = False + +# If true, links to the reST sources are added to the pages. +#html_show_sourcelink = True + +# If true, "Created using Sphinx" is shown in the HTML footer. Default is True. +#html_show_sphinx = True + +# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. +#html_show_copyright = True + +# If true, an OpenSearch description file will be output, and all pages will +# contain a tag referring to it. The value of this option must be the +# base URL from which the finished HTML is served. +#html_use_opensearch = '' + +# This is the file name suffix for HTML files (e.g. ".xhtml"). +#html_file_suffix = None + +# Output file base name for HTML help builder. +htmlhelp_basename = 'testdoc' + + +# -- Options for LaTeX output --------------------------------------------- + +latex_elements = { +# The paper size ('letterpaper' or 'a4paper'). +#'papersize': 'letterpaper', + +# The font size ('10pt', '11pt' or '12pt'). +#'pointsize': '10pt', + +# Additional stuff for the LaTeX preamble. +'preamble': '\usepackage{pxjahyper}', + 'classoptions': ',dvipdfmx,openany' +} + +# Grouping the document tree into LaTeX files. List of tuples +# (source start file, target name, title, +# author, documentclass [howto, manual, or own class]). +latex_documents = [ + ('index', 'mVMC.tex', u'mVMC Documentation', + u'mVMC team', 'manual'), +] + +# The name of an image file (relative to this directory) to place at the top of +# the title page. +latex_logo = '../figs/mVMC.png' + +# For "manual" documents, if this is true, then toplevel headings are parts, +# not chapters. +#latex_use_parts = False + +# If true, show page references after internal links. +#latex_show_pagerefs = False + +# If true, show URL addresses after external links. +#latex_show_urls = False + +# Documents to append as an appendix to all manuals. +#latex_appendices = [] + +# If false, no module index is generated. +#latex_domain_indices = True + + +# -- Options for manual page output --------------------------------------- + +# One entry per manual page. List of tuples +# (source start file, name, description, authors, manual section). +man_pages = [ + ('index', 'mVMC', u'mVMC Documentation', + [u'mVMC team'], 1) +] + +# If true, show URL addresses after external links. +#man_show_urls = False + + +# -- Options for Texinfo output ------------------------------------------- + +# Grouping the document tree into Texinfo files. List of tuples +# (source start file, target name, title, author, +# dir menu entry, description, category) +texinfo_documents = [ + ('index', 'mVMC', u'mVMC Documentation', + u'mVMC team', 'mVMC', 'One line description of project.', + 'Miscellaneous'), +] + +# Documents to append as an appendix to all manuals. +#texinfo_appendices = [] + +# If false, no module index is generated. +#texinfo_domain_indices = True + +# How to display URL addresses: 'footnote', 'no', or 'inline'. +#texinfo_show_urls = 'footnote' + +# If true, do not generate a @detailmenu in the "Top" node's menu. +#texinfo_no_detailmenu = False diff --git a/doc/jp/expert.rst b/doc/jp/expert.rst new file mode 100644 index 00000000..1e07876c --- /dev/null +++ b/doc/jp/expert.rst @@ -0,0 +1,2504 @@ +.. include:: ../bib/ref.txt + +.. _HowToExpert: + +エキスパートモード入力ファイル書式 +================================== + +ここではmVMCで使用する詳細入力ファイル(\*def)のフォーマットに関して説明します。 +入力ファイルの種別は以下の6つで分類されます。 +なお、キーワードの後にある括弧内に記載されているファイル名はvmcdry.outにより作成されるファイル名を表します。 + +(1) リスト: + + **キーワード指定なし (namelist.def)**: 使用するinput + fileの名前のリストを書きます。なお、ファイル名は任意に指定することができます。 + +(2) 基本パラメータ: + + **ModPara (modpara.def)**: + 計算時に必要な基本的なパラメーター(サイトの数、電子数など)を設定します。 + + **LocSpin (locspn.def)**: 局在スピンの位置を設定します。 + +(3) ハミルトニアン: + + 電子系の表式で記載されるハミルトニアン + + .. math:: + + \begin{aligned} + {\cal H}&={\cal H}_T+{\cal H}_U+{\cal H}_V+{\cal H}_H+{\cal H}_E+{\cal H}_P+{\cal H}_I,\\ + {\cal H}_T&={-}\sum_{i, j}\sum_{\sigma_1, \sigma2}t_{ij\sigma_1\sigma_2} c_{i\sigma_1}^{\dagger}c_{j\sigma_2},\\ + {\cal H}_U&=\sum_{i} U_i n_ {i \uparrow}n_{i \downarrow},\\ + {\cal H}_V&=\sum_{i,j} V_{ij}n_ {i}n_{j},\\ + {\cal H}_H&={-}\sum_{i,j}J_{ij}^{\rm Hund} (n_{i\uparrow}n_{j\uparrow}+n_{i\downarrow}n_{j\downarrow}),\\ + {\cal H}_E&=\sum_{i,j}J_{ij}^{\rm Ex} (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow}+c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow}),\\ + {\cal H}_P&=\sum_{i,j}J_{ij}^{\rm Pair} c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{i \downarrow}^{\dagger}c_{j \downarrow},\\ + {\cal H}_I&=\sum_{i,j,k,l}\sum_{\sigma_1,\sigma_2, \sigma_3, \sigma_4} + I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}, + \end{aligned} + + + について設定します。ここで、 :math:`n_{i \sigma}=c_{i\sigma}^{\dagger}c_{i\sigma}` は + スピン :math:`\sigma` を持つサイト :math:`i` の電子密度演算子を、 + :math:`n_i=n_{i\uparrow}+n_{i\downarrow}` はサイト :math:`i` の電子密度演算子を + それぞれ表します。 + 各ハミルトニアンのパラメータは以下のファイルで指定します。 + + **Trans (trans.def)**: + :math:`{\cal H}_T` 内の :math:`t_{ij\sigma_1\sigma_2}` を指定します。 + + **CoulombIntra (coulombintra.def)**: + :math:`{\cal H}_U` 内の :math:`U_i` を指定します。 + + **CoulombInter (coulombinter.def)**: + :math:`{\cal H}_V` 内の :math:`V_{ij}` を指定します。 + + **Hund (hund.def)**: + :math:`{\cal H}_H` 内の :math:`J_{ij}^{\rm Hund}` を指定します。 + + **Exchange (exchange.def)**: + :math:`{\cal H}_E` 内の :math:`J_{ij}^{\rm Ex}` を指定します。 + + **PairHop**: + :math:`{\cal H}_P` 内の :math:`J_{ij}^{\rm Pair}` を指定します。 + + **InterAll**: + :math:`{\cal H}_I` 内の :math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}` を指定します。 + +(4) 最適化対象変分パラメータ: + + 最適化する変分パラメータを指定します。変分波動関数は + + .. math:: + + \begin{aligned} + |\psi \rangle &= {\cal P}_G{\cal P}_J{\cal P}_{d-h}^{(2)}{\cal P}_{d-h}^{(4)}{\cal L}^S{\cal L}^K{\cal L}^P |\phi_{\rm pair} \rangle,\\ + {\cal P}_G&=\exp\left[ \sum_i g_i n_{i\uparrow} n_{i\downarrow} \right],\\ + {\cal P}_J&=\exp\left[\frac{1}{2} \sum_{i\neq j} v_{ij} (n_i-1)(n_j-1)\right],\\ + {\cal P}_{d-h}^{(2)}&= \exp \left[ \sum_t \sum_{n=0}^2 (\alpha_{2nt}^d \sum_{i}\xi_{i2nt}^d+\alpha_{2nt}^h \sum_{i}\xi_{i2nt}^h)\right],\\ + {\cal P}_{d-h}^{(4)}&= \exp \left[ \sum_t \sum_{n=0}^4 (\alpha_{4nt}^d \sum_{i}\xi_{i4nt}^d+\alpha_{4nt}^h \sum_{i}\xi_{i4nt}^h)\right],\\ + {\cal L}_S&=\frac{2S+1}{8 \pi^2}\int d\Omega P_s(\cos \beta) \hat{R}(\Omega),\\ + {\cal L}_K&=\frac{1}{N_s}\sum_{{\boldsymbol R}}e^{i {\boldsymbol K} \cdot{\boldsymbol R} } \hat{T}_{\boldsymbol R},\\ + {\cal L}_P&=\sum_{\alpha}p_{\alpha} \hat{G}_{\alpha}, + \end{aligned} + + で与えられます。ここで、 + :math:`\Omega=(\alpha, \beta, \gamma)` はオイラー角、 + :math:`\hat{R}(\Omega)` は回転演算子、 + :math:`P_S(x)` は :math:`S` 次のルジャンドル多項式、 + :math:`{\boldsymbol K}` は全運動量、 + :math:`\hat{T}_{\boldsymbol R}` は並進ベクトル + :math:`{\boldsymbol R}` に対応する並進演算子、 + :math:`\hat{G}_{\alpha}` は格子の点群演算子、 + :math:`p_\alpha` はパリティをそれぞれ表します。 + ダブロン・ホロン相関因子に関する詳細は文献 [Tahara2008_ ]の説明を参照してください。 + また、一体部分は実空間のペア関数 + + .. math:: + + |\phi_{\rm pair} \rangle = + \left[\sum_{i, j=1}^{N_s} \sum_{\sigma_1, \sigma_2}f_{i\sigma_1j\sigma_2} + c_{i\sigma_1}^{\dagger}c_{j\sigma_2}^{\dagger} \right]^{N/2}|0 \rangle, + + を用いた波動関数で表されます。ここで :math:`N` は全電子数、 + :math:`N_s` は全サイト数です。 + 最適化する変分パラメータは以下のファイルを用いて指定します + ( :math:`{\cal L}_S` は **ModPara** ファイルでパラメータの指定をします)。 + + **Gutzwiller (gutzwilleridx.def)**: + :math:`{\cal P}_G` のうち、最適化の対象とする変分パラメータ :math:`g_i` を指定します。 + + **Jastrow (jastrowidx.def)**: + :math:`{\cal P}_J` のうち、最適化の対象とする変分パラメータ :math:`v_{ij}` を指定します。 + + **DH2**: + :math:`{\cal P}_{d-h}^{(2)}` で表される2サイトのダブロン・ホロン相関因子を指定します。 + + **DH4**: + :math:`{\cal P}_{d-h}^{(4)}` で表される4サイトのダブロン・ホロン相関因子を指定します。 + + **Orbital/OrbitalAntiParallel (orbitalidx.def)**: + スピンが反平行のペア軌道 :math:`|\phi_{\rm pair} \rangle` を設定します。 + + **OrbitalParallel**: + スピンが平行のペア軌道 :math:`|\phi_{\rm pair} \rangle` を設定します。 + + **OrbitalGeneral**: + ペア軌道 :math:`|\phi_{\rm pair} \rangle` を設定します。 + + **TransSym (qptransidx.def)**: + 運動量射影 :math:`{\cal L}_K` と格子対称性射影 :math:`{\cal L}_P` に関する指定を行います。 + +(5) 変分パラメータ初期値: + + 変分パラメータに関する初期値を与えます。 + キーワード指定されない場合には :math:`0` が初期値として設定されます。 + + **InGutzwiller**: + :math:`{\cal P}_G` 内の変分パラメータ :math:`g_i` の初期値を設定します。 + + **InJastrow**: + :math:`{\cal P}_J` 内の変分パラメータ :math:`v_{ij}` の初期値を設定します。 + + **InDH2**: + :math:`{\cal P}_{d-h}^{(2)}` 内の2サイトのダブロン・ホロン相関因子 + :math:`\alpha_{2nt}^{d(h)}` の初期値を設定します。 + + **InDH4**: + :math:`{\cal P}_{d-h}^{(4)}` 内の4サイトのダブロン・ホロン相関因子 + :math:`\alpha_{4nt}^{d(h)}` の初期値を設定します。 + + **InOrbital/InOrbitalAntiParallel**: + ペア軌道 :math:`|\phi_{\rm pair} \rangle` の :math:`f_{i\uparrow j\downarrow}` + に関する初期値を設定します。 + + **InOrbitalParallel**: + ペア軌道 :math:`|\phi_{\rm pair} \rangle` の :math:`f_{i\sigma j\sigma}` + に関する初期値を設定します。 + + **InOrbitalGeneral**: + ペア軌道 :math:`|\phi_{\rm pair} \rangle` の + :math:`f_{i\sigma j\sigma_1}` に関する初期値を設定します。 + +(6) 出力: + + **OneBodyG (greenone.def)**:出力する一体Green関数を指定します。 + + **TwoBodyG (greentwo.def)**:出力する二体Green関数を指定します。 + +.. _InputFileList: + +入力ファイル指定用ファイル(namelist.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +計算で使用する入力ファイル一式を指定します。ファイル形式に関しては、 +以下のようなフォーマットをしています。 + +:: + + ModPara modpara.def + LocSpin zlocspn.def + Trans ztransfer.def + InterAll zinterall.def + Orbital orbitalidx.def + OneBodyG zcisajs.def + TwoBodyG zcisajscktaltdc.def + +ファイル形式 +^^^^^^^^^^^^ + +[string01] [string02] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (固定) + + **説明 :** キーワードを指定します。 + +- [ string02 ] + + **形式 :** string型 + + **説明 :** キーワードにひも付けられるファイル名を指定します(任意)。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- キーワードを記載後、半角空白(複数可)を開けた後にファイル名を書きます。ファイル名は自由に設定できます。 + +- ファイル読込用キーワードはTable[Table:Defs]により指定します。 + +- 必ず指定しなければいけないキーワードはModPara, LocSpin, Orbital, + TransSymです。それ以外のキーワードについては、指定がない場合はデフォルト値が採用されます(変分パラメータについては最適化されず、固定する設定となります)。詳細は各ファイルの説明を参照してください。 + +- 各キーワードは順不同に記述できます。 + +- 指定したキーワード、ファイルが存在しない場合はエラー終了します。 + +- :math:`\#` で始まる行は読み飛ばされます。 + +======================== ======================================================================= + Keywords 対応するファイルの概要 +======================== ======================================================================= + ModPara :math:`^*` 計算用のパラメータを指定します。 + LocSpin :math:`^*` 局在・遍歴スピンを指定します。 + Trans 一般的な一体相互作用を指定します。 + InterAll 一般的な二体相互作用を指定します。 + CoulombIntra 内部クーロン相互作用を指定します。 + CoulombInter サイト間クーロン相互作用を指定します。 + Hund フント結合を指定します。 + PairHop ペアホッピング相互作用を指定します。 + Exchange 交換相互作用を指定します。 + Gutzwiller 最適化するGutzwiller因子を設定します。 + Jastrow 最適化する電荷Jastrow因子を指定します。 + DH2 最適化する2サイトダブロン・ホロン相関因子を指定します。 + DH4 最適化する4サイトダブロン・ホロン相関因子を指定します。 + Orbital :math:`^*` 反平行のスピンを持つペア軌道因子を指定します。 + OrbitalAntiParallel 反平行のスピンを持つペア軌道因子を指定します。 + OrbitalParallel 平行のスピンを持つペア軌道因子を指定します。 + OrbitalGeneral ペア軌道因子を指定します。 + TransSym :math:`^*` 並進・格子対称演算子を設定します。 + InGutzwiller Gutzwiller因子の初期値を設定します。 + InJastrow 電荷Jastrow因子の初期値を設定します。 + InDH2 2サイトダブロン・ホロン相関因子の初期値を設定します。 + InDH4 4サイトダブロン・ホロン相関因子の初期値を設定します。 + InOrbital ペア軌道因子 :math:`f_{i\uparrow j\downarrow}` の初期値を設定します。 + InOrbitalAntiParallel ペア軌道因子 :math:`f_{i\uparrow j\downarrow}` の初期値を設定します。 + InOrbitalParallel ペア軌道因子 :math:`f_{i\sigma j\sigma}` の初期値を設定します。 + InOrbitalGeneral ペア軌道因子 :math:`f_{i\sigma j\sigma'}` の初期値を設定します。 + OneBodyG 出力する一体グリーン関数を指定します。 + TwoBodyG 出力する二体グリーン関数を指定します。 +======================== ======================================================================= + +ModParaファイル (modpara.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +| 計算で使用するパラメータを指定します。以下のようなフォーマットをしています。 + +:: + + -------------------- + Model_Parameters + -------------------- + VMC_Cal_Parameters + -------------------- + CDataFileHead zvo + CParaFileHead zqp + -------------------- + NVMCCalMode 0 + NLanczosMode 0 + -------------------- + NDataIdxStart 1 + NDataQtySmp 1 + -------------------- + Nsite 16 + Nelectron 8 + NSPGaussLeg 1 + NSPStot 0 + NMPTrans 1 + NSROptItrStep 1200 + NSROptItrSmp 100 + DSROptRedCut 0.001 + DSROptStaDel 0.02 + DSROptStepDt 0.02 + NVMCWarmUp 10 + NVMCInterval 1 + NVMCSample 1000 + NExUpdatePath 0 + RndSeed 11272 + NSplitSize 1 + NStore 1 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1 - 5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行: [string01] [string02] + +- 7行: [string03] [string04] + +- 8行: ヘッダ(何が書かれても問題ありません) + +- 9行以降: [string05] [int01] (もしくは[double01]) + +各項目の対応関係は以下の通りです。 + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + アウトプットファイルのヘッダを表すためのキーワード。何を指定しても問題ありません。 + +- [ string02 ] + + **形式 :** string型 (空白不可) + + **説明 :** + アウトプットファイルのヘッダ。例えば、一体のGreen関数の出力ファイル名が **xxx\_cisajs.dat** として出力されます(xxxに指定した文字が記載)。 + +- [ string03 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 最適化された変分パラメータの出力ファイル名のヘッダを表すためのキーワード。何を指定しても問題ありません。 + +- [ string04 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 最適化された変分パラメータの出力ファイル名のヘッダ。最適化された変分パラメータが **xxx\_opt.dat** ファイルとして出力されます(xxxに指定した文字が記載)。 + +- [ string05 ] + + **形式 :** string型 (固定) + + **説明 :** キーワードの指定を行います。 + +- [ int01 ] ([ double01 ] ) + + **形式 :** int (double)型 (空白不可) + + **説明 :** キーワードでひも付けられるパラメータを指定します。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 9行目以降ではキーワードを記載後、半角空白(複数可)を開けた後に整数値を書きます。 + +- 9行目以降では“-”で始まる行は読み込まれません。 + + + +キーワード +^^^^^^^^^^ + +- ``NVMCCalMode`` + + **形式 :** int型 (デフォルト値 = 0) + + **説明 :** [0] 変分パラメータの最適化、[1] 1 体・2 + 体のグリーン関数の計算。 + +- ``NLanczosMode`` + + **形式 :** int型 (デフォルト値 = 0) + + **説明 :** [0] 何もしない、[1] Single Lanczos Step + でエネルギーまで計算、[2] Single Lanczos Step でエネルギー, 1 体・2 + 体のグリーン関数まで計算(条件: 1, 2 は ``NVMCCalMode`` = + 1のみ使用可能。) + +- ``NDataIdxStart`` + + **形式 :** int型 (デフォルト値 = 0) + + **説明 :** 出力ファイルの付加番号。 ``NVMCCalMode`` = 0 + の場合は ``NDataIdxStart`` が出力され、 ``NVMCCalMode`` = 1 + の場合は、 ``NDataIdxStart`` から連番で ``NDataQtySmp`` 個のファイルを出力します。 + +- ``NDataQtySmp`` + + **形式 :** int型 (デフォルト値 = 1) + + **説明 :** 出力ファイルのセット数。 ``NVMCCalMode`` = 1 + の場合に使用します。 + +- ``Nsite`` + + **形式 :** int型 (1以上、必須) + + **説明 :** サイト数を指定する整数。 + +- ``Nelectron`` + + **形式 :** int型 (1以上、必須) + + **説明 :** 電子のペア数(電子数は2 ``Nelectron`` で与えられる)。 + +- ``NCond`` + + **形式 :** int型 (0以上) + + **説明 :** 伝導電子の数。 + +- ``2Sz`` + + **形式 :** int型 + + **説明 :** 2 :math:`S_z` の値。電子がペアを組むため, + 2 :math:`S_z` は偶数で指定する必要がある。 + +- ``NSPGaussLeg`` + + **形式 :** int型 (1以上、デフォルト値 = 8) + + **説明 :** + スピン量子数射影の :math:`\beta` 積分( :math:`S^y` 回転)のGauss-Legendre求積法の分点数。 + +- ``NSPStot`` + + **形式 :** int型 (0以上、デフォルト値 = 0) + + **説明 :** スピン量子数。 + +- ``NMPTrans`` + + **形式 :** int型 (デフォルト値 = 1) + + **説明 :** + ``NMPTrans`` の絶対値で並進・格子対称性の量子数射影の個数を指定する。負の場合は反周期境界条件を与える。 + TransSymファイルで指定した重みで上から ``NMPTrans`` 個まで使用する。射影を行わない場合は1に設定する必要があります。 + +- ``NSROptItrStep`` + + **形式 :** int型 (1以上、デフォルト値 = 1000) + + **説明 :** SR + 法で最適化する場合の全ステップ数。 ``NVMCCalMode`` =0の場合のみ使用されます。 + +- ``NSROptItrSmp`` + + **形式 :** int型 (1以上数、デフォルト値 = ``NSROptItrStep``/10) + + **説明 :** + ``NSROptItrStep`` ステップ中、最後の ``NSROptItrSmp`` ステップでの各変分パラメータの平均値を最適値とする。 ``NVMCCalMode`` =0の場合のみ使用されます。 + +- ``DSROptRedCut`` + + **形式 :** double型 (デフォルト値 = 0.001) + + **説明 :** SR + 法安定化因子。手法論文[Tahara2008_ ]の :math:`\varepsilon_{\rm wf}` に対応。 + +- ``DSROptStaDel`` + + **形式 :** double型 (デフォルト値 = 0.02) + + **説明 :** SR + 法安定化因子。手法論文[Tahara2008_ ]の :math:`\varepsilon` に対応。 + +- ``DSROptStepDt`` + + **形式 :** double型 + + **説明 :** + SR法で使用する刻み幅。手法論文[Tahara2008_ ]の :math:`\Delta t` に対応。 + +- ``NSROptCGMaxIter`` + + **形式 :** int型 (デフォルト値 = 0) + + **説明 :** SR-CG法での、CG法の繰り返し回数の上限。 + 0以下を指定した場合、最大で :math:`S` + 行列のサイズの数だけ実行するようになります。 ``NSRCG``!=0 + の場合のみ使用されます。 + +- ``DSROptCGTol`` + + **形式 :** double型 (デフォルト値 = 1.0e-10) + + **説明 :** + SR-CG法での、CG法の収束判定条件。残差ベクトルの要素の自乗平均平方根がこの値以下になったらCG + 法を終了します。 ``NSRCG``!=0 の場合のみ使用されます。 + +- ``NVMCWarmUp`` + + **形式 :** int型 (1以上、デフォルト値=10) + + **説明 :** マルコフ連鎖の空回し回数。 + +- ``NVMCInterval`` + + **形式 :** int型 (1以上、デフォルト値=1) + + **説明 :** サンプル間のステップ間隔。ローカル更新を ``Nsite`` × + ``NVMCInterval`` 回行います。 + +- ``NVMCSample`` + + **形式 :** int型 (1以上、デフォルト値=1000) + + **説明 :** 期待値計算に使用するサンプル数。 + +- ``NExUpdatePath`` + + **形式 :** int型 (0以上) + + **説明 :** 電子系でローカル更新で2電子交換を[0] 認めない、[1] + 認めるの設定をします。スピン系の場合には2に設定する必要があります。 + +- ``RndSeed`` + + **形式 :** int型 + + **説明 :** 乱数の初期seed。MPI 並列では各計算機に ``RndSeed`` +my + rank+1 で初期seed が与えられます。 + +- ``NSplitSize`` + + **形式 :** int型 (1以上、デフォルト値=1) + + **説明 :** MPI内部並列を行う場合の並列数。 + +- ``NStore`` + + **形式 :** int型 (0もしくは1、デフォルト値=1) + + **説明 :** + 期待値 :math:`\langle O_k O_l \rangle` を計算するとき行列-行列積にして高速化するオプション + (1で機能On、モンテカルロサンプリング数に応じてメモリの消費が増大します [3]_)。 + +- ``NSRCG`` + + **形式 :** int型 (0もしくは1、デフォルト値=0) + + **説明 :** SR法で連立一次方程式 :math:`Sx=g` + を解くときに、 :math:`S` + を陽に構築せずに解くことでメモリを削減する [4]_ オプション[NeuscammanUmrigarChan_ ](1で機能On, + ``NStore`` は1に固定されます)。 + +LocSpin指定ファイル(locspn.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +局在スピンを指定します。以下のようなフォーマットをしています。 + +:: + + ================================ + NlocalSpin 6 + ================================ + ========i_0LocSpn_1IteElc ====== + ================================ + 0 1 + 1 0 + 2 1 + 3 0 + 4 1 + 5 0 + 6 1 + 7 0 + 8 1 + 9 0 + 10 1 + 11 0 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: [int02] [int03] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** 局在スピンの総数を示すキーワード(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 局在スピンの総数を指定する整数。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int03 ] + + **形式 :** int型 (空白不可) + + | **説明 :** 遍歴電子か局在スピンかを指定する整数(0: 遍歴電子, 1: + 局在スピン)。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と [ int03 ] で指定される局在電子数の総数が異なる場合はエラー終了します。 + +- [ int02 ] の総数が全サイト数と異なる場合はエラー終了します。 + +- [ int02 ] が全サイト数以上もしくは負の値をとる場合はエラー終了します。 + +Trans指定ファイル(trans.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +一般的な一体相互作用をハミルトニアンに付け加え、ハミルトニアン中の相互作用パラメータ :math:`t_{ij\sigma_1\sigma2}` を指定します。付け加える項は以下で与えられます。 + +.. math:: + + \begin{aligned} + {\cal H}_T =-\sum_{ij\sigma_1\sigma2} t_{ij\sigma_1\sigma2}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\end{aligned} + +以下にファイル例を記載します。 + +:: + + ======================== + NTransfer 24 + ======================== + ========i_j_s_tijs====== + ======================== + 0 0 2 0 1.000000 0.000000 + 2 0 0 0 1.000000 0.000000 + 0 1 2 1 1.000000 0.000000 + 2 1 0 1 1.000000 0.000000 + 2 0 4 0 1.000000 0.000000 + 4 0 2 0 1.000000 0.000000 + 2 1 4 1 1.000000 0.000000 + 4 1 2 1 1.000000 0.000000 + 4 0 6 0 1.000000 0.000000 + 6 0 4 0 1.000000 0.000000 + 4 1 6 1 1.000000 0.000000 + 6 1 4 1 1.000000 0.000000 + 6 0 8 0 1.000000 0.000000 + 8 0 6 0 1.000000 0.000000 + … + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: [int02] [int03] [int04] [int05] [double01] [double02] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** 定義するパラメータの総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 定義するパラメータの総数を指定します。 + +- [ int02 ], [ int04 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int03 ], [ int05 ] + + **形式 :** int型 (空白不可) + + | **説明 :** スピンを指定する整数。 + | 0: アップスピン + | 1: ダウンスピン + | を選択することが出来ます。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** :math:`t_{ij\sigma_1\sigma_2}` の実部を指定します。 + +- [ double02 ] + + **形式 :** double型 (空白不可) + + **説明 :** :math:`t_{ij\sigma_1\sigma_2}` の虚部を指定します。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- 空行は許されません。 + +- [ int01 ] と定義されているTrasferの総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int05 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +- Hamiltonianがエルミートという制限から :math:`t_{ij\sigma_1\sigma_2}=t_{ji\sigma_2\sigma_1}^{\dagger}` の関係を満たす必要があります。 + +InterAll指定ファイル +~~~~~~~~~~~~~~~~~~~~ + +一般的な二体相互作用をハミルトニアンに付け加え、ハミルトニアン中の相互作用パラメータを指定します。 +付け加える項は以下で与えられます。 + +.. math:: + + {\cal H}_{I}=\sum_{i,j,k,l}\sum_{\sigma_1,\sigma_2, \sigma_3, \sigma_4} + I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4} + +以下にファイル例を記載します。 + +:: + + ====================== + NInterAll 36 + ====================== + ========zInterAll===== + ====================== + 0 0 0 1 1 1 1 0 0.50 0.0 + 0 1 0 0 1 0 1 1 0.50 0.0 + 0 0 0 0 1 0 1 0 0.25 0.0 + 0 0 0 0 1 1 1 1 -0.25 0.0 + 0 1 0 1 1 0 1 0 -0.25 0.0 + 0 1 0 1 1 1 1 1 0.25 0.0 + 2 0 2 1 3 1 3 0 0.50 0.0 + 2 1 2 0 3 0 3 1 0.50 0.0 + 2 0 2 0 3 0 3 0 0.25 0.0 + 2 0 2 0 3 1 3 1 -0.25 0.0 + 2 1 2 1 3 0 3 0 -0.25 0.0 + 2 1 2 1 3 1 3 1 0.25 0.0 + 4 0 4 1 5 1 5 0 0.50 0.0 + 4 1 4 0 5 0 5 1 0.50 0.0 + 4 0 4 0 5 0 5 0 0.25 0.0 + 4 0 4 0 5 1 5 1 -0.25 0.0 + 4 1 4 1 5 0 5 0 -0.25 0.0 + 4 1 4 1 5 1 5 1 0.25 0.0 + … + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: + [int02] [int03] [int04] [int05] [int06] [int07] [int08] [int09] [double01] [double02] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** 二体相互作用の総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 二体相互作用の総数を指定します。 + +- [ int02 ], [ int04 ], + [ int06 ], [ int08 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int03 ], [ int05 ], + [ int07 ], [ int09 ] + + **形式 :** int型 (空白不可) + + **説明 :** スピンを指定する整数。 + + 0: アップスピン + + 1: ダウンスピン + + を選択することが出来ます。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** + :math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}` の実部を指定します。 + +- [ double02 ] + + **形式 :** double型 (空白不可) + + **説明 :** + :math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}` の虚部を指定します。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- ハミルトニアンがエルミートという制限から :math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}=I_{lkji\sigma_4\sigma_3\sigma_2\sigma_1}^{\dagger}` の関係を満たす必要があります。 + +- [ int01 ] と定義されているInterAllの総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int09 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +CoulombIntra指定ファイル(coulombintra.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +オンサイトクーロン相互作用をハミルトニアンに付け加えます。付け加える項は以下で与えられます。 + +.. math:: + + {\cal H}_U =\sum_{i}U_i n_ {i \uparrow}n_{i \downarrow} + +以下にファイル例を記載します。 + +:: + + ====================== + NCoulombIntra 6 + ====================== + ========i_0LocSpn_1IteElc ====== + ====================== + 0 4.000000 + 1 4.000000 + 2 4.000000 + 3 4.000000 + 4 4.000000 + 5 4.000000 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: [int02] [double01] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + オンサイトクーロン相互作用の総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** オンサイトクーロン相互作用の総数を指定します。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** :math:`U_i` を指定します。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されているオンサイトクーロン相互作用の総数が異なる場合はエラー終了します。 + +- [ int02 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +CoulombInter指定ファイル(coulombiter.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +サイト間クーロン相互作用をハミルトニアンに付け加えます。付け加える項は以下で与えられます。 + +.. math:: + + {\cal H}_V = \sum_{i,j}V_{ij} n_ {i}n_{j} + +以下にファイル例を記載します。 + +:: + + ====================== + NCoulombInter 12 + ====================== + ========CoulombInter ====== + ====================== + 0 1 1.500000000000000 + 0 3 1.500000000000000 + 1 2 1.500000000000000 + 1 4 1.500000000000000 + 2 0 1.500000000000000 + 2 5 1.500000000000000 + 3 4 1.500000000000000 + 3 0 1.500000000000000 + 4 5 1.500000000000000 + 4 1 1.500000000000000 + 5 3 1.500000000000000 + 5 2 1.500000000000000 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: [int02] [int03] [double01] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + サイト間クーロン相互作用の総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** サイト間クーロン相互作用の総数を指定します。 + +- [ int02 ], [ int03 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** :math:`V_{ij}` を指定します。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されているオフサイトクーロン相互作用の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int03 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +Hund指定ファイル(hund.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Hundカップリングをハミルトニアンに付け加えます。付け加える項は以下で与えられます。 + +.. math:: + + {\cal H}_H =-\sum_{i,j}J_{ij}^{\rm Hund} (n_{i\uparrow}n_{j\uparrow}+n_{i\downarrow}n_{j\downarrow}) + +以下にファイル例を記載します。 + +:: + + ====================== + NHund 6 + ====================== + ========Hund ====== + ====================== + 0 1 -0.250000 + 1 2 -0.250000 + 2 3 -0.250000 + 3 4 -0.250000 + 4 5 -0.250000 + 5 0 -0.250000 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: [int02] [int03] [double01] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** Hundカップリングの総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** Hundカップリングの総数を指定します。 + +- [ int02 ], [ int03 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** :math:`J_{ij}^{\rm Hund}` を指定します。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されているHundカップリングの総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int03 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +PairHop指定ファイル +~~~~~~~~~~~~~~~~~~~ + +PairHopカップリングをハミルトニアンに付け加えます。付け加える項は以下で与えられます。 + +.. math:: + + {\cal H}_P=\sum_{i,j}J_{ij}^{\rm Pair} + (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{i \downarrow}^{\dagger}c_{j \downarrow} + +c_{j \downarrow}^{\dagger}c_{i \downarrow}c_ {j \uparrow}^{\dagger}c_{i\uparrow}) + +以下にファイル例を記載します。 + +:: + + ====================== + NPairhop 6 + ====================== + ========Pairhop ====== + ====================== + 0 1 0.50000 + 1 2 0.50000 + 2 3 0.50000 + 3 4 0.50000 + 4 5 0.50000 + 5 0 0.50000 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: [int02] [int03] [double01] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + PairHopカップリングの総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** PairHopカップリングの総数を指定します。 + +- [ int02 ], [ int03 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** :math:`J_{ij}^{\rm Pair}` を指定します。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されているPairHopカップリングの総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int03 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +Exchange指定ファイル (exchange.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Exchangeカップリングをハミルトニアンに付け加えます。 電子系の場合には + +.. math:: + + {\cal H}_E =\sum_{i,j}J_{ij}^{\rm Ex} + (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow} + +c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow}) + +が付け加えられ、スピン系の場合には + +.. math:: + + {\cal H}_E =\sum_{i,j}J_{ij}^{\rm Ex} (S_i^+S_j^-+S_i^-S_j^+) + +が付け加えられます。 以下にファイル例を記載します。 + +:: + + ====================== + NExchange 6 + ====================== + ========Exchange ====== + ====================== + 0 1 0.50000 + 1 2 0.50000 + 2 3 0.50000 + 3 4 0.50000 + 4 5 0.50000 + 5 0 0.50000 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: [int02] [int03] [double01] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + Exchangeカップリングの総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** Exchangeカップリングの総数を指定します。 + +- [ int02 ], [ int03 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** :math:`J_{ij}^{\rm Ex}` を指定します。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されているExchangeカップリングの総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int03 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +Gutzwiller指定ファイル(gutzwiller.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Gutzwiller因子 + +.. math:: + + {\cal P}_G=\exp\left[ \sum_i g_i n_{i\uparrow} n_{i\downarrow} \right] + +の設定を行います。指定するパラメータはサイト番号 :math:`i` と :math:`g_i` の変分パラメータの番号です。 +以下にファイル例を記載します。 + +:: + + ====================== + NGutzwillerIdx 2 + ComplexType 0 + ====================== + ====================== + 0 0 + 1 0 + 2 0 + 3 1 + (continue...) + 12 1 + 13 0 + 14 0 + 15 0 + 0 1 + 1 0 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_s` はサイト数、 :math:`N_g` は変分パラメータの種類の数)。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3行: [string02] [int02] + +- 4-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_s`)行: [int03] [int04] + +- (6+ :math:`N_s`) - (5+ :math:`N_s` + :math:`N_g`)行：[int05] [int06] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + :math:`g_i` の変分パラメータの種類の総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** :math:`g_i` の変分パラメータの種類の総数を指定します。 + +- [ string02 ] + + **形式 :** string型 (空白不可) + + **説明 :** + :math:`g_i` の変分パラメータの型を指定するためのキーワード名を指定します(任意)。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの型を指定する整数。0が実数、1が複素数に対応します。 + +- [ int03 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int04 ] + + **形式 :** int型 (空白不可) + + **説明 :** + :math:`g_i` の変分パラメータの種類を表します。0以上[int01]未満で指定します。 + +- [ int05 ] + + **形式 :** int型 (空白不可) + + **説明 :** + :math:`g_i` の変分パラメータの種類を表します(最適化有無の設定用)。0以上[int01]未満で指定します。 + +- [ int06 ] + + **形式 :** int型 (空白不可) + + **説明 :** + [int05]で指定した :math:`g_i` の変分パラメータの最適化有無を設定します。最適化する場合は1、最適化しない場合は0とします。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている変分パラメータの種類の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int06 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +Jastrow指定ファイル(jastrow.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Jastrow因子 + +.. math:: {\cal P}_J=\exp\left[\frac{1}{2} \sum_{i\neq j} v_{ij} (n_i-1) (n_j-1)\right] + + +の設定を行います。指定するパラメータはサイト番号 :math:`i, j` と :math:`v_{ij}` の変分パラメータの番号です。以下にファイル例を記載します。 + +:: + + ====================== + NJastrowIdx 5 + ComplexType 0 + ====================== + ====================== + 0 1 0 + 0 2 1 + 0 3 0 + (continue...) + 0 1 + 1 1 + 2 1 + 3 1 + 4 1 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_s` はサイト数、 :math:`N_j` は変分パラメータの種類の数)。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3行: [string02] [int02] + +- 4-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_s\times (N_s-1)`) 行: [int03] [int04] [int05] + +- (6+ :math:`N_s\times (N_s-1)` ) - + (5+ :math:`N_s\times (N_s-1)` + :math:`N_j`)行：[int06] [int07] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + :math:`v_{ij}` の変分パラメータの種類の総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** :math:`v_{ij}` の変分パラメータの種類の総数を指定します。 + +- [ string02 ] + + **形式 :** string型 (空白不可) + + **説明 :** + :math:`v_{ij}` の変分パラメータの型を指定するためのキーワード名を指定します(任意)。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + :math:`v_{ij}` の変分パラメータの型を指定します。0が実数、1が複素数に対応します。 + +- [ int03 ], [ int04 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int05 ] + + **形式 :** int型 (空白不可) + + **説明 :** + :math:`v_{ij}` の変分パラメータの種類を表します。0以上[int01]未満で指定します。 + +- [ int06 ] + + **形式 :** int型 (空白不可) + + **説明 :** + :math:`v_{ij}` の変分パラメータの種類を表します(最適化有無の設定用)。0以上[int01]未満で指定します。 + +- [ int07 ] + + **形式 :** int型 (空白不可) + + **説明 :** + [int06]で指定した :math:`v_{ij}` の変分パラメータの最適化有無を設定します。最適化する場合は1、最適化しない場合は0とします。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている変分パラメータの種類の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int07 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +DH2指定ファイル +~~~~~~~~~~~~~~~ + +.. math:: + + {\cal P}_{d-h}^{(2)}= \exp \left[ \sum_t \sum_{n=0}^2 + (\alpha_{2nt}^d \sum_{i}\xi_{i2nt}^d+\alpha_{2nt}^h \sum_{i}\xi_{i2nt}^h)\right] + +で表される2サイトのdoublon-holon相関因子の設定を行います。 +指定するパラメータはサイト番号 :math:`i` とその周囲2サイト、 +:math:`\alpha_{2nt}^{d,h}` の変分パラメータの番号で、 +変分パラメータは各サイト毎に :math:`t` 種類設定します。 +各パラメータ、演算子に関する詳細は文献 [Tahara2008_ ]をご覧ください。 +以下にファイル例を記載します。 + +:: + + ==================================== + NDoublonHolon2siteIdx 2 + ComplexType 0 + ==================================== + ==================================== + 0 5 15 0 + 0 13 7 1 + 1 6 12 0 + 1 14 4 1 + (continue...) + 15 0 10 0 + 15 8 2 1 + 0 1 + 1 1 + 2 1 + (continue...) + 10 1 + 11 1 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_s` はサイト数、 :math:`N_{\rm dh2}` は変分パラメータの種類の数)。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3行: [string02] [int02] + +- 4-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_s\times N_{\rm dh2}`)行: + [int03] [int04] [int05] [int06] + +- (6+ :math:`N_s\times N_{\rm dh2}`) - + (5+ :math:`(N_s+6) \times N_{\rm dh2}`)行：[int07] [int08] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータのセット総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータのセット総数を指定します。 + +- [ string02 ] + + **形式 :** string型 (空白不可) + + **説明 + :** 変分パラメータの型を指定するためのキーワード名を指定します(任意)。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの型を指定します。0が実数、1が複素数に対応します。 + +- [ int03 ], [ int04 ], + [ int05 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int06 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの種類を表します。0以上[int01]未満で指定します。 + +- [ int07 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータの種類を表します(最適化有無の設定用)。値は + + - | :math:`n`: 周囲のdoublon(holon)数 (0, 1, 2) + + - | :math:`s`: 中心がdoublonの場合 :math:`0`, + 中心がholonの場合 :math:`1` + + - :math:`t`: 変分パラメータのセット番号(0, :math:`\cdots` [int1]-1) + + として、 :math:`(2n+s)\times` [int01] :math:`+t` を設定します。 + +- [ int08 ] + + **形式 :** int型 (空白不可) + + **説明 :** + [int07]で指定した変分パラメータの最適化有無を設定します。最適化する場合は1、最適化しない場合は0とします。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている変分パラメータの種類の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int08 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +DH4指定ファイル +~~~~~~~~~~~~~~~ + +.. math:: + + {\cal P}_{d-h}^{(4)}= \exp \left[ \sum_t \sum_{n=0}^4 + (\alpha_{4nt}^d \sum_{i}\xi_{i4nt}^d+\alpha_{4nt}^h \sum_{i}\xi_{i4nt}^h)\right] + +で表される4サイトのdoublon-holon相関因子の設定を行います。 +指定するパラメータはサイト番号 :math:`i` とその周囲4サイト、 +:math:`\alpha_{4nt}^{d,h}` の変分パラメータの番号で、 +変分パラメータは各サイト毎に :math:`t` 種類設定します。 +各パラメータ、演算子に関する詳細は文献[Tahara2008_ ]をご覧ください。 +以下にファイル例を記載します。 + +:: + + ==================================== + NDoublonHolon4siteIdx 1 + ComplexType 0 + ==================================== + ==================================== + 0 1 3 4 12 0 + 1 2 0 5 13 0 + 2 3 1 6 14 0 + 3 0 2 7 15 0 + (continue...) + 14 15 13 2 10 0 + 15 12 14 3 11 0 + 0 1 + 1 1 + (continue...) + 8 1 + 9 1 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_s` はサイト数、 :math:`N_{\rm dh4}` は変分パラメータの種類の数)。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3行: [string02] [int02] + +- 4-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_s\times N_{\rm dh4}`)行: + [int03] [int04] [int05] [int06] [int07] [int08] + +- (6+ :math:`N_s\times N_{\rm dh4}`) - + (5+ :math:`(N_s+10) \times N_{\rm dh4}`)行：[int09] [int10] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータのセット総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータのセット総数を指定します。 + +- [ string02 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータの型を指定するためのキーワード名を指定します(任意)。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの型を指定します。0が実数、1が複素数に対応します。 + +- [ int03 ], [ int04 ], + [ int05 ], [ int06 ], + [ int07 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int08 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの種類を表します。0以上[int01]未満で指定します。 + +- [ int09 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータの種類を表します(最適化有無の設定用)。値は + + - | :math:`n`: 周囲のdoublon(holon)数 (0, 1, 2, 3, 4) + + - | :math:`s`: 中心がdoublonの場合 :math:`0`, + 中心がholonの場合 :math:`1` + + - :math:`t`: 変分パラメータのセット番号(0, :math:`\cdots` [int1]-1) + + として、 :math:`(2n+s)\times` [int01] :math:`[2]+t` を設定します。 + +- [ int10 ] + + **形式 :** int型 (空白不可) + + **説明 :** + [int09]で指定した変分パラメータの最適化有無を設定します。最適化する場合は1、最適化しない場合は0とします。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている変分パラメータの種類の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int10 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +Orbital/OrbitalAntiParallel指定ファイル(orbitalidx.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. math:: |\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} f_{ij}c_{i\uparrow}^{\dagger}c_{j\downarrow}^{\dagger} \right]^{N/2}|0 \rangle + +で表されるペア軌道の設定を行います。指定するパラメータはサイト番号 :math:`i, j` と変分パラメータの種類を設定します。以下にファイル例を記載します。 + +:: + + ==================================== + NOrbitalIdx 64 + ComplexType 0 + ==================================== + ==================================== + 0 0 0 + 0 1 1 + 0 2 2 + 0 3 3 + (continue...) + 15 9 62 + 15 10 63 + 0 1 + 1 1 + (continue...) + 62 1 + 63 1 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_s` はサイト数、 :math:`N_{\rm o}` は変分パラメータの種類の数)。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3行: [string02] [int02] + +- 4-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_s^2`)行: [int03] [int04] [int05] [int06] + +- (6+ :math:`N_s^2`) - (5+ :math:`N_s^2+N_{\rm o}`)行：[int07] [int08] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータのセット総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータのセット総数を指定します。 + +- [ string02 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータの型を指定するためのキーワード名を指定します(任意)。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの型を指定します。0が実数、1が複素数に対応します。 + +- [ int03 ], [ int04 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int05 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの種類を表します。0以上[int01]未満で指定します。 + +- [ int06 ] + + **形式 :** int型 + + **説明 :** + 反周期境界条件モードがON( ``ModPara`` ファイルで ``NMPTrans`` が負の場合に有効)の場合、変分パラメータ :math:`f_{ij}` の番号の他に符号を反転するか否かを直接指定する。 [ int06 ] = :math:`\pm1` により符号を指定する。反周期境界条件モードがOFFの場合は省略可能。 + +- [ int07 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの種類を表します(最適化有無の設定用)。0以上[int01]未満で指定します。 + +- [ int08 ] + + **形式 :** int型 (空白不可) + + **説明 :** + [int06]で指定した変分パラメータの最適化有無を設定します。最適化する場合は1、最適化しない場合は0とします。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている変分パラメータの種類の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int08 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +OrbitalParallel指定ファイル +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. math:: |\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} f_{i\sigma j\sigma}c_{i\sigma}^{\dagger}c_{j\sigma}^{\dagger} \right]^{N/2}|0 \rangle + +で表されるペア軌道の設定を行います。指定するパラメータはサイト番号 :math:`i, j` と変分パラメータの種類を設定します。以下にファイル例を記載します。 + +:: + + ==================================== + NOrbitalIdx 120 + ComplexType 0 + ==================================== + ==================================== + 0 1 0 + 0 2 1 + 0 3 2 + (continue...) + 15 13 118 + 15 14 119 + 0 1 + 1 1 + (continue...) + 118 1 + 119 1 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_s` はサイト数、 :math:`N_{\rm o}` は変分パラメータの種類の数)。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3行: [string02] [int02] + +- 4-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_s*(N_s-1)/2`)行: [int03] [int04] [int05] [int06] + +- (6+ :math:`N_s*(N_s-1)/2`) - + (5+ :math:`N_s*(N_s-1)/2+N_{\rm o}`)行：[int07] [int08] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータのセット総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータのセット総数を指定します。 + +- [ string02 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータの型を指定するためのキーワード名を指定します(任意)。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの型を指定します。0が実数、1が複素数に対応します。 + +- [ int03 ], [ int04 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int05 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの種類を表します。0以上[int01]未満で指定します。 + +- [ int06 ] + + **形式 :** int型 + + **説明 :** + 反周期境界条件モードがON( ``ModPara`` ファイルで ``NMPTrans`` が負の場合に有効)の場合、変分パラメータ :math:`f_{ij}` の番号の他に符号を反転するか否かを直接指定する。 [ int06 ] = :math:`\pm1` により符号を指定する。反周期境界条件モードがOFFの場合は省略可能。 + +- [ int07 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの種類を表します(最適化有無の設定用)。0以上[int01]未満で指定します。 + +- [ int08 ] + + **形式 :** int型 (空白不可) + + **説明 :** + [int06]で指定した変分パラメータの最適化有無を設定します。最適化する場合は1、最適化しない場合は0とします。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている変分パラメータの種類の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int08 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +OrbitalGeneral指定ファイル +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. math:: |\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} \sum_{\sigma_1, \sigma_2}f_{i\sigma_1 j \sigma_2}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}^{\dagger} \right]^{N/2}|0 \rangle + +で表されるペア軌道の設定を行います。指定するパラメータはサイト番号 :math:`i, j`, +スピン :math:`\sigma_1, \sigma_2` と変分パラメータの種類を設定します。 :math:`i+\sigma_1 N_s < j+\sigma_2 N_s` (:math:`\sigma=0 ,1`)を満たすように指定する必要があります。以下にファイル例を記載します。 + +:: + + ==================================== + NOrbitalIdx 255 + ComplexType 0 + ==================================== + ==================================== + 0 0 0 1 0 + 0 0 1 1 1 + (continue...) + 14 0 15 1 253 + 15 0 15 1 254 + 0 1 + 1 1 + (continue...) + 253 1 + 254 1 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_s` はサイト数、 :math:`N_{\rm o}` は変分パラメータの種類の数)。 +変分パラメータの総数 :math:`N_p` は :math:`i+\sigma_1 N_s < j+\sigma_2 N_s` (:math:`\sigma=0 ,1`)を満たすペアの総数に対応し、 +:math:`S_z=0` の場合は :math:`N_p=N_s^2` 、 :math:`S_z` 非保存の場合は :math:`N_p=2N_s^2-N_s` 個となります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3行: [string02] [int02] + +- 4-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_p`)行: + [int03] [int04] [int05] [int06] [int07] [int08] + +- (6+ :math:`N_p`) - (5+ :math:`N_p+N_{\rm o}`)行：[int09] [int10] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータのセット総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータのセット総数を指定します。 + +- [ string02 ] + + **形式 :** string型 (空白不可) + + **説明 :** + 変分パラメータの型を指定するためのキーワード名を指定します(任意)。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの型を指定します。0が実数、1が複素数に対応します。 + +- [ int03 ], [ int05 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int04 ], [ int06 ] + + **形式 :** int型 (空白不可) + + **説明 :** スピンを指定する整数。0が :math:`\uparrow` スピン, + 1が :math:`\downarrow` スピンに対応します。 + +- [ int07 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの種類を表します。0以上[int01]未満で指定します。 + +- [ int08 ] + + **形式 :** int型 + + **説明 :** + 反周期境界条件モードがON( ``ModPara`` ファイルで ``NMPTrans`` が負の場合に有効)の場合、変分パラメータ :math:`f_{ij}` の番号の他に符号を反転するか否かを直接指定する。 [ int08 ] = :math:`\pm1` により符号を指定する。反周期境界条件モードがOFFの場合は省略可能。 + +- [ int09 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 変分パラメータの種類を表します(最適化有無の設定用)。0以上[int01]未満で指定します。 + +- [ int10 ] + + **形式 :** int型 (空白不可) + + **説明 :** + [int06]で指定した変分パラメータの最適化有無を設定します。最適化する場合は1、最適化しない場合は0とします。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている変分パラメータの種類の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int10 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +TransSym指定ファイル(qptransidx.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +運動量射影 :math:`{\cal L}_K=\frac{1}{N_s}\sum_{{\boldsymbol R}}e^{i {\boldsymbol K} \cdot{\boldsymbol R} } \hat{T}_{\boldsymbol R}` と格子対称性射影 :math:`{\cal L}_P=\sum_{\alpha}p_{\alpha} \hat{G}_{\alpha}` について、重みとサイト番号に関する指定を行います。射影するパターンは :math:`(\alpha, {\boldsymbol R})` で指定されます。射影を行わない場合も重み1.0 +で“恒等演算”を指定してください。 以下にファイル例を記載します。 + +:: + + ==================================== + NQPTrans 4 + ==================================== + == TrIdx_TrWeight_and_TrIdx_i_xi == + ==================================== + 0 1.000000 + 1 1.000000 + 2 1.000000 + 3 1.000000 + 0 0 0 + (continue...) + 3 12 1 + 3 13 2 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_s` はサイト数、 :math:`N_{\rm TS}` は射影演算子の種類の総数)。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_{\rm TS}`)行: [int02] [double01] + +- (6+ :math:`N_{\rm TS}`) - + (5+ :math:`(N_s+1) \times N_{\rm TS}`)行：[int03] [int04] [int05] [int06] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** 射影パターンの総数に関するキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 射影パターンの総数を指定します。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 射影パターン :math:`(\alpha, {\boldsymbol R})` を指定する整数。0以上 + [ int01 ] 未満で指定します。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** + 射影パターン :math:`(\alpha, {\boldsymbol R})` の重み :math:`p_{\alpha}\cos ({\boldsymbol K}\cdot {\boldsymbol R})` を指定します。 + +- [ int03 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 射影パターン :math:`(\alpha, {\boldsymbol R})` を指定する整数。0以上 + [ int01 ] 未満で指定します。 + +- [ int04 ], [ int05 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 [ int03 ] で指定した並進・点群移動をサイト番号 [ int04 ] に作用させた場合の行き先が、サイト番号 [ int05 ] となるように設定します。 + +- [ int06 ] + + **形式 :** int型 (空白不可) + + **説明 :** + 反周期境界条件モードがON( ``ModPara`` ファイルで ``NMPTrans`` が負の場合に有効)の場合、並進演算で生成消滅演算子の符号が反転するか否かを直接指定する。 [ int06 ] = :math:`\pm1` により符号を指定する。反周期境界条件モードがOFFの場合は省略可能。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている射影パターンの総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int06 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +.. _InputParam: + +変分パラメータ初期値指定ファイル +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +各変分パラメータの初期値を設定することが可能です。 +変分パラメータの種類は :ref:`InputFileList` において +``InGutzwiller``, ``InJastrow``, ``InDH2``, ``InDH4``, ``InOrbital``, +``InOrbitalAntiParallel``, ``InOrbitalParallel``, ``InOrbitalGeneral`` +をキーワードとして指定することで区別します。なお、ファイルフォーマットは全て共通です。 +以下、 ``InJastrow`` ファイルの例を記載します。 + +:: + + ====================== + NJastrowIdx 28 + ====================== + == i_j_JastrowIdx === + ====================== + 0 -8.909963465082626488e-02 0.000000000000000000e+00 + 1 5.521681211878626955e-02 0.000000000000000000e+00 + (continue...) + 27 -9.017586139930480749e-02 0.000000000000000000e+00 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります( :math:`N_v` は変分パラメータの種類の総数)。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6 - (5+ :math:`N_v`)行: [int02] [double01] [double02] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** 変分パラメータ総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータ総数を指定します。 + +- [ int02 ] + + **形式 :** int型 (空白不可) + + **説明 :** 変分パラメータの種類を指定する整数。0以上 + [ int01 ] で指定します。 + +- [ double01 ] + + **形式 :** double型 (空白不可) + + **説明 :** 変分パラメータの初期値の実部を与えます。 + +- [ double02 ] **形式 :** double型 (空白不可) + + **説明 :** 変分パラメータの初期値の虚部を与えます。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている変分パラメータの総数が異なる場合はエラー終了します。 + +OneBodyG指定ファイル(greenone.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +計算・出力する一体グリーン関数 :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle` を指定します。以下にファイル例を記載します。 + +:: + + =============================== + NCisAjs 24 + =============================== + ======== Green functions ====== + =============================== + 0 0 0 0 + 0 1 0 1 + 1 0 1 0 + 1 1 1 1 + 2 0 2 0 + 2 1 2 1 + 3 0 3 0 + 3 1 3 1 + 4 0 4 0 + 4 1 4 1 + 5 0 5 0 + 5 1 5 1 + 6 0 6 0 + 6 1 6 1 + 7 0 7 0 + 7 1 7 1 + 8 0 8 0 + 8 1 8 1 + 9 0 9 0 + 9 1 9 1 + 10 0 10 0 + 10 1 10 1 + 11 0 11 0 + 11 1 11 1 + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: [int02] [int03] [int04] [int05] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** 一体グリーン関数成分総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 一体グリーン関数成分の総数を指定します。 + +- [ int02 ], [ int04 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int03 ], [ int05 ] + + **形式 :** int型 (空白不可) + + | **説明 :** スピンを指定する整数。 + | 0: アップスピン + | 1: ダウンスピン + | を選択することが出来ます。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている一体グリーン関数成分の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int05 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +TwoBodyG指定ファイル(greentwo.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +計算・出力する二体グリーン関数 :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle` を指定します。 +以下にファイル例を記載します。 + +:: + + ============================================= + NCisAjsCktAltDC 576 + ============================================= + ======== Green functions for Sq AND Nq ====== + ============================================= + 0 0 0 0 0 0 0 0 + 0 0 0 0 0 1 0 1 + 0 0 0 0 1 0 1 0 + 0 0 0 0 1 1 1 1 + 0 0 0 0 2 0 2 0 + 0 0 0 0 2 1 2 1 + 0 0 0 0 3 0 3 0 + 0 0 0 0 3 1 3 1 + 0 0 0 0 4 0 4 0 + 0 0 0 0 4 1 4 1 + 0 0 0 0 5 0 5 0 + 0 0 0 0 5 1 5 1 + 0 0 0 0 6 0 6 0 + 0 0 0 0 6 1 6 1 + 0 0 0 0 7 0 7 0 + 0 0 0 0 7 1 7 1 + 0 0 0 0 8 0 8 0 + 0 0 0 0 8 1 8 1 + 0 0 0 0 9 0 9 0 + 0 0 0 0 9 1 9 1 + 0 0 0 0 10 0 10 0 + 0 0 0 0 10 1 10 1 + 0 0 0 0 11 0 11 0 + 0 0 0 0 11 1 11 1 + 0 1 0 1 0 0 0 0 + … + +ファイル形式 +^^^^^^^^^^^^ + +以下のように行数に応じ異なる形式をとります。 + +- 1行: ヘッダ(何が書かれても問題ありません)。 + +- 2行: [string01] [int01] + +- 3-5行: ヘッダ(何が書かれても問題ありません)。 + +- 6行以降: + [int02] [int03] [int04] [int05] [int06] [int07] [int08] [int09] + +パラメータ +^^^^^^^^^^ + +- [ string01 ] + + **形式 :** string型 (空白不可) + + **説明 :** 二体グリーン関数成分総数のキーワード名を指定します(任意)。 + +- [ int01 ] + + **形式 :** int型 (空白不可) + + **説明 :** 二体グリーン関数成分の総数を指定します。 + +- [ int02 ], [ int04 ], + [ int06 ], [ int08 ] + + **形式 :** int型 (空白不可) + + **説明 :** + サイト番号を指定する整数。0以上 ``Nsite`` 未満で指定します。 + +- [ int03 ], [ int05 ], + [ int07 ], [ int09 ] + + **形式 :** int型 (空白不可) + + | **説明 :** スピンを指定する整数。 + | 0: アップスピン + | 1: ダウンスピン + | を選択することが出来ます。 + +使用ルール +^^^^^^^^^^ + +本ファイルを使用するにあたってのルールは以下の通りです。 + +- 行数固定で読み込みを行う為、ヘッダの省略はできません。 + +- [ int01 ] と定義されている二体グリーン関数成分の総数が異なる場合はエラー終了します。 + +- [ int02 ]-[ int09 ] を指定する際、範囲外の整数を指定した場合はエラー終了します。 + +.. [3] + 使用メモリ量が、 :math:`O(N_\text{p}^2)` から + :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})` になります。 + +.. [4] + 使用メモリ量は、 :math:`O(N_\text{p}) + O(N_\text{p}N_\text{MCS})` + です。 diff --git a/doc/jp/fourier/fourier_contact_ja.rst b/doc/jp/fourier/fourier_contact_ja.rst new file mode 100644 index 00000000..67240997 --- /dev/null +++ b/doc/jp/fourier/fourier_contact_ja.rst @@ -0,0 +1,14 @@ +Contact +======= + +このユーティリティについてのご意見, ご質問, +バグ報告等ありましたら下記までお問い合わせください。 + +河村光晶 + +:: + + mkawamura_at_issp.u-tokyo.ac.jp + +``_at_`` を ``@`` に変えてください. + diff --git a/doc/jp/fourier/fourier_format_ja.rst b/doc/jp/fourier/fourier_format_ja.rst new file mode 100644 index 00000000..f78ad8c3 --- /dev/null +++ b/doc/jp/fourier/fourier_format_ja.rst @@ -0,0 +1,250 @@ +.. _fileformat: + +ファイルフォーマット +==================== + +.. _geometry: + +ジオメトリー +------------ + +:ref:`tutorial` でのファイル名は ``geometry.dat`` . +mVMC/:math:`{\mathcal H}\Phi` のスタンンダードモードを用いた場合には +上記のファイル名で自動的に生成されるので, とくに気にする必要はない. + +:: + + 1.000000 0.000000 0.000000 (1) + 0.000000 1.000000 0.000000 (1) + 0.000000 0.000000 1.000000 (1) + 0.000000 0.000000 0.000000 (2) + 4 0 0 (3) + 0 4 0 (3) + 0 0 1 (3) + 0.000000 0.000000 0.000000 (4) + 1.000000 0.000000 0.000000 (4) + 2.000000 0.000000 0.000000 (4) + 3.000000 0.000000 0.000000 (4) + 0.000000 1.000000 0.000000 (4) + 1.000000 1.000000 0.000000 (4) + 2.000000 1.000000 0.000000 (4) + 3.000000 1.000000 0.000000 (4) + 0.000000 2.000000 0.000000 (4) + 1.000000 2.000000 0.000000 (4) + 2.000000 2.000000 0.000000 (4) + 3.000000 2.000000 0.000000 (4) + 0.000000 3.000000 0.000000 (4) + 1.000000 3.000000 0.000000 (4) + 2.000000 3.000000 0.000000 (4) + 3.000000 3.000000 0.000000 (4) + +#. 単位格子ベクトル. 任意の単位. +#. 1体項がシミュレーションセルの境界を跨いだときに付く位相(単位degree) +#. シミュレーションセルの形状を指定する三本の整数ベクトル. + スタンダードモードの入力パラメーター ``a0W``, ``a0L``, ``a0H``, ``a1W``... + に対応する. +#. 各サイトの座標. 単位格子ベクトルに対するフラクショナル座標として入力する. + + +サイト表示の1体および2体相関関数 +-------------------------------- + +.. _greenindex: + +計算する相関関数のインデックスの指定 +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +mVMC/:math:`{\mathcal H}\Phi` で計算する相関関数を指定する. +スタンダードモードを使った場合には自動的に生成される. +総合的な説明はmVMC/:math:`{\mathcal H}\Phi` のマニュアルを参照. +:ref:`tutorial` でのファイル名は ``greenone.def`` (1体)および ``greentwo.def`` (2体)である. + +:ref:`supported` にある相関関数を計算するためには, +以下のようにインデックスを指定する必要がある. + +- :math:`\langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle` + + :math:`\langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle` + に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅するようにする. + +- :math:`\langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle` + + :math:`\langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle` + に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅するようにする. + +- :math:`\langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle` および + :math:`\langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle` + + :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i \sigma} {\hat c}_{j \sigma'}^{\dagger} {\hat c}_{j \sigma'}\rangle` + に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅し, + :math:`\sigma` および :math:`\sigma'` が :math:`\uparrow`, :math:`\downarrow` を網羅するようにする. + +- :math:`\langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle` および + :math:`\langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle` + + :math:`{\mathcal H}\Phi` の場合は + :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i -\sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{j \sigma}\rangle` + に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅し, + :math:`\sigma` が :math:`\uparrow`, :math:`\downarrow` を網羅するようにする. + mVMC の場合は + :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{j \sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{i -\sigma}\rangle` + に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅し, + :math:`\sigma` が :math:`\uparrow`, :math:`\downarrow` を網羅するようにする. + いずれの場合も演算子の順番に注意にすること. + +スタンダードモードのデフォルト(``outputmode="corr"``)では, +自動的に上記のインデックスが指定されるため, 特に気にする必要はない. + +.. _zvocisajs: + +サイト表示の1体および2体相関関数の計算結果 +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +:ref:`greenindex` で指定したインデックスを持つ相関関数が +mVMC/:math:`{\mathcal H}\Phi` によって計算され, +ファイルに出力される. +総合的な説明はmVMC/:math:`{\mathcal H}\Phi` のマニュアルを参照. +:ref:`tutorial` でのファイル名は +``output/zvo_cisajs_001.dat`` および ``output/zvo_cisajscktalt_001.dat`` (mVMC), +``output/zvo_cisajs.dat`` および ``output/zvo_cisajscktalt.dat`` (:math:`{\mathcal H}\Phi`). + +``fourier`` ユーティリティはこのファイルを読み込んで計算を行う. +この時, (スタンダードモードを使わず自分でインデックスを指定するなどにより) +:ref:`greenindex` で挙げたインデックスの相関関数のなかで欠けているものがある場合, +それを 0 として扱う. + +.. _zvocorr: + +プリミティブゾーン内の相関関数 +------------------------------ + +Fourier変換された相関関数(波数表示)が入っている. +ユーティリイティ ``fourier`` によって生成される. +:ref:`tutorial` でのファイル名は ``output/zvo_corr.dat`` である. + +:: + + #HPhi 16 (1) + # kx[1] ky[2] kz[3](Cart.) UpUp[4,5] (Re. Im.) DownDown[6,7] (2) + # Density[8,9] SzSz[10,11] S+S-[12,13] S-S+[14,15] (2) + #k-offset 0.0000000 0.0000000 0.0000000 (3) + 0.00000E+00 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) + 0.15708E+01 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) + : : + +#. ``HPhi`` の出力から作成された場合には ``"#HPhi"``, + ``vmc.out`` の出力から作成された場合には ``"#mVMC"`` と書かれる. + それに続く整数は, プリミティブ ブリルアンゾーン内の :math:`k` 点の数である. +#. 各カラムに出力されている量の説明. +#. シミュレーションセルの境界を跨ぐ一体項に位相が付く場合の, + 一体相関関数の :math:`k` 点の変位. + すなわち, この後の行の4〜7列目の一体相関関数は, + 1〜3列目の :math:`k` 点からこのオフセットの分だけずれた点のものである. +#. :math:`k` 点(デカルト座標)と相関関数. + それぞれの相関関数の実部と虚部が書かれている. + +.. _kpoint: + +corplot用 *k* 点ファイル +------------------------ + +``fourier`` ユーティリティで生成され, +``corplot`` ユーティリティでプロットを行う時に読み込まれる. +ファイル名は ``kpoint.dat`` である. + +:: + + 81 9 (1) + 0.62832E+01 0.00000E+00 0.00000E+00 (2) + 0.00000E+00 0.62832E+01 0.00000E+00 (2) + 0.00000E+00 0.00000E+00 0.62832E+01 (2) + -0.62832E+01 -0.62832E+01 0.00000E+00 1 (3) + -0.47124E+01 -0.62832E+01 0.00000E+00 2 (3) + -0.31416E+01 -0.62832E+01 0.00000E+00 3 + -0.15708E+01 -0.62832E+01 0.00000E+00 4 + 0.00000E+00 -0.62832E+01 0.00000E+00 1 + 0.15708E+01 -0.62832E+01 0.00000E+00 2 + 0.31416E+01 -0.62832E+01 0.00000E+00 3 + 0.47124E+01 -0.62832E+01 0.00000E+00 4 + +#. ``corplot`` でプロットされる :math:`k` 点の総数および + gnuplot のsplotで表示する時の :math:`k` 点の区切り. +#. 逆格子ベクトル(デカルト座標) +#. :math:`k` ベクトル(デカルト座標)と, + その :math:`k` 点と等価なプリミティブゾーン内の :math:`k` 点のインデックス. + このインデックスは :ref:`zvocorr` での :math:`k` 点の番号に対応している. + +.. _gnuplot: + +gnuplot スクリプト +------------------ + +``corplot`` にて作成され, +内部で起動した gnuplot によって読み込まれる. +``corplot`` とは別に 直接gnuplotを起動して, ``load`` でよみこむことも可能である. +ファイル名は ``correlation.gp`` である. + +.. code-block:: gnuplot + + #set terminal pdf color enhanced \ (1) + #dashed dl 1.0 size 20.0cm, 20.0cm (1) + #set output 'correlation.pdf' (1) + #set view 60.0, 30.0 (1) + + set view equal xy + set ticslevel 0 + set hidden3d + set xlabel 'kx' + set ylabel 'ky' + set zrange [ 0.25000E-10: 0.18435E+00] + + set pm3d + set pm3d interpolate 5, 5 + set view 0.0, 0.0 + + ##### Set Brillouin-Zone Boundary ##### + + set arrow from -0.31416E+01, -0.31416E+01, ... + set arrow from -0.31416E+01, 0.31416E+01, ... + : + ##### End Set Brillouin-Zone Boundary ##### + + splot \ + 'correlation.dat' u 1:2:3 w l tit '1' (2) + pause -1 + +#. 図をPDFファイルに出力したい時には, + この行の先頭のコメントアウトを外す. + 論文等に貼る図を作るときには, 適宜この後にフォントの設定等を書く. + 詳しくは gnuplot のマニュアル等を参照. +#. :ref:`correlation` のファイルをプロットしている. + +.. _correlation: + +広範囲の *k* 点での相関関数 +--------------------------- + +``corplot`` にて作成され, +内部で起動した gnuplot によって, +:ref:`gnuplot` を経由して読み込まれる. +ファイル名は ``correlation.dat`` + +:: + + -0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 + -0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 + -0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 + -0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 + 0.00000E+00 -0.62832E+01 0.18435E+00 0.00000E+00 + 0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 + 0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 + 0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 + 0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 + + -0.62832E+01 -0.47124E+01 0.36159E-01 0.00000E+00 + -0.47124E+01 -0.47124E+01 0.20921E-01 0.00000E+00 + -0.31416E+01 -0.47124E+01 0.11372E-01 0.00000E+00 + : + +1, 2列目は :math:`k` ベクトル(デカルト座標)を表す. +3列目は相関関数, 4列目はその標準誤差を表す. diff --git a/doc/jp/fourier/fourier_overview_ja.rst b/doc/jp/fourier/fourier_overview_ja.rst new file mode 100644 index 00000000..6a32c9a8 --- /dev/null +++ b/doc/jp/fourier/fourier_overview_ja.rst @@ -0,0 +1,63 @@ +概要 +==== + +本資料は, mVMC および :math:`{\mathcal H}\Phi` で計算された +サイト表示の相関関数をFourier変換し, 出力するユーティリティに関するマニュアルである. + +要件 +---- + +本ユーティリティの使用要件はmVMC および :math:`{\mathcal H}\Phi` と同じである. + +.. _supported: + +対応する量 +---------- + +本ユーティリティは以下の相関関数のFourier変換に対応している. + +1体相関 + +.. math:: + :nowrap: + + \begin{align} + \langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle + &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle + \\ + \langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle + &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle + \end{align} + +密度-密度相関 + +.. math:: + + \begin{align} + \langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle + \equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle ({\hat \rho}_{i} - \langle {\hat \rho}_{i} \rangle) + ({\hat \rho}_{j} - \langle {\hat \rho}_{j} \rangle) \rangle + \end{align} + +スピン-スピン相関 + +.. math:: + :nowrap: + + \begin{align} + \langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat S}_{i}^{z} {\hat S}_{j}^{z} \rangle + \\ + \langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat S}_{i}^{+} {\hat S}_{j}^{-} \rangle + \\ + \langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat {\bf S}}_{i} \cdot {\hat {\bf S}}_{j} \rangle + \end{align} + diff --git a/doc/jp/fourier/fourier_tutorial_ja.rst b/doc/jp/fourier/fourier_tutorial_ja.rst new file mode 100644 index 00000000..ca87068a --- /dev/null +++ b/doc/jp/fourier/fourier_tutorial_ja.rst @@ -0,0 +1,115 @@ +.. _tutorial: + +チュートリアル +============== + +このチュートリアルは ``sample/Standard/Spin/HeisenbergSquare/`` +にあるインプットファイルを用いて行う. + +HPhi/vmc.out の実行 +------------------- + +- :math:`{\mathcal H}\Phi` の場合 + + 基底状態および相関関数の計算を行う. + + .. code-block:: bash + + $ ../../../../src/HPhi -s StdFace.def + +- mVMC の場合 + + 変分波動関数の最適化を行う. + + .. code-block:: bash + + $ ../../../../src/vmc.out -s StdFace.def + + 相関関数を計算するために, ``StdFace.def`` に以下の行を付け加える. + + :: + + NVMCCalMode = 1 + + 相関関数を計算する. + + .. code-block:: bash + + $ ../../../../src/vmc.out -s StdFace.def output/zqp_opt.dat + +これにより, カレントディレクトリの ``output/`` 以下に +1体および2体の相関関数が出力される. + +関連するファイル + +- StdFace.def (mVMC/:math:`{\mathcal H}\Phi` のマニュアル参照) +- zqp_opt.dat (mVMCのマニュアル参照) +- greenone.def (:ref:`greenindex`) +- greentwo.def (:ref:`greenindex`) + +相関関数のフーリエ変換 +---------------------- + +ユーティリティプログラム ``fourier`` を使って, +相関関数をフーリエ変関する. + +.. code-block:: bash + + $ ../../../../tool/fourier namelist.def geometry.dat + +これにより, カレントディレクトリの ``output/`` 以下に +フーリエ変換された相関関数が出力される. + +関連するファイル + +- output/zvo_cisajs_001.dat (:ref:`zvocisajs`) +- output/zvo_cisajs.dat (:ref:`zvocisajs`) +- output/zvo_cisajscktalt_001.dat (:ref:`zvocisajs`) +- output/zvo_cisajscktalt.dat (:ref:`zvocisajs`) +- geometry.dat (:ref:`geometry`) +- output/zvo_corr.dat (:ref:`zvocorr`) + +相関関数のプロット +------------------ + +ユーティリティプログラム ``corplot`` を使って, +相関関数を :math:`k` 空間でプロットする. + +.. code-block:: bash + + $ ../../../../tool/corplot output/zvo_corr.dat + +この時, ターミナルには次のように標準入力を促すメッセージが現れる. + +:: + + ##### Plot Start ##### + + Please specify target number from below (0 or Ctrl-C to exit): + + Real Part Without ErrorBar + [ 1] Up-Up [ 2] Down-Down [ 3] Density-Density [ 4] SzSz [ 5] S+S- [ 6] S-S+ + Imaginary Part Without ErrorBar + [11] Up-Up [12] Down-Down [13] Density-Density [14] SzSz [15] S+S- [16] S-S+ + Real Part With ErrorBar + [21] Up-Up [22] Down-Down [23] Density-Density [24] SzSz [25] S+S- [26] S-S+ + Imaginary Part With ErrorBar + [31] Up-Up [32] Down-Down [33] Density-Density [34] SzSz [35] S+S- [36] S-S+ + + Target : + +プロットしたい量に対応する数字(例えば4)を入力し, +``Enter`` キーを押すと gnuplot が起動して3Dグラフが表示される(図 :num:`corplotpng` ). + +.. _corplotpng: + +.. figure:: ../../figs/corplot.png + + Target : 4 としてプロットした図. + 黒線は第一ブリルアンゾーンを表す. + +関連するファイル + +- kpoint.dat (:ref:`kpoint`) +- correlation.gp (:ref:`gnuplot`) +- correlation.dat (:ref:`correlation`) diff --git a/doc/jp/fourier/fourier_util_ja.rst b/doc/jp/fourier/fourier_util_ja.rst new file mode 100644 index 00000000..fe995e6f --- /dev/null +++ b/doc/jp/fourier/fourier_util_ja.rst @@ -0,0 +1,94 @@ +各ユーティリティの動作について +============================== + +``fourier`` ユーティリティ +-------------------------- + +このユーティリティーは, 次のようにして使う. + +.. code-block:: bash + + $ ${PATH}/fourier ${NAMELIST} ${GEOMETRY} + +ここで, ``${PATH}`` は ``fourier`` ユーティリティのバイナリのあるディレクトリのパス, +${NAMELIST}は :math:`{\mathcal H}\Phi`/mVMC の NameList インプットファイル名, +${GEOMETRY}は :ref:`geometry` ファイルへのパスである. + +:math:`{\mathcal H}\Phi` の各モード +(Lanczos, TPQ, 全対角化, LOBCG)および mVMC のどの計算で得られた +相関関数のFourier変換を行うかによって, 動作が若干異なる. +以下では ModPara インプットファイルの ``CDataFileHead`` が +``"zvo"`` (デフォルト値)であるとする. + +HPhi-Lanczos +~~~~~~~~~~~~ + +この場合に ``HPhi`` が ``output/`` ディレクトリに出力するサイト表示の相関関数は, +``zvo_cisajs.dat`` (1体), ``zvo_cisajscktalt.dat`` (2体)である. +``fourier`` ユーティリティーは, これらを読み込みFourier変換を行った後, +単一のファイル ``zvo_corr.dat`` を ``output/`` ディレクトリに出力する. + +HPhi-TPQ +~~~~~~~~ + +この場合に ``HPhi`` は, 各試行/TPQステップ毎に +``zvo_cisajs_run*step*.dat`` (1体), ``zvo_cisajscktalt_run*step*.dat`` (2体)というファイルを +``output/`` ディレクトリに出力する. +``fourier`` ユーティリティーは, 各試行/TPQステップ毎に +1体および2体の相関関数を読み込みFourier変換を行った後, +``zvo_corr_run*step*.dat`` という名前のファイルとして ``output/`` ディレクトリに出力する. + +HPhi-全対角化およびLOBCG +~~~~~~~~~~~~~~~~~~~~~~~~ + +この場合に ``HPhi`` は, 各波動関数ごとに +``zvo_cisajs_eigen*.dat`` (1体), ``zvo_cisajscktalt_eigen*.dat`` (2体)というファイルを +``output/`` ディレクトリに出力する. +``fourier`` ユーティリティーは, 各波動関数ごとに +1体および2体の相関関数を読み込みFourier変換を行った後, +``zvo_corr_eigen*.dat`` という名前のファイルとして ``output/`` ディレクトリに出力する. + +mVMC +~~~~ + +この場合に ``vmc.out`` は, ``ModPara`` インプットファイルで指定された +``NDataIdxStart`` および ``NDataQtySmp`` というパラメーターに応じて +試行を行いインデックスをつけられた +``zvo_cisajs_???.dat`` (1体), ``zvo_cisajscktalt_???.dat`` (2体)というファイルを +``output/`` ディレクトリに出力する. +``fourier`` ユーティリティーはそれらのファイルを読み込み, +各試行に対してFourier変換を行った後, +それらの実部, 虚部ごとに平均値 + +.. math:: + + \begin{align} + \langle A \rangle = \frac{1}{N_{\rm Try}} \sum_{i=1}^{N_{\rm Try}} A_i + \end{align} + +および標準誤差 + +.. math:: + + \begin{align} + \delta A = \frac{1}{N_{\rm Try} - 1} + \sqrt{\frac{1}{N_{\rm Try}} \sum_{i=1}^{N_{\rm Try}} (A_i - \langle A \rangle)^2} + \end{align} + +を計算し, 平均値と誤差を含んだ単一のファイル +``zvo_corr_eigen*.dat`` を ``output/`` ディレクトリに出力する. + +``corplot`` ユーティリティ +-------------------------- + +このユーティリティーは, 次のようにして使う. + +.. code-block:: bash + + $ ${PATH}/corplot ${CORR1} ${CORR2} ${CORR3} ... + +ここで, ``${PATH}`` は ``corplot`` ユーティリティのバイナリのあるディレクトリのパス, +${CORR1}, ${CORR2}, ${CORR3}, ...は ``fourier`` ルーチンによって生成された +:ref:`zvocorr` ファイルへのパスである. +すなわち, このユーティリティーでは, (TPQ計算による温度依存性を調べる等の用途で) +複数の相関関数ファイルを読み込み, それらを同時にプロットすることができる. diff --git a/doc/jp/fourier/index.rst b/doc/jp/fourier/index.rst new file mode 100644 index 00000000..32e7e7ca --- /dev/null +++ b/doc/jp/fourier/index.rst @@ -0,0 +1,26 @@ +.. test documentation master file, created by + sphinx-quickstart on Sat Jan 7 22:10:04 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +.. _fourier: + +相関関数のFourier変換ユーティリティー +===================================== + +.. toctree:: + :maxdepth: 3 + + fourier_overview_ja.rst + fourier_tutorial_ja.rst + fourier_format_ja.rst + fourier_util_ja.rst + fourier_contact_ja.rst + +.. Indices and tables +.. ================== + +.. * :ref:`genindex` +.. * :ref:`modindex` +.. * :ref:`search` + diff --git a/doc/jp/index.rst b/doc/jp/index.rst new file mode 100644 index 00000000..27031302 --- /dev/null +++ b/doc/jp/index.rst @@ -0,0 +1,29 @@ +.. test documentation master file, created by + sphinx-quickstart on Sat Jan 7 22:10:04 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +汎用多変数変分モンテカルロ法パッケージ mVMC マニュアル +====================================================== + +.. toctree:: + :maxdepth: 2 + + intro.rst + start.rst + tutorial.rst + standard.rst + expert.rst + output.rst + algorithm.rst + appendix.rst + fourier/index + acknowledge.rst + +.. Indices and tables +.. ================== + +.. * :ref:`genindex` +.. * :ref:`modindex` +.. * :ref:`search` + diff --git a/doc/jp/intro.rst b/doc/jp/intro.rst new file mode 100644 index 00000000..9fa14364 --- /dev/null +++ b/doc/jp/intro.rst @@ -0,0 +1,140 @@ +.. include:: ../bib/ref.txt + +What is mVMC? +============= + +mVMCとは？ +---------- + +量子多体系の理論模型の高精度解析は +高温超伝導・量子スピン液体に代表される新奇量子相の +発現機構を解明するうえで重要な役割を果たすことが期待できます。 +また、現実の物質を記述する有効模型を非経験的に導出する手法も +近年発展しており [ImadaMiyake_ ]、その有効模型の高精度解析を行うことは、 +現実物質の物性を非経験的に解明して、さらに制御につなげるうえで +重要なステップとなっています。 +有効模型解析で最も信頼できる手法は厳密対角化法であるものの、 +その適用できるサイズには強い制限があるのが大きな問題でした。 +厳密対角化法を超えたシステムサイズに対して高精度な計算が行える +計算手法の一つとして、変分モンテカルロ法があります [Gros_ ]。 +従来の変分モンテカルロ法では、 使用する変分波動関数の強い制限に +よる精度の低下が問題となっていましたが、 +近年の理論手法及び計算機の発展によって、 +変分モンテカルロ法で使用する波動関数の制限を +大幅に緩和することが可能になっており、 +変分モンテカルロ法の計算精度は劇的に向上しています [Tahara2008_, Misawa2014_, Morita2015_ ]。 + +この背景のもと、 多変数変分モンテカルロ法(many-variable variational +Monte Carlo method [mVMC])は +簡便かつ柔軟なユーザー・インタフェースとともに +大規模並列に対応したソフトウェアとして開発されました。 +ハバード模型・ハイゼンベルグ模型・近藤格子模型などの +基本的な模型に対しては、 ユーザーは10行程度の +一つのファイルを用意するだけで 容易に計算を実行することができます。 +また、同一のファイルを用いて、 +:math:`\mathcal{H}\Phi` [HPhi_ ]による厳密対角化法の計算も実行できることから、 +ユーザーは小さなシステムサイズで計算精度を確認しながら, +厳密対角化では到達できないシステムサイズの 計算を行なうことができます。 +mVMCを実験研究者や量子化学の研究者などの 分野を超えた幅広いユーザー +の方にご利用頂ければ幸いです。 + +プログラム概要 +~~~~~~~~~~~~~~ + +このプログラムを利用することで以下の事項が計算可能です。 + +- 与えられた変分自由度の範囲でハミルトニアンの期待値が最小 (極小) + 値を持つような変分波動関数 を数値的に生成します. + 量子数で分割された部分空間に限定して計算することも可能です。 + +- 得られた変分波動関数における各種物理量 (相関関数など) + の期待値を計算することができます。 + +mVMCでは以下の流れで計算を行います。 + +#. 入力ファイル(\*.def)の読込 + +#. :math:`\langle {\cal H} \rangle`\ を最小化するように変分パラメータ\ :math:`\vec{\alpha}`\ を最適化 + +#. 一体・二体Green関数の計算 + +#. 変分パラメータ・期待値の出力 + +計算では「実空間配置 +:math:`|x\rangle`\ の生成からサンプリングまでを並列して行い、期待値を計算する際に一つにまとめる」という単純な並列化を行っています。各計算機クラスターで所定の手続きに従って、 +並列数を指定すれば MPI +を用いた並列計算を勝手に行われますが、並列を行わない場合 (single core) +もMPI を呼び出すため、MPI ジョブを禁止してる環境 (物性研 system B +のフロントエンドなど) +ではプログラム実行することができません。なお、本プログラムではパフィアンの計算にあたりPFAPACKを利用した計算を行っています +[PFAPACK_ ]。 + +ライセンス +~~~~~~~~~~ + +本ソフトウェアのプログラムパッケージおよびソースコード一式はGNU General +Public License version 3（GPL v3）に準じて配布されています。 + +| mVMCを引用する際には、以下のURLを記載してください + (mVMCに関する代表論文執筆後は、そちらへの引用に変更する予定です)。 +| URL: https://github.com/issp-center-dev/mVMC + +コピーライト +~~~~~~~~~~~~ + + *©2016- The University of Tokyo.* *All rights reserved.* + +本ソフトウェアは2016年度 東京大学物性研究所 +ソフトウェア高度化プロジェクトの支援を受け開発されています。 + +開発貢献者 +~~~~~~~~~~ + +本ソフトウェアは以下の開発貢献者により開発されています。 + +- ver.1.0.1 (2017/6/8リリース) + +- ver.1.0.0 (2017/5/23リリース) + +- ver.0.2.0 (2017/3/16リリース) + +- ver.0.1.1 (2016/12/16リリース) + +- ver.0.1.0 (2016/10/26リリース) + + - 開発者 + + - 三澤 貴宏 (東京大学 物性研究所) + + - 森田 悟史 (東京大学 物性研究所) + + - 大越 孝洋 (東京大学 大学院工学系研究科) + + - 井戸 康太 (東京大学 大学院工学系研究科) + + - 今田 正俊 (東京大学 大学院工学系研究科) + + - 本山 裕一 (東京大学 物性研究所) + + - 河村 光晶 (東京大学 物性研究所) + + - 吉見 一慶 (東京大学 物性研究所) + + - プロジェクトコーディネーター + + - 加藤 岳生 (東京大学 物性研究所) + +動作環境 +-------- + +以下の環境で動作することを確認しています。 + +- 東京大学物性研究所スーパーコンピューターシステムB「sekirei」 + +- 京コンピューター + +- OpenMPI + Intel Compiler + MKL + +- MPICH + Intel Compiler + MKL + +- MPICH + GNU Compiler + MKL diff --git a/doc/jp/output.rst b/doc/jp/output.rst new file mode 100644 index 00000000..15f8512a --- /dev/null +++ b/doc/jp/output.rst @@ -0,0 +1,330 @@ +.. include:: ../bib/ref.txt + +.. _outputfile: + +出力ファイル +------------ + +出力ファイルの一覧は下記の通りです。\*\*\*には ``ModPara`` ファイルの ``CParaFileHead`` で指定されるヘッダが、xxxには ``CDataFileHead`` で指定されるヘッダが、yyyには ``ModPara`` ファイルの ``NDataIdxStart``, +``NDataQtySmp`` に従い ``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp`` の順に記載されます。また、zzzには ``ModPara`` ファイルの ``NDataIdxStart`` が記載されます。 + +[h!] + ++--------------------------------------+-----------------------------------------------+ +| ファイル名 | 対応するファイルの中身 | ++======================================+===============================================+ +| \*\*\*\_opt.dat | 最適化された全パラメータ. | ++--------------------------------------+-----------------------------------------------+ +| \*\*\*\_gutzwiller\_opt.dat | 最適化されたGutzwiller因子. | ++--------------------------------------+-----------------------------------------------+ +| \*\*\*\_jastrow\_opt.dat | 最適化されたJastrow因子. | ++--------------------------------------+-----------------------------------------------+ +| \*\*\*\_doublonHolon2site\_opt.dat | 最適化された2サイトダブロン-ホロン相関因子. | ++--------------------------------------+-----------------------------------------------+ +| \*\*\*\_doublonHolon4site\_opt.dat | 最適化された4サイトダブロン-ホロン相関因子. | ++--------------------------------------+-----------------------------------------------+ +| \*\*\*\_orbital\_opt.dat | 最適化されたペア軌道因子. | ++--------------------------------------+-----------------------------------------------+ +| xxx\_out\_yyy.dat | エネルギーとその分散. | ++--------------------------------------+-----------------------------------------------+ +| xxx\_var\_yyy.dat | パラメータ最適化過程の情報. | ++--------------------------------------+-----------------------------------------------+ +| xxx\_CalcTimer.dat | 各プロセスに対する計算時間に関する情報. | ++--------------------------------------+-----------------------------------------------+ +| xxx\_time\_zzz.dat | モンテカルロサンプリングの過程に関する情報. | ++--------------------------------------+-----------------------------------------------+ +| xxx\_cisajs\_yyy.dat | 一体グリーン関数. | ++--------------------------------------+-----------------------------------------------+ +| xxx\_cisajscktalt\_yyy.dat | 二体グリーン関数. | ++--------------------------------------+-----------------------------------------------+ + +変分パラメータ出力ファイル(\*\*\*\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +SR法で最適化された変分パラメータとエネルギーが一斉出力されます。 +変分パラメータが一斉に読み込めるため、変分パラメータ最適化後の物理量の計算を行う場合に使用します。 +出力されるデータは + +.. math:: \langle H \rangle, \langle H^2 \rangle, g_i, v_{ij}, \alpha_{2nt}^{d(h)}, \alpha_{4nt}^{d(h)}, f_{ij} \nonumber + + +で、それぞれの平均値と標準偏差が出力されます(平均値は実数、虚数の順に、標準偏差は実数のみ出力)。 +なお、全データが1行で出力され、数値の間は半角空白で区切られます。 +\*\*\*には ``ModPara`` ファイルの ``CParaFileHead`` で指定されるヘッダが記載されます。 + +ステップ別変分パラメータ出力ファイル(xxx\_var\_yyy.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +SR 法の各ステップにおける変分パラメータとエネルギーがzqp\_opt.dat +と同形式で“追記しながら” 出力されます(標準偏差はゼロ)が出力されます。 +xxxには ``CDataFileHead`` で指定されるヘッダが、yyyには ``ModPara`` ファイルの ``NDataIdxStart``, +``NDataQtySmp`` に従い ``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp`` の順に記載されます。 + +Gutzwiller因子出力ファイル(\*\*\*\_gutzwiller\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +SR法で最適化されたGutzwiller因子が出力されます。 +出力形式は :ref:`InputParam` のInGutzwiller指定ファイルと同じです。 + +Jastrow因子出力ファイル(\*\*\*\_jastrow\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +SR法で最適化されたJastrow因子が出力されます。 +出力形式は :ref:`InputParam` のInJastrow指定ファイルと同じです。 + +2サイトダブロンホロン相関因子出力ファイル +(\*\*\*\_doublonHolon2site\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +SR法で最適化された2サイトのdoublon-holon相関因子が出力されます。 +出力形式は :ref:`InputParam` のInDH2指定ファイルと同じです。 + +4サイトダブロンホロン相関因子出力ファイル +(\*\*\*\_doublonHolon4site\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +SR法で最適化された4サイトのdoublon-holon相関因子が出力されます。 +出力形式は :ref:`InputParam` のInDH4指定ファイルと同じです。 + +ペア軌道出力ファイル(\*\*\*\_orbital\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +SR法で最適化されたペア軌道の変分パラメータが出力されます。 +出力形式は :ref:`InputParam` のInOrbital指定ファイルと同じです。 + +xxx\_out\_yyy.dat +~~~~~~~~~~~~~~~~~ + +ビン毎の計算情報として、 + +.. math:: + + \langle H \rangle, \langle H^2 \rangle, \frac{\langle H^2 \rangle- \langle H \rangle^2 }{\langle H \rangle^2}, + \langle S^z \rangle, \langle (S^z)^2 \rangle + \nonumber. + + +が順に出力されます。 :math:`\langle H \rangle` については実部と虚部がそれぞれ出力され、それ以外は実部のみ出力されます。 +xxxには ``CDataFileHead`` で指定されるヘッダが、yyyには ``ModPara`` ファイルの ``NDataIdxStart``, +``NDataQtySmp`` に従い ``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp`` の順に記載されます。以下に出力例を記載します。 + +13cm + +:: + + 1.151983765704212992e+01 8.124622418360909482e-01 \ + 1.619082955438887268e+02 2.019905203939084959e-01 + 1.288482613817423150e+01 5.006903733262847433e-01 + 1.972000325276957824e+02 1.824505193695792893e-01 + 1.308897206011880421e+01 5.701244886956570168e-01 \ + 2.072610167083121837e+02 2.029162857569105916e-01 + … + +xxx\_CalcTimer.dat +~~~~~~~~~~~~~~~~~~~ + +計算終了後に、処理毎の計算処理時間が処理名、処理に割り当てられた識別番号、実行秒数の順に出力されます。出力例は以下の通りです。 + +15.5cm + +:: + + All [0] 15.90724 + Initialization [1] 0.04357 + read options [10] 0.00012 + ReadDefFile [11] 0.00082 + SetMemory [12] 0.00002 + InitParameter [13] 0.03026 + VMCParaOpt [2] 15.86367 + VMCMakeSample [3] 12.85650 + makeInitialSample [30] 0.20219 + make candidate [31] 0.02553 + hopping update [32] 12.51967 + UpdateProjCnt [60] 7.41864 + CalculateNewPfM2 [61] 3.67098 + CalculateLogIP [62] 0.07599 + UpdateMAll [63] 1.27466 + exchange update [33] 0.00000 + UpdateProjCnt [65] 0.00000 + CalculateNewPfMTwo2 [66] 0.00000 + CalculateLogIP [67] 0.00000 + UpdateMAllTwo [68] 0.00000 + recal PfM and InvM [34] 0.08294 + save electron config [35] 0.00232 + VMCMainCal [4] 2.45481 + CalculateMAll [40] 0.47556 + LocEnergyCal [41] 0.79754 + CalHamiltonian0 [70] 0.00259 + CalHamiltonian1 [71] 0.18765 + CalHamiltonian2 [72] 0.00107 + ReturnSlaterElmDiff [42] 0.40035 + calculate OO and HO [43] 0.68045 + StochasticOpt [5] 0.30489 + preprocess [50] 0.02587 + stcOptMain [51] 0.25471 + initBLACS [55] 0.06564 + calculate S and g [56] 0.05603 + DPOSV [57] 0.09833 + gatherParaChange [58] 0.02774 + postprocess [52] 0.02372 + UpdateSlaterElm [20] 0.02556 + WeightAverage [21] 0.06676 + outputData [22] 0.10554 + SyncModifiedParameter [23] 0.02151 + +xxx\_time\_zzz.dat +~~~~~~~~~~~~~~~~~~~ + +| 計算情報としてビン毎にサンプリング数、hoppingおよびexchangeのアップデートに対するacceptance + ratio(acc\_hopp, acc\_ex)、それぞれのアップデートの試行回数(n\_hopp, + n\_ex)および実行した際の時間を順に出力します。xxxには ``CDataFileHead`` で指定されるヘッダが、zzzには ``ModPara`` ファイルの ``NDataIdxStart`` が記載されます。 + 出力例は以下の通りです。 + +15.5cm + +:: + + 00000 acc_hop acc_ex n_hop n_ex : Mon Jul 25 14:03:29 2016 + 00001 0.59688 0.00000 320 0 : Mon Jul 25 14:03:30 2016 + 00002 0.47727 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + 00003 0.50000 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + 00004 0.49432 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + 00005 0.57386 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + 00006 0.55114 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + … + +xxx\_cisajs\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~ + +OneBodyG指定ファイルで指定された一体グリーン関数 :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle` の計算結果を出力します。 +xxxには ``CDataFileHead`` で指定されるヘッダが、yyyには ``ModPara`` ファイルの ``NDataIdxStart``, +``NDataQtySmp`` に従い ``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp`` の順に記載されます。以下にファイル例を記載します。 + +12.5cm + +:: + + 0 0 0 0 0.4452776740 0.0000000000 + 0 1 0 1 0.4452776740 0.0000000000 + 1 0 1 0 0.5000000000 0.0000000000 + 1 1 1 1 0.5000000000 0.0000000000 + 2 0 2 0 0.4452776740 0.0000000000 + 2 1 2 1 0.4452776740 0.0000000000 + 3 0 3 0 0.5000000000 0.0000000000 + 3 1 3 1 0.5000000000 0.0000000000 + … + +ファイル形式 +^^^^^^^^^^^^ + +- :math:`[` int01 :math:`]` :math:`[` int02 :math:`]` :math:`[` int03 :math:`]` :math:`[` int04 :math:`]` :math:`[` double01 :math:`]` :math:`[` double02 :math:`]` + +パラメータ +^^^^^^^^^^ + +- :math:`[` int01 :math:`]`, :math:`[` int03 :math:`]` + + **形式 :** int型 + + **説明 :** + サイト番号を指定する整数。 :math:`[` int01 :math:`]` が :math:`i` サイト、 :math:`[` int03 :math:`]` が :math:`j` サイトを表します。 + +- :math:`[` int02 :math:`]`, :math:`[` int04 :math:`]` + + **形式 :** int型 + + | **説明 :** + スピンを指定する整数。 :math:`[` int02 :math:`]` が :math:`\sigma_1` 、 :math:`[` int03 :math:`]` が :math:`\sigma_2` に対応します。 + | 0: アップスピン + | 1: ダウンスピン + | を表します。 + +- :math:`[` double01 :math:`]`, :math:`[` double02 :math:`]` + + **形式 :** double型 + + | **説明 :** + :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle` の値を表します。 + | :math:`[` double01 :math:`]` が実部、 :math:`[` double02 :math:`]` が虚部を表します。 + +xxx\_cisajscktalt\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +TwoBodyG指定ファイルで指定された二体グリーン関数 :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle` の計算結果を出力します。xxxには ``CDataFileHead`` で指定されるヘッダが、yyyには ``ModPara`` ファイルの ``NDataIdxStart``, +``NDataQtySmp`` に従い ``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp`` の順に記載されます。以下にファイル例を記載します。 + +15cm + +:: + + 0 0 0 0 0 0 0 0 0.4452776740 0.0000000000 + 0 0 0 0 0 1 0 1 0.1843355815 0.0000000000 + 0 0 0 0 1 0 1 0 0.1812412105 0.0000000000 + 0 0 0 0 1 1 1 1 0.2640364635 0.0000000000 + 0 0 0 0 2 0 2 0 0.0279690007 0.0000000000 + 0 0 0 0 2 1 2 1 0.2009271524 0.0000000000 + 0 0 0 0 3 0 3 0 0.2512810778 0.0000000000 + 0 0 0 0 3 1 3 1 0.1939965962 0.0000000000 + … + +ファイル形式 +^^^^^^^^^^^^ + +- :math:`[` int01 :math:`]` :math:`[` int02 :math:`]` :math:`[` int03 :math:`]` :math:`[` int04 :math:`]` :math:`[` int05 :math:`]` :math:`[` int06 :math:`]` :math:`[` int07 :math:`]` :math:`[` int08 :math:`]` :math:`[` double01 :math:`]` :math:`[` double02 :math:`]` + +パラメータ +^^^^^^^^^^ + +- :math:`[` int01 :math:`]`, + :math:`[` int03 :math:`]`, :math:`[` int05 :math:`]`, + :math:`[` int07 :math:`]` + + **形式 :** int型 + + **説明 :** サイト番号を指定する整数。 + :math:`[` int01 :math:`]` が :math:`i` サイト、 :math:`[` int03 :math:`]` が :math:`j` サイト、 :math:`[` int05 :math:`]` が :math:`k` サイト、 :math:`[` int07 :math:`]` が :math:`l` サイトを表します。 + +- :math:`[` int02 :math:`]`, + :math:`[` int04 :math:`]`, :math:`[` int06 :math:`]`, + :math:`[` int08 :math:`]` + + **形式 :** int型 + + | **説明 :** スピンを指定する整数。 + :math:`[` int02 :math:`]` が :math:`\sigma_1` 、 :math:`[` int04 :math:`]` が :math:`\sigma_2` 、 :math:`[` int06 :math:`]` が :math:`\sigma_3` 、 :math:`[` int08 :math:`]` が :math:`\sigma_4` に対応します。 + | 0: アップスピン + | 1: ダウンスピン + | を表します。 + +- :math:`[` double01 :math:`]`, :math:`[` double02 :math:`]` + + **形式 :** double型 + + | **説明 :** + :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle` の値を表します。 + | :math:`[` double01 :math:`]` が実部、 :math:`[` double02 :math:`]` が虚部を表します。 + +xxx\_ls\_out\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~~ + +Power Lanczos法により求めた :math:`\langle H \rangle`, +:math:`\langle H^2\rangle` および最適化パラメータ :math:`\alpha` の順に出力されます。 +``ModPara`` 指定ファイルで ``NVMCCalMode`` =1, ``NLanczosmode`` =1, +2に設定することで計算されます。 +xxxには ``CDataFileHead`` で指定されるヘッダが、yyyには ``ModPara`` ファイルの ``NDataIdxStart``, +``NDataQtySmp`` に従い ``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp`` の順に記載されます。 + +xxx\_ls\_cisajs\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~~~~~ + +Power Lanczos法により求めた, +OneBodyG指定ファイルで指定された一体グリーン関数 :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle` の計算結果を出力します。 +ファイル形式はxxx\_cisajs\_yyy.datファイルと同じです。 ``ModPara`` 指定ファイルで ``NVMCCalMode`` =1, +``NLanczosmode`` =2に設定することで計算されます。 + +xxx\_ls\_cisajscktalt\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Power Lanczos法により求めた, +TwoBodyG指定ファイルで指定された二体グリーン関数 :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle` の計算結果を出力します。ファイル形式はxxx\_cisajscktalt\_yyy.datファイルと同じです。 ``ModPara`` 指定ファイルで ``NVMCCalMode`` += 1, ``NLanczosmode`` = 2 に設定することで計算されます。 diff --git a/doc/jp/standard.rst b/doc/jp/standard.rst new file mode 100644 index 00000000..1f53fc2d --- /dev/null +++ b/doc/jp/standard.rst @@ -0,0 +1,673 @@ +.. include:: ../bib/ref.txt + +.. _HowToStandard: + +スタンダードモード用入力ファイル書式 +==================================== + +スタンダードモード用入力ファイルは次のような格好をしています。 + +:: + + W = 2 + L = 4 + model = "spin" + + lattice = "triangular lattice" + //mu = 1.0 + // t = -1.0 + // t' = -0.5 + // U = 8.0 + //V = 4.0 + //V'=2.0 + J = -1.0 + J'=-0.5 + // nelec = 8 + +大まかなルールは次のとおりです。 + +- 各行にはひと組ずつキーワード(``=`` の前)と + パラメーター(``=`` の後)が書かれており間は ``=`` で区切られています。 + +- 各キーワードは順不同に記述できます。 + +- 空白行、または ``//`` で始まる行(コメントアウト)は読み飛ばされます。 + +- 各キーワード、パラメーターの大文字 :math:`\cdot` 小文字は区別されません。 + ダブルクオート、空白は無視されます。 + +- 必ず指定しなければいけないパラメーター、 + 指定しない場合デフォルト値が使われるパラメーター、 + (他のパラメーターの組み合わせによっては)使われないパラメーターが存在します。 + 使われないパラメーターが指定された場合にはプログラムは終了し、 + 入力ファイルをチェックするようにというメッセージが英語で表示されます。 + +次に各キーワードの説明をします。 + +計算の種類に関する必須パラメーター +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +- ``model`` + + **形式 :** 文字列( ``"Fermion Hubbard"``, ``"Spin"``, + ``"Kondo Lattice"`` , ``"Fermion HubbardGC"``, ``"SpinGC"``, + ``"Kondo LatticeGC"`` のいずれか) + + **説明 :** 計算対象の模型を指定します。 + 文字列 ``"Fermion Hubbard"`` は、カノニカル集団のフェルミ粒子Hubbard模型 + + .. math:: + :label: hubbard + + \begin{aligned} + H = - \mu \sum_{i \sigma} c^\dagger_{i \sigma} c_{i \sigma} + - \sum_{i \neq j \sigma} t_{i j} c^\dagger_{i \sigma} c_{j \sigma} + + \sum_{i} U n_{i \uparrow} n_{i \downarrow} + + \sum_{i \neq j} V_{i j} n_{i} n_{j}, + \end{aligned} + + 文字列 ``"Spin"`` はカノニカル集団のスピン模型 + ( :math:`\sigma_1, \sigma_2=x, y, z` ) + + .. math:: + :label: spin + + \begin{aligned} + H &= -h \sum_{i} S_{i z} - \Gamma \sum_{i} S_{i x} + D \sum_{i} S_{i z} S_{i z} + \nonumber \\ + &+ \sum_{i j, \sigma_1}J_{i j \sigma_1} S_{i \sigma_1} S_{j \sigma_1}+ \sum_{i j, \sigma_1 \neq \sigma_2} J_{i j \sigma_1 \sigma_2} S_{i \sigma_1} S_{j \sigma_2} , + \end{aligned} + + 文字列 ``"Kondo Lattice"`` はカノニカル集団の近藤格子模型 + (Hubbard模型と同様に :math:`U` と :math:`J` を入れることも可能) + + .. math:: + :label: kondo + + \begin{aligned} + H &= - \mu \sum_{i \sigma} c^\dagger_{i \sigma} c_{i \sigma} + - t \sum_{\langle i j \rangle \sigma} c^\dagger_{i \sigma} c_{j \sigma} + + \frac{J}{2} \sum_{i} \left\{ + S_{i}^{+} c_{i \downarrow}^\dagger c_{i \uparrow} + + S_{i}^{-} c_{i \uparrow}^\dagger c_{i \downarrow} + + S_{i z} (n_{i \uparrow} - n_{i \downarrow})\right\} + \nonumber \\ + & + \sum_{i} U n_{i \uparrow} n_{i \downarrow} + + \sum_{i \neq j} V_{i j} n_{i} n_{j} + , + \end{aligned} + + に対応します。 また、 + ``"Fermion HubbardGC"`` 、 ``"SpinGC"`` 、 ``"Kondo LatticeGC"`` はそれぞれ + :math:`S_z` 非保存でのフェルミ粒子Hubbard模型[式 :eq:`hubbard` ]、 + スピン模型[式 :eq:`spin` ]、 + 近藤格子模型[式 :eq:`kondo` ]に対応します。 + :math:`{\mathcal H}\Phi` との互換性からGC(=グランドカノニカル)と付いていますが、 + 粒子数は保存していますのでご注意ください。 + +- ``lattice`` + + **形式 :** 文字列( ``"Chain Lattice"``, ``"Square Lattice"``, + ``"Triangular Lattice"``, ``"Honeycomb Lattice"``, ``"Kagome"``, + ``"Ladder"`` のいずれか) + + **説明 :** 格子の形状を指定します。 上記文字列はそれぞれ1次元鎖(Fig. + [ :num:`latticepng` ](a))、 2次元正方格子(Fig. + [ :num:`latticepng` ](b))、 2次元三角格子(Fig. + [ :num:`latticepng` ](c))、 2次元異方的蜂の巣格子(Fig. + [ :num:`honeycombpng` ])、 カゴメ格子(Fig. [ :num:`kagomepng` ])、 + 梯子格子(Fig. [ :num:`ladderpng` ])に対応します。 + + .. _latticepng: + + .. figure:: ../figs/chap04_1_lattice.png + :width: 15.00000cm + + (a)1次元鎖、(b)2次元正方格子、(c)2次元三角格子の模式図. + ホッピング積分、オフサイトクーロン積分、スピン結合は、 + 再近接サイト間(マゼンタの実線)ではそれぞれ :math:`t,V,J` となり、 + 次近接サイト間(緑の破線)ではそれぞれ :math:`t',V',J'` となります。 + + .. _honeycombpng: + + .. figure:: ../figs/chap04_1_honeycomb.png + :width: 15.00000cm + + 2次元異方的蜂の巣格子の模式図. + ホッピング積分、オフサイトクーロン積分、スピン結合は、 + ボンドの方向によって異なります。 + また、次近接のホッピング積分、オフサイトクーロン積分、スピン結合 + には対応していません。 + + .. _kagomepng: + + .. figure:: ../figs/kagome.png + :width: 15.00000cm + + カゴメ格子の模式図. + + .. _ladderpng: + + .. figure:: ../figs/ladder.png + :width: 10.00000cm + + 梯子格子の模式図. + +格子に関するパラメーター +~~~~~~~~~~~~~~~~~~~~~~~~ + +1次元鎖 +^^^^^^^ + +Fig. [ :num:`latticepng` ](a) + +- ``L`` + + **形式 :** 自然数 + + **説明 :** 鎖の長さを指定します. + +梯子格子 +^^^^^^^^ + +Fig. [ :num:`ladderpng` ] + +- ``L`` + + **形式 :** 自然数 + + **説明 :** 梯子の長さを指定します. + +- ``W`` + + **形式 :** 自然数 + + **説明 :** 梯子の本数を指定します. + +.. _unitlatticepng: + +.. figure:: ../figs/chap04_1_unitlattice.png + :width: 15.00000cm + + 三角格子において、 :math:`{\vec a}_0 = (6, 2), {\vec a}_1 = (2, 4)` とした場合のセル形状。 + :math:`{\vec a}_0` (マゼンタ)および :math:`{\vec a}_1` (グリーン) + で囲まれた部分(サイト数は20)が計算するセルとなる。 + +正方格子、 三角格子、 蜂の巣格子、 カゴメ格子 +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +正方格子[Fig. [ :num:`latticepng` ](b)]、 三角格子[Fig. [ :num:`latticepng` ](c)]、 蜂の巣格子(Fig. [ :num:`honeycombpng` ])、 カゴメ格子(Fig. [ :num:`kagomepng` ]) + +これらの格子では、標準の単位胞(図中の黒の破線を参照)を用いて格子形状を指定する方法と、 +それらとは別の方向に格子ベクトルを取る方法が選択できます。 +また、両方を指定した場合にはプログラムを終了します。 + +- ``W``, ``L`` + + **形式 :** 自然数 + + **説明 :** 標準の単位胞の並び方を指定します。 + +- ``a0W``, ``a0L``, ``a1W``, ``a1L`` + + **形式 :** 自然数 + + **説明 :** + 格子を指定する2本のベクトル( :math:`{\vec a}_0, {\vec a}_1`) + を指定します (Fig. [ :num:`unitlatticepng` ])。 + これらのベクトルは標準の並進ベクトルを基底とした座標(Fractional + coordinate) で指定されます。 + +スタンダードモードで出力される ``lattice.gp`` (1次元鎖、梯子格子では出力されません) +というファイルを使うと、 +自分の意図した通りの格子のとり方になっているかどうかを確かめる事が出来ます。 +このファイルは、次のようにして ``gnuplot`` に読み込ませることが出来ます。 + +:: + + $ gnuplot lattice.gp + +副格子 +~~~~~~ + +以下パラメータを用いると変分波動関数のペア軌道部分に副格子の周期性を持たせることが出来ます。 + +- ``a0Wsub``, ``a0Lsub``, ``a1Wsub``, ``a1Lsub``, ``Wsub``, ``Lsub`` + + **形式 :** 自然数。デフォルトでは ``a0Wsub=a0W``, ``a0Lsub=a0L``, + ``a1Wsub=a1W``, ``a1Lsub=a1L``, ``Wsub=W``, ``Lsub=L`` となる。 + すなわち副格子を用いず、変分波動関数のすべてのパラメーターが独立に変化する。 + + **説明 :** これらのパラメーターの指定の仕方は ``a0W``, ``a0L``, + ``a1W``, ``a1L``, ``W``, ``L`` と同様です。 + ただし、元の計算セルが副格子に整合しない場合にはプログラムを終了します。 + +ハミルトニアンの各項の係数 +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +デフォルト値は特に記載されていないものについては0に設定してあります。 +型が複素数のパラメータは「実部, 虚部」(間に“,”)の形式で指定し、 +実数の場合には「実部」で指定が可能です。 + +局所項 +^^^^^^ + +- ``mu`` + + **形式 :** 実数 + + **説明 :** + Hubbardおよび近藤格子模型での化学ポテンシャルを指定します。 + +- ``U`` + + **形式 :** 実数 + + **説明 :** + Hubbardおよび近藤格子模型でのオンサイトクーロン積分を指定します。 + +- ``Jx``, ``Jy``, ``Jz``, ``Jxy``, ``Jyx``, ``Jxz``, ``Jzx``, ``Jyz``, + ``Jzy`` + + **形式 :** 実数 + + **説明 :** + 近藤格子模型での、局在電子と遍歴電子のスピン結合を指定します。 + また対角項について, + ``Jx, Jy, Jz`` を指定する代わりに、パラメータ ``J`` を指定すると + ``Jx = Jy = Jz = J`` が代入されます。 ``J`` を指定した上で ``Jx``, + ``Jy``, ``Jz`` を指定した場合はプログラムを終了します。 + +- ``h``, ``Gamma``, ``D`` + + **形式 :** 実数 + + **説明 :** + スピン模型での縦磁場、横磁場、異方性パラメータを指定します。 + +下記の非局所項は、梯子格子の場合とそれ以外(１次元鎖、矩形格子、三角格子、蜂の巣格子、カゴメ格子) +の場合で指定の仕方が異なります。 +また、各格子で指定可能なパラメーターをTable +[table\_interactions]に表します。 + +============================ ======= ======== ======== ========== ========== ======== +相互作用 1次元鎖 矩形格子 三角格子 蜂の巣格子 カゴメ格子 梯子格子 +============================ ======= ======== ======== ========== ========== ======== +``J``, ``t``, ``V`` (省略形) OK OK OK OK OK NG +``J'``, ``t'``, ``V'`` OK OK OK OK OK NG +``J0``, ``t0``, ``V0`` OK OK OK OK OK OK +``J1``, ``t1``, ``V1`` NG OK OK OK OK OK +``J2``, ``t2``, ``V2`` NG NG OK OK OK OK +``J1'``, ``t1'``, ``V1'`` NG NG NG NG NG OK +``J2'`` , ``t2'``, ``V2'`` NG NG NG NG NG OK +============================ ======= ======== ======== ========== ========== ======== + +Table: 各格子で定義可能な相互作用一覧。ただし、スピン結合については行列として与えることが可能。 + +非局所項[梯子格子] +^^^^^^^^^^^^^^^^^^ + +Fig. [ :num:`ladderpng` ] + +- ``t0``, ``t1``, ``t1'``, ``t2``, ``t2'`` + + **形式 :** 複素数 + + **説明 :** 梯子格子でのホッピング(Fig. + [ :num:`ladderpng` ]参照)を指定します。 + +- ``V0``, ``V1``, ``V1'``, ``V2``, ``V2'`` + + **形式 :** 実数 + + **説明 :** 梯子格子でのオフサイトクーロン積分 (Fig. + [ :num:`ladderpng` ]参照)を指定します。 + +- ``J0x``, ``J0y``, ``J0z``, ``J0xy``, ``J0yx``, ``J0xz``, ``J0zx``, + ``J0yz``, ``J0zy`` + +- ``J1x``, ``J1y``, ``J1z``, ``J1xy``, ``J1yx``, ``J1xz``, ``J1zx``, + ``J1yz``, ``J1zy`` + +- ``J1'x``, ``J1'y``, ``J1'z``, ``J1'xy``, ``J1'yx``, ``J1'xz``, + ``J1'zx``, ``J1'yz``, ``J1'zy`` + +- ``J2x``, ``J2y``, ``J2z``, ``J2xy``, ``J2yx``, ``J2xz``, ``J2zx``, + ``J2yz``, ``J2zy`` + +- ``J2'x``, ``J2'y``, ``J2'z``, ``J2'xy``, ``J2'yx``, ``J2'xz``, + ``J2'zx``, ``J2'yz``, ``J2'zy`` + + **形式 :** 実数 + + **説明 :** 梯子格子でのスピン相互作用 (Fig. + [ :num:`ladderpng` ]参照)を指定します。 + また対角項について、例えば ``J0x, J0y, J0z`` を指定する代わりに + パラメータ ``J0`` を指定すると + ``J0x = J0y = J0z = J0`` が代入されます。 + ``J0`` を指定した上で ``J0x, J0y, J0z`` 等も指定した場合はプログラムを終了します。 + ``J1``, ``J1'``, ``J2``, ``J2'`` についても同様です。 + +非局所項 (梯子格子以外) +^^^^^^^^^^^^^^^^^^^^^^^ + +Figs. [ :num:`latticepng` ], [ :num:`honeycombpng` ], [ :num:`kagomepng` ])] + +- ``t0``, ``t1``, ``t2`` + + **形式 :** 複素数 + + **説明 :** + Hubbardおよび近藤格子模型での、最近接サイト間の各方向のホッピングを指定します。 + Figs. [ :num:`latticepng` ], + [ :num:`honeycombpng` ],[ :num:`kagomepng` ] + のそれぞれのボンド(異なる線種で表されています)に対応するホッピングに関して別々の値を取るように + 刷ることが可能です。 また、最近接ホッピング( ``t0``, ``t1``, + ``t2``)に関して、 ボンド方向依存性(もしくは異方性) + がない場合は ``t0``, ``t1``, ``t2`` を + 別々に指定する代わりにパラメータ ``t`` で一括指定( ``t0 = t1 = t2 = t``) + を行うことが出来ます。 + ``t`` と ``t0`` 等の両方が指定された場合にはプログラムを終了します。 + +- ``V0``, ``V1``, ``V2`` + + **形式 :** 実数 + + **説明 :** + Hubbardおよび近藤格子模型での、最近接サイト間のCoulomb積分を指定します。 + また、最近接サイト間のCoulomb積分( ``V0``, ``V1``, ``V2``)に関して、 + ボンド方向依存性(もしくは異方性) がない場合は ``V0``, ``V1``, + ``V2`` を + 別々に指定する代わりにパラメータ ``V`` で一括指定( ``V0 = V1 = V2 = V``) + を行うことが出来ます。 + ``V`` と ``V0`` 等の両方が指定された場合にはプログラムを終了します。 + +- ``J0x``, ``J0y``, ``J0z``, ``J0xy``, ``J0yx``, ``J0xz``, ``J0zx``, + ``J0yz``, ``J0zy`` + +- ``J1x``, ``J1y``, ``J1z``, ``J1xy``, ``J1yx``, ``J1xz``, ``J1zx``, + ``J1yz``, ``J1zy`` + +- ``J2x``, ``J2y``, ``J2z``, ``J2xy``, ``J2yx``, ``J2xz``, ``J2zx``, + ``J2yz``, ``J2zy`` + + **形式 :** 実数 + + **説明 :** + スピン模型での、最近接サイト間のスピン相互作用を指定します。 + また対角項について、例えば ``J0x, J0y, J0z`` を指定する代わりに + パラメータ ``J0`` を指定すると + ``J0x = J0y = J0z = J0`` が代入されます。 + ``J0`` を指定した上で ``J0x, J0y, J0z`` 等も指定した場合はプログラムを終了します。 + ``J1``, ``J2`` についても同様です。 + + 最近接スピン間相互作用のボンド方向依存性がない場合には、 ``Jx``, + ``Jy``, ``Jz``, ``Jxy``, ``Jyx``, ``Jxz``, ``Jzx``, ``Jyz``, ``Jzy`` + を指定すると、 ``J0x = J1x = J2x = Jx`` のようにすべてのボンド方向のスピン間相互作用に + 同じ値を代入することが出来ます。 + ``Jx`` :math:`\sim` ``Jzy`` 系列のどれかと ``J0x`` :math:`\sim` ``J2zy`` 系列のどれかを両方指定した + 場合にはプログラムを終了します。 + 以下に最近接間スピン相互作用の指定方法の例を挙げます。 + + - ボンド方向依存性、スピン方向依存性、相互作用の非対角成分( :math:`J_{x y}` 等)がない場合 + + ``J`` を指定 + + - ボンド方向依存性、相互作用の非対角成分がなく、スピン方向依存性がある場合 + + ``Jx, Jy, Jz`` のうち ``0`` でないものを指定 + + - ボンド方向依存性がなく、スピン方向依存性、相互作用の非対角成分がある場合 + + ``Jx, Jy, Jz, Jxy, Jyz, Jxz, Jyx, Jzy, Jzx`` のうち ``0`` でないものを指定 + + - スピン方向依存性、相互作用の非対角成分がなく、ボンド方向依存性がある場合 + + ``J0, J1, J2`` のうち ``0`` でないものを指定 + + - スピン方向依存性がなく、ボンド方向依存性、相互作用の非対角成分がある場合 + + ``J0x, J0y, J0z, J1x, J1y, J1z, J2x, J2y, J2z`` のうち ``0`` でないものを指定 + + - ボンド方向依存性、スピン方向依存性、相互作用の非対角成分がある場合 + + ``J0x`` :math:`\sim` ``J2zy`` のすべてのうち ``0`` でないものを指定 + +- ``t'`` + + **形式 :** 複素数 + + **説明 :** + Hubbardおよび近藤格子模型での、次近接サイト間の各方向のホッピングを指定します。 + +- ``V'`` + + **形式 :** 実数 + + **説明 :** + Hubbardおよび近藤格子模型での、次近接サイト間のCoulomb積分を指定します。 + +- ``J'x``, ``J'y``, ``J'z``, ``J'xy``, ``J'yx``, ``J'xz``, ``J'zx``, + ``J'yz``, ``J'zy`` + + **形式 :** 実数 + + **説明 :** + スピン模型での、次近接サイト間のスピン相互作用を指定します。 + また対角項について、 ``J'x, J'y, J'z`` を指定する代わりに + パラメータ ``J'`` を指定すると + ``J'x = J'y = J'z = J'`` が代入されます。 + ``J'`` を指定した上で ``J'x, J'y, J'z`` も指定した場合はプログラムを終了します。 + +- ``phase0``, ``phase1`` + + **形式 :** 実数 (デフォルトでは``0.0``) + + **説明 :** + 計算するセルの境界をまたいだホッピング項に付く因子の位相を指定することが出来ます + (単位:度)。 + :math:`\vec{a}_0` 方向、 :math:`\vec{a}_1` 方向それぞれ別の位相因子を用いることが出来ます。 + １次元系では ``phase0`` のみ使用できます。 + 例えば、 :math:`i` サイトから :math:`j` サイトへのホッピングで、 + 正の方向に境界をまたいだ場合には次のようになります。 + + .. math:: + + \begin{aligned} + \exp(i \times {\rm phase0} \times \pi/180) \times t {\hat c}_{j \sigma}^\dagger {\hat c}_{i \sigma} + + \exp(-i \times {\rm phase0} \times\pi/180) \times t^* {\hat c}_{i \sigma}^\dagger {\hat c}_{j \sigma} + \end{aligned} + +計算条件のパラメーター +~~~~~~~~~~~~~~~~~~~~~~ + +- ``nelec`` + + **形式 :** int型 (1以上、必須) + + **説明 :** 伝導電子の数。 + :math:`\uparrow` 電子と :math:`\downarrow` 電子の個数を足したものを入力してください。 + +- ``NVMCCalMode`` + + **形式 :** int型 (デフォルト値 = 0) + + **説明 :** [0] 変分パラメータの最適化、[1] 1 体・2 + 体のグリーン関数の計算。 + +- ``NDataIdxStart`` + + **形式 :** int型 (デフォルト値 = 1) + + **説明 :** 出力ファイルの付加番号。 ``NVMCCalMode`` = 0 + の場合は ``NDataIdxStart`` が出力され、 ``NVMCCalMode`` = 1 + の場合は、 ``NDataIdxStart`` から連番で ``NDataQtySmp`` 個のファイルを出力します。 + +- ``NDataQtySmp`` + + **形式 :** int型 (デフォルト値 = 1) + + **説明 :** 出力ファイルのセット数。 ``NVMCCalMode`` = 1 + の場合に使用します。 + +- ``NSPGaussLeg`` + + **形式 :** int型 + (1以上、デフォルト値は:math:`S_z` 保存系で ``2Sz=0`` の時は ``8``) + + **説明 :** + スピン量子数射影の :math:`\beta` 積分( :math:`S^y` 回転)のGauss-Legendre求積法の分点数。 + :math:`S_z` 保存系で ``2Sz=0`` ではない場合と :math:`S_z` 非保存系では使われません。 + +- ``NSPStot`` + + **形式 :** int型 (0以上、デフォルト値 = 0) + + **説明 :** 全スピン量子数。 + +- ``2Sz`` + + **形式 :** int型 (0以上、デフォルト値 = 0) + + **説明 :** スピン量子数 :math:`S_z` 。 + +- ``NMPTrans`` + + **形式 :** int型 (1以上、デフォルト値は1) + + **説明 :** 運動量・格子対称性の量子数射影の個数。 + TransSymファイルで指定した重みで上から ``NMPTrans`` 個まで使用する。射影を行わない場合は1に設定する。 + +- ``NSROptItrStep`` + + **形式 :** int型 (1以上、デフォルト値 = 1000) + + **説明 :** SR + 法で最適化する場合の全ステップ数。 ``NVMCCalMode`` =0の場合のみ使用されます。 + +- ``NSROptItrSmp`` + + **形式 :** int型 (1以上数、デフォルト値 = ``NSROptItrStep``/10) + + **説明 :** + ``NSROptItrStep`` ステップ中、最後の ``NSROptItrSmp`` ステップでの各変分パラメータの平均値を最適値とする。 ``NVMCCalMode`` =0の場合のみ使用されます。 + +- ``DSROptRedCut`` + + **形式 :** double型 (デフォルト値 = 0.001) + + **説明 :** SR + 法安定化因子。手法論文[Tahara2008_ ]の :math:`\varepsilon_{\rm wf}` に対応。 + +- ``DSROptStaDel`` + + **形式 :** double型 (デフォルト値 = 0.02) + + **説明 :** SR + 法安定化因子。手法論文[Tahara2008_ ]の :math:`\varepsilon` に対応。 + +- ``DSROptStepDt`` + + **形式 :** double型 (デフォルト値 = 0.02) + + **説明 :** + SR法で使用する刻み幅。手法論文[Tahara2008_ ]の :math:`\Delta t` に対応。 + +- ``NVMCWarmUp`` + + **形式 :** int型 (1以上、デフォルト値=10) + + **説明 :** マルコフ連鎖の空回し回数。 + +- ``NVMCInterval`` + + **形式 :** int型 (1以上、デフォルト値=1) + + **説明 :** サンプル間のステップ間隔。ローカル更新を ``Nsite`` × + ``NVMCInterval`` 回行います。 + +- ``NVMCSample`` + + **形式 :** int型 (1以上、デフォルト値=1000) + + **説明 :** 期待値計算に使用するサンプル数。 + +- ``RndSeed`` + + **形式 :** int型 (デフォルト値 = 123456789) + + **説明 :** 乱数の初期seed。MPI 並列では各計算機に ``RndSeed`` +my + rank+1 で初期seed が与えられます。 + +- ``NSplitSize`` + + **形式 :** int型 (1以上、デフォルト値=1) + + **説明 :** MPI内部並列を行う場合の並列数。 + +- ``NStore`` + + **形式 :** int型 (0もしくは1、デフォルト値=1) + + **説明 :** + 期待値 :math:`\langle O_k O_l \rangle` を計算するとき行列-行列積にして高速化するオプション(1で機能On、モンテカルロサンプリング数に応じてメモリの消費が増大します [1]_)。 + +- ``NSRCG`` + + **形式 :** int型 (0もしくは1、デフォルト値=0) + + **説明 :** SR法で連立一次方程式 :math:`Sx=g` + を解くときに、 :math:`S` + を陽に構築せずに解くことでメモリを削減する [2]_ オプション[NeuscammanUmrigarChan_ ](1で機能On, + ``NStore`` は1に固定されます)。 + +- ``ComplexType`` + + **形式 :** int型 + (``0`` もしくは ``1`` 、デフォルト値は :math:`S_z` 保存系では ``0`` 、非保存系では ``1``) + + **説明 :** + ``0`` のとき変分パラメータの実部のみを、 ``1`` のとき実部/虚部両方を最適化します。 + +- ``OutputMode`` + + **形式 :** ``"none"``, ``"correlation"``, ``"full"`` のいずれか + (デフォルトは``correlation``) + + **説明 :** 計算を行う相関関数を指定します。 + ``"none"`` の場合は相関関数を計算しません。 + ``"correlation"`` を指定した場合には、付属のユーティリティ + ``fourier`` でサポートするものに対応した相関関数を計算します。 + 詳しくは ``doc/fourier/`` 内のマニュアルを参照してください。 + ``"full"`` を指定した場合には、 + 1体部分はすべての :math:`i, j, \sigma, \sigma'` について + :math:`\langle c_{i \sigma}^{\dagger}c_{j \sigma'} \rangle` を、 + 2体部分はすべての :math:`i_1, i_2, i_3, i_4, \sigma_1, \sigma_2, \sigma_3, \sigma_4` について + :math:`\langle c_{i_1 \sigma_1}^{\dagger}c_{i_2 \sigma_2} c_{i_3 \sigma_3}^{\dagger}c_{i_4 \sigma_4} \rangle` + を計算します。 + スピン系の演算子はBogoliubov表現により生成消滅演算子で表されています。 + 詳しくは :ref:`BogoliubovRep` をご覧ください。 + +- ``CDataFileHead`` + + **形式 :** string型 (デフォルト値 ``"zvo"``) + + **説明 :** + アウトプットファイルのヘッダ。例えば、一体のGreen関数の出力ファイル名が **xxx\_cisajs.dat** として出力されます(xxxに ``CDataFileHead`` で指定した文字が記載)。 + +- ``CParaFileHead`` + + **形式 :** string型 (デフォルト値 ``"zqp"``) + + **説明 :** + 最適化された変分パラメータの出力ファイル名のヘッダ。最適化された変分パラメータが **xxx\_opt.dat** ファイルとして出力されます(xxxに ``CParaFileHead`` で指定した文字が記載)。 + +.. [1] + + 使用メモリ量が、 :math:`O(N_\text{p}^2)` から + :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})` になります。 + +.. [2] + 使用メモリ量は、 :math:`O(N_\text{p}) + O(N_\text{p}N_\text{MCS})` + です。 + diff --git a/doc/jp/start.rst b/doc/jp/start.rst new file mode 100644 index 00000000..e53739ac --- /dev/null +++ b/doc/jp/start.rst @@ -0,0 +1,350 @@ +How to use mVMC? +================ + +要件 +---- + +mVMCのコンパイル :math:`\cdot` 使用には次のものが必要です。 + +- Cコンパイラ (インテル、富士通、GNUなど) + +- MPIライブラリ + +- LAPACKライブラリ (インテルMKL, 富士通, ATLASなど) + +- オプション：ScaLAPACKライブラリ + +.. note:: + + **intelコンパイラーでの設定** + + intelコンパイラを使用する場合には、コンパイラに付属の設定用スクリプトを使用するのが簡単です。 + + 64ビットOSでbashを使っている場合には + + .. code-block:: bash + + $ source /opt/intel/bin/compilervars.sh intel64 + + または + + .. code-block:: bash + + $ source /opt/intel/bin/iccvars.sh intel64 + $ source /opt/intel/mkl/bin/mklvars.sh + + 等を ``~/.bashrc`` に記載してください。 + 詳しくはお手持ちのコンパイラ、ライブラリのマニュアルをお読みください。 + +インストール方法 +---------------- + +mVMC は次の場所からダウンロードできます。 +https://github.com/issp-center-dev/mVMC/releases + +ダウンロードしたファイルを次のように展開してください。 + +.. code-block:: bash + + $ tar xzvf mVMC-xxx.tar.gz + +mVMCは次の2通りの方法でインストールできます。 + +``mVMCconfig.sh`` を使う方法 +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +展開したディレクトリのなかにある ``mVMCconfig.sh`` スクリプトを次のように実行してください。 +(物性研システムB”sekirei”の場合) + +.. code-block:: bash + + $ bash mVMCconfig.sh sekirei + +これによりコンパイル環境設定ファイル ``make.sys`` が ``src/`` ディレクトリに作られます。 +``mVMCconfig.sh`` の引数は次のものに対応しています。 + +- ``sekirei`` : 物性研究所システムB "sekirei" + +- ``kei`` : 京コンピューターおよび物性研究所システムC "maki"(FX10) + +- ``intel-openmpi`` : Intel コンパイラ + OpenMPI + +- ``intel-mpich`` : Intelコンパイラ + MPICH2 + +- ``intel-intelmpi`` : Intelコンパイラ + IntelMPI + +- ``gcc-mpich-mkl`` : GCC + MPICH + MKL + +- ``gcc-openmpi`` : GCC + OpenMPI + +``make.sys`` の中身は次のようになっています(物性研システムB +"sekirei"の場合)。 + +.. code-block:: makefile + + CC = mpicc + F90 = mpif90 + CFLAGS = -O3 -no-prec-div -xHost -qopenmp -Wno-unknown-pragmas + FFLAGS = -O3 -implicitnone -xHost + LIBS = -L $(MKLROOT)/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 \ + -lmkl_intel_thread -lmkl_core -lmkl_blacs_sgimpt_lp64 -lpthread -lm + SFMTFLAGS = -no-ansi-alias -DHAVE_SSE2 + +となります。それぞれのマクロ(変数)の説明は次のとおりです。 + +- ``CC`` : C コンパイラー( ``mpicc``, ``mpifccpx`` など) + +- ``F90`` : fortran コンパイラー( ``ifort``, ``frtpx`` など) + +- ``LIBS`` : リンカーオプション。 + +- ``CFLAGS`` : C コンパイルオプション。 + +- ``FFLAGS`` : fortran コンパイルオプション。 + +これでコンパイルのための準備が整います。その後 + +.. code-block:: bash + + $ make mvmc + +とすることで実行可能ファイル ``vmc.out`` 、 ``vmcdry.out`` が ``src/内に`` 生成されるので、 +このディレクトリにパスを通すか、 +パスの通っている場所にシンボリックリンクを作ってください。 + +実行ファイルにパスを通す時には、次のようにします。 +``$ export PATH=${PATH}:`` ``/src/`` +この設定を常に残すには、例えばログインシェルが ``bash`` の場合には +``~/.bashrc`` ファイルに上記のコマンドを記載します。 + +cmakeを使う方法 +~~~~~~~~~~~~~~~ + +mVMCを展開したディレクトリのパスを$PathTomvmc、ビルドディレクトリを$HOME/build/mvmc +(任意の場所を指定可能)とした場合に、 + +.. code-block:: bash + + cd $HOME/build/mvmc + cmake -DCONFIG=gcc $PathTomvmc + make + +でコンパイルすることができます。コンパイル後、 ``$HOME/build/mvmc`` +直下に ``src`` フォルダが作成され、実行ファイルである ``vmc.out`` がそのフォルダ内に作成されます。 + +なお、上の例ではgccコンパイラを前提としたコンパイルになっていますが、 + +- ``sekirei`` : 物性研究所システムB "sekirei" + +- ``fujitsu`` : 富士通コンパイラ + +- ``intel`` : intelコンパイラ + Linux PC + +- ``gcc`` : GCC + Linux PC + +のオプションが用意されています。以下、mVMCを展開したディレクトリでビルドする例を示します(intelコンパイラの場合)。 + +.. code-block:: bash + + mkdir ./build + cd ./build + cmake -DCONFIG=intel ../ + make + +実行後、 ``build/`` フォルダ直下に ``src/`` フォルダが作成され、 ``vmc.out`` が ``src/`` フォルダ内に作成されます。 +また、LAPACKに代わりScaLAPACKを計算に使用することが可能です。その場合には、 + +:: + + -DUSE_SCALAPACK=ON -DSCALAPACK_LIBRARIES="xxx" + +をcmakeをする際に付け加えてください(xxxにはScaLAPACKを利用するためのライブラリ一式を指定します)。 +なお、コンパイラを変更しコンパイルし直したい場合には、都度buildフォルダごと削除を行った上で、新規に上記作業を行うことをお薦めします。 + +.. note:: + + sekirei で cmake を利用するには + + .. code-block:: bash + + $ source /home/issp/materiapps/tool/env.sh + + をあらかじめ実行する必要があります。 + + またScaLAPACK を利用するには + + .. code-block:: bash + + cmake -DCONFIG=sekirei ../ -DUSE_SCALAPACK=ON + + を行うと、デフォルトで + + :: + + -DSCALAPACK_LIBRARIES="\${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 + -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core + -lmkl_blacs_sgimpt_lp64" + +が指定されます。ライブラリへのパスが異なる場合には、 ``-DSCALAPACK_LIBRARIES`` を適宜変更してください。 + +ディレクトリ構成 +---------------- + +| mVMC-xxx.gzを解凍後に構成されるディレクトリ構成を以下に示します。 +| ├──COPYING +| ├──mVMCconfig.sh +| ├──doc/ +| │      ├──bib/ +| │      │      ├──elsart-num\_mod.bst +| │      │      └──userguide.bib +| │      ├──figs/ +| │      │      ├──\*.pdf +| │      │      └──\*.xbb +| │      ├──fourier/ +| │      │      ├──en/ +| │      │      ├──figs/ +| │      │      └──ja/ +| │      ├──jp/ +| │      │      └──\*.tex +| │      └──en/ +| │             └──\*.tex +| ├──sample/ +| │      └──Standard/ +| │                  ├──Hubbard/ +| │                  │      ├─square/ +| │                  │      │      ├──StdFace.def +| │                  │      │      └──reference/ +| │                  │      │                 └──\*\*.dat +| │                  │      └─triangular/ +| │                  │            └── :math:`\cdots` +| │                  ├──Kondo/ +| │                  │      └─chain/ +| │                  │            └── :math:`\cdots` +| │                  └──Spin/ +| │                              ├─HeisenbergChain/ +| │                              │      └── :math:`\cdots` +| │                              ├─HeisenbergSquare/ +| │                              │      └── :math:`\cdots` +| │                              └─Kagome/ +| │                                     └── :math:`\cdots` +| ├──src/ +| │          ├──mVMC/ +| │          │      ├─ \*\*.c +| │          │      └──include/ +| │          │              └──\*\*.h +| │          ├──ComplexUHF/ +| │          │      ├─ \*\*.c +| │          │      └──include/ +| │          │              └──\*\*.h +| │          ├──StdFace/ +| │          │       ├──\*\*.c +| │          │       └──\*\*.h +| │          ├──pfapack/ +| │          │       ├──makefile\_pfapack +| │          │       └──\*\*.f +| │          └──sfmt/ +| │                  ├──makefkie\_sfmt +| │                  ├──\*\*.c +| │                  └──\*\*.h +| └──tool/ +|            ├──\*\*.f90 +|            └──makefile\_tool + +基本的な使い方 +-------------- + +mVMCは次の二つのいずれかのモードで動作します。 + +- エキスパートモード + + mVMCでは一般的な格子フェルミオン/スピン系に対応しており、 + 各サイト毎にホッピング等を別々に指定することが出来ます。 + これにより計算対象の柔軟な指定が可能となりますが、用意する入力ファイルは多く、 + 計算のセットアップは比較的煩雑になります。 + +- スタンダードモード + + 典型的なモデル(正方格子上のHeisenbergモデルなど)では、 + 計算するセルのサイズや共通の相互作用項の大きさなど少数のパラメーターのみを入力して + エキスパートモード用の入力ファイルを自動生成し、計算をすることが出来ます。 + 計算対象はエキスパートモードに比べて限られますが、比較的容易に計算をセットアップすることが出来ます。 + また、エキスパートモード用の入力ファイルを自動生成した後、計算をする前にそれらを手動で編集して + より広範なモデルに対応させることも可能です。 + +これらのモードを用いて次の用に計算を行います。 + +#. 計算用ディレクトリの作成 + + 計算シナリオ名を記載したディレクトリを作成します。 + +#. スタンダードモードの入力ファイルの作成 + + あらかじめ用意されたいくつかのモデル(HeisenbergモデルやHubbardモデル)や格子(正方格子など)を指定し、 + それらに対するいくつかのパラメーター(最近接 :math:`\cdot` 次近接スピン結合やオンサイトクーロン積分など)を設定します。 + 各ファイルは :ref:`HowToStandard` に従い記載してください。 + +#. 実行 + + 作成した入力ファイル名を引数として ``vmc.out`` を実行します。 + このとき入力ファイル名の前にオプション ``-s`` を付けます。 + + .. code-block:: bash + + $ mpiexec -np プロセス数 パス/vmc.out -s 入力ファイル + + ワークステーションやスパコン等でキューイングシステムを利用している場合は + プロセス数をジョブ投入コマンドの引数として与える場合があります。 + 詳しくはお使いのシステムのマニュアルをご参照ください。 + +#. 途中経過 + + 計算実行の経過についてカレントディレクトリ直下の ``output/`` + ディレクトリ(無ければ作られる)にログファイルが出力されます。 + 出力されるファイルの詳細に関しては :ref:`outputfile` を参考にしてください。 + +#. 最終結果 + + 計算が正常終了した場合、 計算モードに従い ``output/`` + ディレクトリに計算結果ファイルが出力されます。 + 出力されるファイルの詳細に関しては :ref:`outputfile` を参考にしてください。 + +#. エキスパートモードの入力ファイルの作成と実行 + + 上の例ではエキスパートモードのファイルを自動生成した後そのまま計算を開始していますが、 + エキスパートモードのファイルの生成のみを行う場合には ``vmcdry.out`` を実行します。 + MPIは使用しません。 + + .. code-block:: bash + + $ パス/vmcdry.out 入力ファイル + + このとき生成されたファイルを必要に応じて手動で編集したのち、 ``-e`` + というオプションの後に + ``namelist/def`` というファイルを引数として ``vmcd.out`` + を実行します。 + + .. code-block:: bash + + $ mpiexec -np プロセス数 パス/vmc.out -e namelist.def + + 以降はスタンダードモードと同様です。 + +**OpenMPスレッド数の指定** + +実行時のOpenMPのスレッド数を指定する場合は、 +``vmc.out`` を実行する前に以下の様にしてください(16スレッドの場合)。 + +.. code-block:: bash + + export OMP_NUM_THREADS=16 + +バージョン番号の確認 +~~~~~~~~~~~~~~~~~~~~ + +次のように ``-v`` オプションをつけて ``vmc.out``, +``vmcdry.out`` を実行すると, バージョン番号を標準出力した後終了します。 + +.. code-block:: bash + + $ パス/vmcdry.out -v + $ パス/vmc.out -v diff --git a/doc/jp/tutorial.rst b/doc/jp/tutorial.rst new file mode 100644 index 00000000..c8b75c67 --- /dev/null +++ b/doc/jp/tutorial.rst @@ -0,0 +1,332 @@ +チュートリアル +============== + +サンプルファイル一覧 +-------------------- + +mVMCでは ``sample/Standard/`` 以下に次のサンプルを用意しています。 + +- 2次元正方格子Hubbardモデル + + (``sample/Standard/Hubbard/square/``) + +- 2次元三角格子Hubbardモデル + + (``sample/Standard/Hubbard/triangular/``) + +- 1次元近藤格子モデル + + (``sample/Standard/Kondo/chain/``) + +- 1次元反強磁性的Heisenbergモデル + + (``sample/Standard/Spin/HeisenbergChain/``) + +- 2次元正方格子反強磁性的Heisenbergモデル + + (``sample/Standard/Spin/HeisenbergSquare/``) + +- 2次元カゴメ格子反強磁性的Heisenbergモデル + + (``sample/Standard/Spin/Kagome/``) + +これらのチュートリアルの実行方法は全て同じ手順で実行することが可能です。 +以下ではHeisenberg模型について説明します。 + +Heisenberg模型 +-------------- + +以下のチュートリアルはディレクトリ + +:: + + sample/Standard/Spin/HeisenbergChain/ + +内で行います。 このディレクトには以下のファイルがあります. + +Heisenberg模型におけるサンプル入力ファイル: ``StdFace.def`` + +参照用出力ディレクトリ: ``reference/`` + +この例では1次元のHeisenberg鎖(最近接サイト間の反強磁性的スピン結合のみを持つ)を考察します。 + +.. math:: + + \begin{aligned} + {\hat H} = J \sum_{i=1}^{L} {\hat {\boldsymbol S}}_i \cdot {\hat {\boldsymbol S}}_{i+1}\end{aligned} + +| インプットファイルの中身は次のとおりです。 + +10cm + +:: + + L = 16 + Lsub=4 + model = "Spin" + lattice = "chain lattice" + J = 1.0 + 2Sz = 0 + NMPtrans=1 + +| +| この例ではスピン結合 :math:`J=1` (任意単位)とし、サイト数は16としました。 + +計算実行 +^^^^^^^^ + +実行コマンドは次のとおりです。 + +``$ mpiexec -np `` `` `` ``/vmc.out -s StdFace.def`` + +使っているシステムによっては ``mpiexec`` コマンドではなく ``mpirun`` や ``mpijob`` 、 +``poe`` となる場合もあります。 + +この実行による標準出力は次のとおりです。 + +:: + + ###### Standard Intarface Mode STARTS ###### + + Open Standard-Mode Inputfile StdFace.def + + KEYWORD : l | VALUE : 16 + KEYWORD : lsub | VALUE : 4 + KEYWORD : model | VALUE : spin + KEYWORD : lattice | VALUE : chain + KEYWORD : j | VALUE : 1.0 + KEYWORD : nmptrans | VALUE : 1 + + ####### Parameter Summary ####### + + @ Lattice Size & Shape + + L = 16 + Lsub = 4 + L = 16 + W = 1 + phase0 = 0.00000 ###### DEFAULT VALUE IS USED ###### + + @ Hamiltonian + + 2S = 1 ###### DEFAULT VALUE IS USED ###### + h = 0.00000 ###### DEFAULT VALUE IS USED ###### + Gamma = 0.00000 ###### DEFAULT VALUE IS USED ###### + D = 0.00000 ###### DEFAULT VALUE IS USED ###### + J0x = 1.00000 + J0y = 1.00000 + J0z = 1.00000 + + @ Numerical conditions + + Lsub = 4 + Wsub = 1 + ioutputmode = 1 ###### DEFAULT VALUE IS USED ###### + + ###### Print Expert input files ###### + + qptransidx.def is written. + filehead = zvo ###### DEFAULT VALUE IS USED ###### + filehead = zqp ###### DEFAULT VALUE IS USED ###### + NVMCCalMode = 0 ###### DEFAULT VALUE IS USED ###### + NLanczosMode = 0 ###### DEFAULT VALUE IS USED ###### + NDataIdxStart = 1 ###### DEFAULT VALUE IS USED ###### + NDataQtySmp = 1 ###### DEFAULT VALUE IS USED ###### + NSPGaussLeg = 8 ###### DEFAULT VALUE IS USED ###### + NMPTrans = 1 + NSROptItrStep = 1000 ###### DEFAULT VALUE IS USED ###### + NSROptItrSmp = 100 ###### DEFAULT VALUE IS USED ###### + NVMCWarmUp = 10 ###### DEFAULT VALUE IS USED ###### + NVMCInterval = 1 ###### DEFAULT VALUE IS USED ###### + NVMCSample = 1000 ###### DEFAULT VALUE IS USED ###### + NExUpdatePath = 2 + RndSeed = 123456789 ###### DEFAULT VALUE IS USED ###### + NSplitSize = 1 ###### DEFAULT VALUE IS USED ###### + NStore = 0 ###### DEFAULT VALUE IS USED ###### + DSROptRedCut = 0.00100 ###### DEFAULT VALUE IS USED ###### + DSROptStaDel = 0.02000 ###### DEFAULT VALUE IS USED ###### + DSROptStepDt = 0.02000 ###### DEFAULT VALUE IS USED ###### + NSPStot = 0 ###### DEFAULT VALUE IS USED ###### + ComplexType = 0 ###### DEFAULT VALUE IS USED ###### + locspn.def is written. + trans.def is written. + interall.def is written. + jastrowidx.def is written. + coulombintra.def is written. + coulombinter.def is written. + hund.def is written. + exchange.def is written. + orbitalidx.def is written. + gutzwilleridx.def is written. + namelist.def is written. + modpara.def is written. + greenone.def is written. + greentwo.def is written. + + ###### Input files are generated. ###### + + ----------- + Start: Read *def files. + Read File namelist.def . + Read File 'modpara.def' for ModPara. + Read File 'locspn.def' for LocSpin. + Read File 'trans.def' for Trans. + Read File 'coulombintra.def' for CoulombIntra. + Read File 'coulombinter.def' for CoulombInter. + Read File 'hund.def' for Hund. + Read File 'exchange.def' for Exchange. + Read File 'gutzwilleridx.def' for Gutzwiller. + Read File 'jastrowidx.def' for Jastrow. + Read File 'orbitalidx.def' for Orbital. + Read File 'qptransidx.def' for TransSym. + Read File 'greenone.def' for OneBodyG. + Read File 'greentwo.def' for TwoBodyG. + End : Read *def files. + Start: Read parameters from *def files. + End : Read parameters from *def files. + Start: Set memories. + End : Set memories. + Start: Initialize parameters. + End : Initialize parameters. + Start: Initialize variables for quantum projection. + End : Initialize variables for quantum projection. + Start: Optimize VMC parameters. + End : Optimize VMC parameters. + ----------- + +この実行でははじめにエキスパートモード用の入力ファイルとして、 +ハミルトニアンの詳細を記述するファイル + +- ``locspin.def`` + +- ``trans.def`` + +- ``coulombinter.def`` + +- ``coulombintra.def`` + +- ``exchange.def`` + +- ``hund.def`` + +- ``namelist.def`` + +- ``modpara.def`` + +と、変分パラメータを設定するファイル + +- ``gutzwilleridx.def`` + +- ``jastrowidx.def`` + +- ``orbitalidx.def`` + +- ``qptransidx.def`` + +結果として出力する相関関数の要素を指定するファイル + +- ``greenone.def`` + +- ``greentwo.def`` + +が生成されます。 各ファイルの詳細については :ref:`HowToExpert` をご覧ください。 + +その後実際に計算が行われ、以下のファイルが情報として ``output/`` ディレクトリに出力されます。 + +12cm + +:: + + zvo_SRinfo.dat + zvo_out_001.dat + zvo_time_001.dat + zvo_var_001.dat + zvo_CalcTimer.dat + +なお、 ``zvo_out_001.dat`` には、ビン毎の計算情報として、 + +.. math:: \langle H \rangle, \langle H^2 \rangle, \frac{\langle H^2 \rangle- \langle H \rangle^2 }{\langle H \rangle^2} \nonumber + +が順に出力されますので、収束性の目安として利用することが可能です。 +gnuplotを用いる場合には、次のようにして表示することが出来ます( :math:`\langle H \rangle` の場合)。 + +:: + + plot "zvo_out_001.dat" u 1 + +| 各ファイルの詳細については :ref:`outputfile` をご覧ください。 + +計算結果出力 +^^^^^^^^^^^^ + +| 計算が正常終了すると、エネルギー、エネルギーの分散、 + 変分パラメータおよび計算実行時間を記載したファイルが ``output/`` + ディレクトリに出力されます。 + 以下に、このサンプルでの出力ファイルを記載します。 + +12cm + +:: + + gutzwiller_opt.dat + jastrow_opt.dat + orbital_opt.dat + zqp_opt.dat + ClacTimer.dat + +各ファイルの詳細については :ref:`outputfile` をご覧ください。 + +Green関数の計算 +^^^^^^^^^^^^^^^ + +``modpara.def`` ファイル中の ``NVMCCalMode`` を0から1に変更の上、以下のコマンドを実行します。 +下記のように 実行時のコマンドライン引数として +``"namelist.dat"`` の後ろに ``"zqp_opt.dat"`` を付け加えることで、 +一つ前の計算で最適化された変分パラメータを使用した計算が行われます。 + +``$ `` ``/vmc.out -e namelist.def output/zqp_opt.dat`` + +| 計算が終了すると以下のファイルが ``output/`` + ディレクトリに出力されます。 + +12cm + +:: + + zvo_cisajs_001.dat + zvo_cisajscktalt_001.dat + +| +| 各ファイルの詳細については :ref:`outputfile` をご覧ください。 + +エキスパートユーザー向け +------------------------ + +mVMCでは、以下の6つに分類される入力ファイルを読み込み、計算実行を行います。 + +(1) List: + 詳細入力ファイルの種類と名前を指定するファイル + +(2) Basic parameters: + 基本的なパラメータを指定するファイル + +(3) Set Hamiltonian: + ハミルトニアンを指定するファイル + +(4) Set condition of variational parameters : + 最適化する変分パラメータを指定するファイル + +(5) Initial variational parameters: + 変分パラメータの初期値を指定するファイル + +(6) Output: + 出力する一体・二体グリーン関数の成分を指定するファイル + +上記で分類されるファイルを直接作成・指定することで、より複雑な計算を行うことが可能です。 +ファイルの詳細については :ref:`HowToExpert` をご覧ください。 + +相関関数のフーリエ変換 +---------------------- + +このパッケージには、上で求めた相関関数をフーリエ変換し、プロットするユーティリティーが付属しています。 +詳しくは :ref:`fourier` を参照してください。 From 2b4c5d03c440e1ec324d43cc12c3b0268c89ec38 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Wed, 31 Jan 2018 16:46:57 +0900 Subject: [PATCH 14/34] Introduce sphinx (English) --- doc/en/Makefile | 177 ++ doc/en/acknowledge.rst | 11 + doc/en/algorithm.rst | 355 ++++ doc/en/appendix.rst | 245 +++ doc/en/conf.py | 263 +++ doc/en/expert.rst | 2659 ++++++++++++++++++++++++ doc/en/fourier/fourier_contact_en.rst | 12 + doc/en/fourier/fourier_format_en.rst | 252 +++ doc/en/fourier/fourier_overview_en.rst | 63 + doc/en/fourier/fourier_tutorial_en.rst | 116 ++ doc/en/fourier/fourier_util_en.rst | 94 + doc/en/fourier/index.rst | 26 + doc/en/index.rst | 29 + doc/en/intro.rst | 161 ++ doc/en/output.rst | 349 ++++ doc/en/standard.rst | 742 +++++++ doc/en/start.rst | 353 ++++ doc/en/tutorial.rst | 341 +++ doc/jp/appendix.rst | 69 +- 19 files changed, 6292 insertions(+), 25 deletions(-) create mode 100644 doc/en/Makefile create mode 100644 doc/en/acknowledge.rst create mode 100644 doc/en/algorithm.rst create mode 100644 doc/en/appendix.rst create mode 100644 doc/en/conf.py create mode 100644 doc/en/expert.rst create mode 100644 doc/en/fourier/fourier_contact_en.rst create mode 100644 doc/en/fourier/fourier_format_en.rst create mode 100644 doc/en/fourier/fourier_overview_en.rst create mode 100644 doc/en/fourier/fourier_tutorial_en.rst create mode 100644 doc/en/fourier/fourier_util_en.rst create mode 100644 doc/en/fourier/index.rst create mode 100644 doc/en/index.rst create mode 100644 doc/en/intro.rst create mode 100644 doc/en/output.rst create mode 100644 doc/en/standard.rst create mode 100644 doc/en/start.rst create mode 100644 doc/en/tutorial.rst diff --git a/doc/en/Makefile b/doc/en/Makefile new file mode 100644 index 00000000..91b27399 --- /dev/null +++ b/doc/en/Makefile @@ -0,0 +1,177 @@ +# Makefile for Sphinx documentation +# + +# You can set these variables from the command line. +SPHINXOPTS = +SPHINXBUILD = sphinx-build +PAPER = +BUILDDIR = _build + +# User-friendly check for sphinx-build +ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $$?), 1) +$(error The '$(SPHINXBUILD)' command was not found. 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The pseudo-XML files are in $(BUILDDIR)/pseudoxml." diff --git a/doc/en/acknowledge.rst b/doc/en/acknowledge.rst new file mode 100644 index 00000000..1d570be1 --- /dev/null +++ b/doc/en/acknowledge.rst @@ -0,0 +1,11 @@ +Acknowledgement +=============== + +We would like to express our sincere gratitude to Mr. Daisuke Tahara for +providing us his code of variational Monte Carlo method. A part of mVMC +is based on his original code. We also acknowledge Dr. Hiroshi Shinaoka, +Dr. Youhei Yamaji, Dr. Moyuru Kurita, and Dr. Ryui Kaneko for their +cooperation on developing mVMC. We would also like to thank the support +from “Project for advancement of software usability in materials +science” by The Institute for Solid State Physics, The University of +Tokyo, for development of mVMC ver.0.1, ver. 0.2, and ver. 1.0. diff --git a/doc/en/algorithm.rst b/doc/en/algorithm.rst new file mode 100644 index 00000000..5e1d67f9 --- /dev/null +++ b/doc/en/algorithm.rst @@ -0,0 +1,355 @@ +.. include:: ../bib/ref.txt + +Algorithm +========= + +Variational Monte Calro Method +------------------------------ + +The variational Monte Carlo (VMC) method is a method for calculating +approximate wave functions of a ground state and low-lying excited +states by optimizing variational parameters included in a trial wave +function. In calculating expectation values of physical quantities for +the trial wave functions, the Markov chain Monte Carlo method is applied +for efficient important sampling. + +In the mVMC package, we choose a spatial configuration for electrons as +a complete set of bases in sampling: + +.. math:: + + | x\rangle = \prod_{n=1}^{N/2} c_{r_{n\uparrow}}^{\dagger} \prod_{n=1}^{N/2} c_{r_{n\downarrow}}^{\dagger} |0 \rangle, + +where :math:`r_{n\sigma}` is a position of :math:`n`\ -th electron with +:math:`\sigma (=\uparrow \rm{or} \downarrow)` spin, and +:math:`c_{r_{n\sigma}}^{\dagger}` is a creation operator of electrons. By +using this basis set, the expectation value of an operator :math:`A` is +expressed as + +.. math:: + + \langle A \rangle =\frac{\langle \psi| A| \psi \rangle}{\langle \psi | \psi \rangle} + =\sum_x \frac{\langle \psi| A | x\rangle \langle x| \psi \rangle}{\langle \psi |\psi \rangle}. + +If we define a weight of the Markov chain Monte Carlo method as + +.. math:: + + \rho(x)=\frac{|\langle x| \psi \rangle|^2}{\langle \psi | \psi \rangle} \ge 0, \quad \sum_{x} \rho(x)=1, + +we can rewrite :math:`\langle A \rangle` in the following form: + +.. math:: + + \langle A \rangle =\sum_x \rho(x) \frac{\langle \psi| A | x\rangle }{\langle \psi |x \rangle}. + +By using this form, the Markov chain Monte Carlo method is performed +for sampling with respect to :math:`x`. The local Green’s function +:math:`G_{ij\sigma\sigma'}(x)`, which is defined as + +.. math:: + + G_{ij\sigma\sigma'}(x)=\frac{\langle \psi | c_{i\sigma}^{\dagger} c_{j\sigma'} | \psi \rangle}{\langle \psi | x \rangle}, + +is also evaluated by the same sampling method by taking +:math:`A = c_{i\sigma}^{\dagger} c_{j\sigma'}`. We adopt the Mersenne +twister method as a random number generator for +sampling [Mutsuo2008_ ]. + +Bogoliubov representation +------------------------- + +In the VMC calculation for spin systems, we use the Bogoliubov +representation. In the input files defining the one-body term +(``transfer``) and the two-body term (``InterAll``), and the output +files for correlation functions, the indices must be assigned by the +Bogoliubov representation, in which the spin operators are generally +expressed by creation/annihilation operators of fermions as + +.. math:: + + \begin{aligned} + S_{i z} &= \sum_{\sigma = -S}^{S} \sigma c_{i \sigma}^\dagger c_{i \sigma}, + \\ + S_{i}^+ &= \sum_{\sigma = -S}^{S-1} + \sqrt{S(S+1) - \sigma(\sigma+1)} + c_{i \sigma+1}^\dagger c_{i \sigma}, + \\ + S_{i}^- &= \sum_{\sigma = -S}^{S-1} + \sqrt{S(S+1) - \sigma(\sigma+1)} + c_{i \sigma}^\dagger c_{i \sigma+1}. + \end{aligned} + +Since the present package support only :math:`S=1/2` spin systems, the +Bogoliubov representation obtained by substituting :math:`S=1/2` into +the above equations is used. + +.. _PuffAndSlater: + +Properties of the Pfaffian-Slater determinant +--------------------------------------------- + +In this section, we explain some properties of the Pfaffian-Slater +determinant. We derive the general relation between a Pfaffian-Slater +determinant and a single Slater determinant in :ref:`Antiparallel Pfaffian ` +and :ref:`General Pfaffian ` . We also discuss meaning of the singular value +decomposition of coefficients :math:`f_{ij}` in +:ref:`SVD `. + +.. _PfaffianAP: + +Relation between :math:`f_{ij}` and :math:`\Phi_{in\sigma}` (the case of the anti-parallel pairing) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +In the many-variable variational Monte Carlo (mVMC) method, the one-body +part of the trial wave function is expressed by the Pfaffian Slater +determinant defined as + +.. math:: + + |\phi_{\rm Pf}\rangle=\Big(\sum_{i,j=1}^{N_{s}}f_{ij} + c_{i\uparrow}^{\dagger}c_{j\downarrow}^{\dagger}\Big)^{N_{\rm e}/2}|0\rangle, + +where :math:`N_{s}` is number of sites, :math:`N_{e}` is number of +total particles, and :math:`f_{ij}` are variational parameters. For +simplicity, we assume that :math:`f_{ij}` are a real number. The single +Slater determinant is defined as + +.. math:: + + \begin{aligned} + |\phi_{\rm SL}\rangle&=\Big(\prod_{n=1}^{N_{e}/2}\psi_{n\uparrow}^{\dagger}\Big) + \Big(\prod_{m=1}^{N_{e}/2}\psi_{m\downarrow}^{\dagger}\Big)|0\rangle, \\ + \psi_{n\sigma}^{\dagger}&=\sum_{i=1}^{N_{s}}\Phi_{in\sigma}c^{\dagger}_{i\sigma}, + \end{aligned} + +Here, :math:`\Phi_{in\sigma}` is an orthonormal basis, i.e., satisfies + +.. math:: \sum_{i=1}^{N_{s}}\Phi_{in\sigma}\Phi_{im\sigma}=\delta_{nm}, + +where :math:`\delta_{nm}` is the Kronecker’s delta. From this +orthogonality, we can prove the relation + +.. math:: + + \begin{aligned} + [\psi^{\dagger}_{n\sigma},\psi_{m\sigma}]_{+}&=\delta_{nm},\\ + G_{ij\sigma}=\langle c_{i\sigma}^{\dagger}c_{j\sigma}\rangle + &=\frac{\langle \phi_{\rm SL}| c_{i\sigma}^{\dagger}c_{j\sigma} | \phi_{\rm SL}\rangle}{\langle \phi_{\rm SL}|\phi_{\rm SL}\rangle } \\ + &=\sum_{n} \Phi_{in\sigma} \Phi_{jn\sigma}. + \end{aligned} + +Next, let us prove the relation between :math:`f_{ij}` and +:math:`\Phi_{in\sigma}` by modifying :math:`|\phi_{\rm SL}\rangle`. By +the commutation relation for :math:`\psi^{\dagger}_{n\sigma}`, +:math:`|\phi_{\rm SL}\rangle` is rewritten as + +.. math:: + + \begin{aligned} + |\phi_{\rm SL}\rangle \propto \prod_{n=1}^{N_{e}/2}\Big(\psi_{n\uparrow}^{\dagger}\psi_{\mu(n)\downarrow}^{\dagger}\Big)|0\rangle, + \end{aligned} + +where :math:`\mu(n)` represents permutation of a sequence of natural +numbers, :math:`n= 1, 2, \cdots, N_{e}/2`. For simplicity, let us take +identity permutation (:math:`\mu(n) = n`). By defining +:math:`K_{n}^{\dagger}=\psi_{n\uparrow}^{\dagger}\psi_{n\downarrow}^{\dagger}`, +and by using the relation +:math:`K_{n}^{\dagger}K_{m}^{\dagger}=K_{m}^{\dagger}K_{n}^{\dagger}`, +we can derive the relation + +.. math:: + + \begin{aligned} + |\phi_{\rm SL}\rangle &\propto \prod_{n=1}^{N_{e}/2}\Big(\psi_{n\uparrow}^{\dagger}\psi_{n\downarrow}^{\dagger}\Big)|0\rangle + =\prod_{n=1}^{N_{e}/2} K_{n}^{\dagger}|0\rangle \\ + &\propto\Big(\sum_{n=1}^{\frac{N_{e}}{2}}K_{n}^{\dagger}\Big)^{\frac{N_{e}}{2}} |0\rangle + =\Big(\sum_{i,j=1}^{N_{s}}\Big[\sum_{n=1}^{\frac{N_{e}}{2}}\Phi_{in\uparrow}\Phi_{jn\downarrow}\Big] + c_{i\uparrow}^{\dagger}c_{j\downarrow}^{\dagger}\Big)|0\rangle. + \end{aligned} + +This result indicates that :math:`f_{ij}` is expressed by the +coefficients of the single Slater determinant as + +.. math:: + + \begin{aligned} + f_{ij}=\sum_{n=1}^{\frac{N_{e}}{2}}\Phi_{in\uparrow}\Phi_{jn\downarrow}. + \end{aligned} + +We note that this is one of a number of possible expressions of +:math:`f_{ij}` derived from one single Slater determinant. Since +:math:`f_{ij}` depends not only on the choice of the pairing degrees of +freedom (i.e., the choice of :math:`\mu(n)`) but also on the choice of +the gauge degrees of freedom (i.e., the sign of +:math:`\Phi_{in\sigma}`), the parameter :math:`f_{ij}` has huge +redundancy. + +.. _PfaffianP: + +Relation between :math:`F_{IJ}` and :math:`\Phi_{In\sigma}` (the case of the general pairing) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +We extend the relation between the Pfaffian-Slater wave function and the +single Slater wave function into the general pairing case including the +spin-parallel pairing. We define the Pfaffian-Slater wave function and +the single Slater wave function as + +.. math:: + + \begin{aligned} + |\phi_{\rm Pf}\rangle&=\Big(\sum_{I,J=1}^{2N_{s}}F_{IJ}c_{I}^{\dagger}c_{J}^{\dagger}\Big)^{N_{\rm e}/2}|0\rangle, \\ + |\phi_{\rm SL}\rangle&=\Big(\prod_{n=1}^{N_{e}}\psi_{n}^{\dagger}\Big)|0\rangle,~~\psi_{n}^{\dagger}=\sum_{I=1}^{2N_{s}}\Phi_{In}c^{\dagger}_{I}, + \end{aligned} + +respectively, where :math:`I`, :math:`J` denote the site index +including the spin degrees of freedom. By the similar argument as the +anti-parallel pairing case, we can derive the following relation: + +.. math:: + + \begin{aligned} + F_{IJ}=\sum_{n=1}^{\frac{N_{e}}{2}}\Big(\Phi_{In}\Phi_{Jn+1}-\Phi_{Jn}\Phi_{In+1}\Big). + \end{aligned} + +Because this relation hold for the case of anti-parallel pairing, we +employ this relation in mVMC ver 1.0 and later. + +.. _PfaffianSingular: + +Singular value decomposition of :math:`f_{ij}` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +We define matrices :math:`F`, :math:`\Phi_{\uparrow}`, +:math:`\Phi_{\downarrow}`, and :math:`\Sigma` as + +.. math:: + + \begin{aligned} + &(F)_{ij}=f_{ij},~~~ + (\Phi_{\uparrow})_{in}=\Phi_{in\uparrow},~~~ + (\Phi_{\downarrow})_{in}=\Phi_{in\downarrow}, \\ + &\Sigma={\rm diag}[\underbrace{1,\cdots,1}_{N_e/2},0,0,0]. + \end{aligned} + +When :math:`f_{ij}` (i.e., the matrix :math:`F`) is related with a +single Slater determinant of the wave function, we can show that the +singular value decomposition of :math:`F` becomes + +.. math:: + + \begin{aligned} + F=\Phi_{\uparrow}\Sigma\Phi_{\downarrow}^{t}. + \end{aligned} + +This result indicates that when the number of nonzero singular values +is :math:`N_{e}/2`, and when all the nonzero singular values of +:math:`F` are one in the singular value decomposition of :math:`F`, the +Pfaffian-Slater wave function parametrized by :math:`f_{ij}` coincides +with a single Slater determinant (i.e. a solution of the mean-field +approximation). In other words, the numbers of the nonzero singular +values and their difference from one offer a quantitative criterion how +the Pfaffian-Slater determinant deviates from the single Slate +determinant. + +Power Lanczos method +-------------------- + +In this section, we show how to determine :math:`\alpha` in the +power-Lanczos method. We also explain the calculation of physical +quantities after the single-step Lanczos method. + +Determination of :math:`\alpha` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +First, we briefly explain the sampling procedure of the variational +Monte Carlo (VMC) method. Physical properties :math:`\hat{A}` are +calculated as follows: + +.. math:: + + \begin{aligned} + &\langle \hat{A}\rangle = \frac{\langle \phi| \hat{A}|\phi \rangle}{\langle \phi| \phi \rangle} = \sum_{x} \rho(x) F(x, {\hat{A}}),\\ + & \rho(x)=\frac{|\langle \phi|x\rangle|^2}{\langle \phi | \phi \rangle}, ~~~~F(x, {\hat{A}}) = \frac{\langle x| \hat{A}|\phi \rangle}{\langle x| \phi \rangle}. + \end{aligned} + +There are two ways to calculate the product of the operators +:math:`\hat{A}\hat{B}`. + +.. math:: + + \begin{aligned} + &\langle \hat{A} \hat{B}\rangle = \sum_{x} \rho(x) F(x, {\hat{A}\hat{B}}),\\ + &\langle \hat{A} \hat{B}\rangle = \sum_{x} \rho(x) F^{\dagger}(x, {\hat{A})F(x, \hat{B}}). + \end{aligned} + +As we explain later, in general, the latter way is numerical stable +one. For example, we consider the expectation value of the variance, +which is defined as +:math:`\sigma^2=\langle (\hat{H}-\langle \hat{H}\rangle)^2\rangle`. +There are two ways to calculate the variance. + +.. math:: + + \begin{aligned} + \sigma^2&=\sum_{x} \rho(x) F(x, (\hat{H}-\langle \hat{H}\rangle)^2) = \sum_{x} \rho(x) F(x, \hat{H}^2) - \left[ \sum_{x} \rho(x) F(x, \hat{H})\right]^2 ,\\ + \sigma^2&=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}-\langle \hat{H}\rangle)F(x, \hat{H}-\langle \hat{H}\rangle) \nonumber \\ + &= \sum_{x} \rho(x) F^{\dagger}(x, \hat{H}) F(x, \hat{H})- \left[ \sum_{x} \rho(x) F(x, \hat{H})\right]^2 + \end{aligned} + +From its definition, the latter way gives the positive definitive +variance even for the finite sampling while the former way does not +guarantee the positive definitiveness of the variance. Here, we consider +the expectation values of energy and variance for the (single-step) +power Lanczos wave function +:math:`|\phi\rangle =(1+\alpha \hat{H}) |\psi \rangle`. The energy is +calculated as + +.. math:: + + \begin{aligned} + E_{LS}(\alpha) =\frac{\langle \phi| \hat{H} |\phi\rangle}{\langle \phi|\phi\rangle}=\frac{h_1 + \alpha(h_{2(20)} + h_{2(11)}) + \alpha^2 h_{3(12)}}{1 + 2\alpha h_1 + \alpha^2 h_{2(11)}}, + \end{aligned} + +where we define :math:`h_1`, :math:`h_{2(11)},~h_{2(20)},` and +:math:`h_{3(12)}` as + +.. math:: + + \begin{aligned} + &h_1 =\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}),\\ + &h_{2(11)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}) F(x, \hat{H}),\\ + &h_{2(20)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}^2),\\ + &h_{3(12)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H})F(x, \hat{H}^2). + \end{aligned} + +From the condition +:math:`\frac{\partial E_{LS}(\alpha)}{\partial \alpha}=0`, i.e., by +solving the quadratic equations, we can determine the :math:`\alpha`. +The variance is calculate in the similar way. + +Calculation of physical quantities +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +By using the optimized parameter :math:`\alpha`, we can calculate the +expected value of the operator :math:`\hat{A}` as + +.. math:: + + \begin{aligned} + A_{LS}(\alpha) =\frac{\langle \phi| \hat{A} |\phi\rangle}{\langle \phi|\phi\rangle}=\frac{A_0 + \alpha(A_{1(10)} + A_{1(01)}) + \alpha^2 A_{2(11)}}{1 + 2\alpha h_1 + \alpha^2 h_{2(11)}}, + \end{aligned} + +where we define :math:`A_0`, :math:`A_{1(10)},~A_{1(01)},` and +:math:`A_{2(11)}` as + +.. math:: + + \begin{aligned} + &A_0 =\sum_{x} \rho(x) F(x, \hat{A}),\\ + &A_{1(10)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H}) F(x, \hat{A}),\\ + &A_{1(01)}=\sum_{x} \rho(x) F(x, \hat{A}\hat{H}),\\ + &A_{2(11)}=\sum_{x} \rho(x) F^{\dagger}(x, \hat{H})F(x, \hat{A}\hat{H}). + \end{aligned} + + diff --git a/doc/en/appendix.rst b/doc/en/appendix.rst new file mode 100644 index 00000000..22685d6d --- /dev/null +++ b/doc/en/appendix.rst @@ -0,0 +1,245 @@ +Program for the unrestricted Hartree-Fock approximation +======================================================= + +In mVMC package, there is a program to calculate the initial values of +the pair orbital parameters :math:`f_{ij}` by using the unrestricted +Hartree-Fock (UHF) approximation (relation between Pfaffian Slater +determinant and single Slater determinant is explained in sec. +:ref:`PuffAndSlater`). It is noted that the target system of this program +is the itinerant electron system. + +Overview +-------- + +In UHF approximation, two-body interaction terms are approximated as +one-body interaction terms by taking into account of the fluctuation, +:math:`\delta A \equiv A-\langle A \rangle`, up to the first order. As +an example, we consider the inter-site coulomb interactions + +.. math:: + + {\cal H}_V = \sum_{i,j}V_{ij} n_ {i}n_{j}, + +where we define :math:`i\equiv (i, \sigma)`, +:math:`j\equiv (j, \sigma')` for simplicity. Then, the interaction terms +can be approximated as + +.. math:: + + \begin{aligned} + n_ {i}n_{j} &= (\langle n_{i} \rangle +\delta n_i) (\langle n_{j} \rangle +\delta n_j) + - \left[ \langle c_{i}^{\dagger}c_j \rangle +\delta (c_{i}^{\dagger}c_j ) \right] + \left[ \langle c_{j}^{\dagger}c_i \rangle +\delta (c_{j}^{\dagger}c_i )\right] + \nonumber\\ + &\sim + \langle n_{i} \rangle n_j+\langle n_{j} \rangle n_i - \langle c_{i}^{\dagger}c_j \rangle c_{j}^{\dagger}c_i + - \langle c_{j}^{\dagger}c_i \rangle c_{i}^{\dagger}c_j + - \langle n_{i} \rangle \langle n_j \rangle + \langle c_{j}^{\dagger}c_i \rangle \langle c_{i}^{\dagger}c_j \rangle. + \end{aligned} + +Also for other types of interaction, the problem can be attributed to a +one-body problem by using a similar approximation. Actual calculation is +performed iteratively until that self-consistent solution for the mean +values of the above observables are obtained. + +Source code +~~~~~~~~~~~ + +A set of source codes are included in the directory +``src/ComplexUHF/src``. + +How to compile +~~~~~~~~~~~~~~ + +To compile source codes, move to the directory just below the main +directory of mVMC, and execute + +.. code-block:: bash + + $ make mvmc + +in a similar way as the compile of mVMC. After compiling, an executable +file ``UHF`` is generated in ``src/ComplexUHF/src``. + +Input files +~~~~~~~~~~~ + +A file for assigning input files (namelsit.def) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The following files are needed to use the program of UHF. The format +of ``namelist.def`` is the same as defined in :ref:`InputFileList`. + +- ``ModPara`` + +- ``LocSpin`` + +- ``Trans`` + +- ``CoulombIntra`` + +- ``CoulombInter`` + +- ``Hund`` + +- ``PairHop`` + +- ``Exchange`` + +- ``Orbital`` / ``OrbitalAntiParallel`` + +- ``OrbitalParallel`` + +- ``OrbitalGeneral`` + +- ``Initial`` + +Although the format of these files are the same as those for mVMC +basically, the following items are different: + +- Parameters assigned in ``ModPara`` file. + +- Addition of ``Initial`` file. + +We explain details of the format of these files as follows. + +Parameters assigned in ModPara file +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The parameters needed in the program of UHF are as follows: + +- ``Nsite`` + +- ``Ne`` + +- ``Mix`` + +- ``EPS`` + +- ``IterationMax`` + +The parameters, ``Nsite`` and ``Ne``, are common as mVMC. The other +three parameters are specific to UHF: + +- ``Mix`` + + Linear mixing is assigned by double-type. When mix=1, a new Green’s + function is fully updated without using a old one. + +- ``EPS`` + + A condition for convergence is assigned by int-type. When a + residual error between a new Green’s function and a previous one is + less than :math:`10^{-\verb|eps|}`, the iteration of calculation is + stopped. + +- ``IterationMax`` + + A maximum number of the loop is assigned by int-type. + +If there are the other parameters for mVMC in this file , warning is +output to the standard output (the calculation is not stopped). + +Initial file +^^^^^^^^^^^^ + +Initial values of Green’s function +:math:`G_{ij\sigma_1\sigma_2}\equiv \langle c_{i\sigma_1}^\dagger c_{j\sigma_2}\rangle` +are given. The format is the same as ``Trans`` file, and instead of +:math:`t_{ij\sigma_1\sigma_2}`, values of :math:`G_{ij\sigma_1\sigma_2}` +are described. Green’s function is set as zero if values are not given. + +Usage +----- + +Calculation of UHF is performed by the same way as mVMC, i.e., by +executing the command + +:: + + $ UHF namelist.def + +The routine of the calculation is as follows. + +#. Reading files + +#. Construction of a Hamiltonian + +#. Self-consistent calculation of Green’s function + +#. Output of :math:`f_{ij}` and other files + +Examples of output after calculation are as follows. + +- zvo\_result.dat: + + The energy and the particle number are output. + + :: + + energy -15.2265348135 + num 36.0000000000 + +- zvo\_check.dat: + + The step number of the iteration, the mean of the + absolute value of the residual error in Green’s function, the energy + in convergence process, and the particle number are output in order. + + :: + + 0 0.004925645652 -544.963484605164 36.000000 + 1 0.002481594941 -278.304285708488 36.000000 + 2 0.001274395448 -147.247026925130 36.000000 + 3 0.000681060599 -82.973664527606 36.000000 + ... + +- zvo\_UHF\_cisajs.dat: + + Convergent one-body Green’s function + :math:`G_{ij\sigma_1\sigma_2}\equiv\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle` + is output. + For all the components, + :math:`i, \sigma_1, j, \sigma_2, {\rm Re}\left[G_{ij\sigma_1\sigma_2}\right], {\rm Im}\left[G_{ij\sigma_1\sigma_2}\right]` + are output in order. + + :: + + 0 0 0 0 0.5037555283 0.0000000000 + 0 0 0 1 0.4610257618 0.0003115503 + 0 1 0 0 0.4610257618 -0.0003115503 + 0 1 0 1 0.4962444717 0.0000000000 + ... + +- zvo\_eigen.dat: + + Convergent eigenvalues of the Hamiltonian are + output in ascending order. + + :: + + 1 -2.9425069199 + 2 -2.9425069198 + 3 -1.5005359205 + ... + +- zvo\_gap.dat: + + For the total electron number :math:`N_{\rm tot}`, the + energy difference :math:`\Delta E= E(N_{\rm tot}+1)-E(N_{\rm tot})` + is output. + + :: + + 5.2208232631 + +- zvo\_orbital\_opt.dat: + + :math:`f_{ij}` generated from the Slater + determinant. The file with the same format as + ``InOrbital``,\ ``InOrbitalAntiParallel``, + ``InOrbitalParallel``,\ ``InOrbitalAntiGeneral`` file is output. By + referring ``Orbital``, ``OrbitalAntiParallel``, + ``OrbitalParallel``,\ ``OrbitalAntiGeneral`` file, :math:`f_{ij}` is + calculated (for the same type of parameters, the averaged value is + calculated). diff --git a/doc/en/conf.py b/doc/en/conf.py new file mode 100644 index 00000000..b2879e71 --- /dev/null +++ b/doc/en/conf.py @@ -0,0 +1,263 @@ +# -*- coding: utf-8 -*- +# +# mVMC documentation build configuration file, created by +# sphinx-quickstart on Sat Jan 7 22:10:04 2017. +# +# This file is execfile()d with the current directory set to its +# containing dir. +# +# Note that not all possible configuration values are present in this +# autogenerated file. +# +# All configuration values have a default; values that are commented out +# serve to show the default. + +import sys +import os + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +#sys.path.insert(0, os.path.abspath('.')) + +# -- General configuration ------------------------------------------------ + +# If your documentation needs a minimal Sphinx version, state it here. +#needs_sphinx = '1.0' + +# Add any Sphinx extension module names here, as strings. They can be +# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# ones. +extensions = [ + 'sphinx.ext.mathjax', + 'sphinx_numfig' +] + +# Add any paths that contain templates here, relative to this directory. +templates_path = ['_templates'] + +# The suffix of source filenames. +source_suffix = '.rst' + +# The encoding of source files. +#source_encoding = 'utf-8-sig' + +# The master toctree document. +master_doc = 'index' + +# General information about the project. +project = u'mVMC' +copyright = u'2017, mVMC team' + +# The version info for the project you're documenting, acts as replacement for +# |version| and |release|, also used in various other places throughout the +# built documents. +# +# The short X.Y version. +version = '1.0' +# The full version, including alpha/beta/rc tags. +release = '1.0.2' + +# The language for content autogenerated by Sphinx. Refer to documentation +# for a list of supported languages. +language = 'en' + +# There are two options for replacing |today|: either, you set today to some +# non-false value, then it is used: +#today = '' +# Else, today_fmt is used as the format for a strftime call. +#today_fmt = '%B %d, %Y' + +# List of patterns, relative to source directory, that match files and +# directories to ignore when looking for source files. +exclude_patterns = ['_build'] + +# The reST default role (used for this markup: `text`) to use for all +# documents. +#default_role = None + +# If true, '()' will be appended to :func: etc. cross-reference text. +#add_function_parentheses = True + +# If true, the current module name will be prepended to all description +# unit titles (such as .. function::). +#add_module_names = True + +# If true, sectionauthor and moduleauthor directives will be shown in the +# output. They are ignored by default. +#show_authors = False + +# The name of the Pygments (syntax highlighting) style to use. +pygments_style = 'sphinx' + +# A list of ignored prefixes for module index sorting. +#modindex_common_prefix = [] + +# If true, keep warnings as "system message" paragraphs in the built documents. +#keep_warnings = False + + +# -- Options for HTML output ---------------------------------------------- + +# The theme to use for HTML and HTML Help pages. See the documentation for +# a list of builtin themes. +html_theme = 'default' + +# Theme options are theme-specific and customize the look and feel of a theme +# further. For a list of options available for each theme, see the +# documentation. +#html_theme_options = {} + +# Add any paths that contain custom themes here, relative to this directory. +#html_theme_path = [] + +# The name for this set of Sphinx documents. If None, it defaults to +# " v documentation". +#html_title = None + +# A shorter title for the navigation bar. Default is the same as html_title. +#html_short_title = None + +# The name of an image file (relative to this directory) to place at the top +# of the sidebar. +html_logo = '../figs/mVMC.png' + +# The name of an image file (within the static path) to use as favicon of the +# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 +# pixels large. +#html_favicon = None + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +html_static_path = ['_static'] + +# Add any extra paths that contain custom files (such as robots.txt or +# .htaccess) here, relative to this directory. These files are copied +# directly to the root of the documentation. +#html_extra_path = [] + +# If not '', a 'Last updated on:' timestamp is inserted at every page bottom, +# using the given strftime format. +#html_last_updated_fmt = '%b %d, %Y' + +# If true, SmartyPants will be used to convert quotes and dashes to +# typographically correct entities. +#html_use_smartypants = True + +# Custom sidebar templates, maps document names to template names. +#html_sidebars = {} + +# Additional templates that should be rendered to pages, maps page names to +# template names. +#html_additional_pages = {} + +# If false, no module index is generated. +#html_domain_indices = True + +# If false, no index is generated. +#html_use_index = True + +# If true, the index is split into individual pages for each letter. +#html_split_index = False + +# If true, links to the reST sources are added to the pages. +#html_show_sourcelink = True + +# If true, "Created using Sphinx" is shown in the HTML footer. Default is True. +#html_show_sphinx = True + +# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. +#html_show_copyright = True + +# If true, an OpenSearch description file will be output, and all pages will +# contain a tag referring to it. The value of this option must be the +# base URL from which the finished HTML is served. +#html_use_opensearch = '' + +# This is the file name suffix for HTML files (e.g. ".xhtml"). +#html_file_suffix = None + +# Output file base name for HTML help builder. +htmlhelp_basename = 'testdoc' + + +# -- Options for LaTeX output --------------------------------------------- + +latex_elements = { +# The paper size ('letterpaper' or 'a4paper'). +#'papersize': 'letterpaper', + +# The font size ('10pt', '11pt' or '12pt'). +#'pointsize': '10pt', + +# Additional stuff for the LaTeX preamble. +#'preamble': '\usepackage{pxjahyper}', + 'babel': '\\usepackage[english]{babel}', + 'classoptions': ',dvipdfmx,openany' +} + +# Grouping the document tree into LaTeX files. List of tuples +# (source start file, target name, title, +# author, documentclass [howto, manual, or own class]). +latex_documents = [ + ('index', 'mVMC.tex', u'mVMC Documentation', + u'mVMC team', 'manual'), +] + +# The name of an image file (relative to this directory) to place at the top of +# the title page. +latex_logo = '../figs/mVMC.png' + +# For "manual" documents, if this is true, then toplevel headings are parts, +# not chapters. +#latex_use_parts = False + +# If true, show page references after internal links. +#latex_show_pagerefs = False + +# If true, show URL addresses after external links. +#latex_show_urls = False + +# Documents to append as an appendix to all manuals. +#latex_appendices = [] + +# If false, no module index is generated. +#latex_domain_indices = True + + +# -- Options for manual page output --------------------------------------- + +# One entry per manual page. List of tuples +# (source start file, name, description, authors, manual section). +man_pages = [ + ('index', 'mVMC', u'mVMC Documentation', + [u'mVMC team'], 1) +] + +# If true, show URL addresses after external links. +#man_show_urls = False + + +# -- Options for Texinfo output ------------------------------------------- + +# Grouping the document tree into Texinfo files. List of tuples +# (source start file, target name, title, author, +# dir menu entry, description, category) +texinfo_documents = [ + ('index', 'mVMC', u'mVMC Documentation', + u'mVMC team', 'mVMC', 'One line description of project.', + 'Miscellaneous'), +] + +# Documents to append as an appendix to all manuals. +#texinfo_appendices = [] + +# If false, no module index is generated. +#texinfo_domain_indices = True + +# How to display URL addresses: 'footnote', 'no', or 'inline'. +#texinfo_show_urls = 'footnote' + +# If true, do not generate a @detailmenu in the "Top" node's menu. +#texinfo_no_detailmenu = False diff --git a/doc/en/expert.rst b/doc/en/expert.rst new file mode 100644 index 00000000..5a5a2fd4 --- /dev/null +++ b/doc/en/expert.rst @@ -0,0 +1,2659 @@ +.. include:: ../bib/ref.txt + +.. _HowToExpert: + +Input files for Expert mode +=========================== + +In this section, detailed input files (\*.def) are explained. Input +files are categorized by the following six parts. The files that are +listed in parentheses correspond to the file made by vmcdry.out. + +(1) List: + + No keyword (namelist.def): This file is a list of input file names + with keywords. Each keywords is fixed, but file names are free to + be determined. + +(2) Basic parameters: + + **ModPara** (modpara.def): Set the parameters for basic parameters + such as site number, electron number, Lanczos step *etc*. + **LocSpin (locspn.def)**: Set the location of local spin. + +(3) Hamiltonian: + + Hamiltonian for mVMC is denoted by + + .. math:: + + \begin{aligned} + {\cal H}&={\cal H}_T+{\cal H}_U+{\cal H}_V+{\cal H}_H+{\cal H}_E+{\cal H}_P+{\cal H}_I,\\ + {\cal H}_T&=-\sum_{i, j}\sum_{\sigma_1, \sigma2}t_{ij\sigma_1\sigma_2} c_{i\sigma_1}^{\dagger}c_{j\sigma_2},\\ + {\cal H}_U&=\sum_{i} U_i n_ {i \uparrow}n_{i \downarrow},\\ + {\cal H}_V&=\sum_{i,j} V_{ij}n_ {i}n_{j},\\ + {\cal H}_H&=-\sum_{i,j}J_{ij}^{\rm Hund} (n_{i\uparrow}n_{j\uparrow}+n_{i\downarrow}n_{j\downarrow}),\\ + {\cal H}_E&=\sum_{i,j}J_{ij}^{\rm Ex} (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow}+c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow}),\\ + {\cal H}_P&=\sum_{i,j}J_{ij}^{\rm Pair} c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{i \downarrow}^{\dagger}c_{j \downarrow},\\ + {\cal H}_I&=\sum_{i,j,k,l}\sum_{\sigma_1,\sigma_2, \sigma_3, \sigma_4} + I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}, \end{aligned} + + as the format of interactions for electron system. Here, we + define the charge density operator with spin :math:`\sigma` at + site :math:`i` as + :math:`n_{i \sigma}=c_{i\sigma}^{\dagger}c_{i\sigma}` and the total + charge density operator at site :math:`i` as + :math:`n_i=n_{i\uparrow}+n_{i\downarrow}`. Each parameters are + specified by the following files, respectively; + + **Trans (trans.def)**: :math:`t_{ij\sigma_1\sigma_2}` in + :math:`{\cal H}_T`, + + **CoulombIntra (coulombintra.def)**: :math:`U_i` in + :math:`{\cal H}_U`, + + **CoulombInter (coulombinter.def)**: :math:`V_{ij}` in + :math:`{\cal H}_V`, + + **Hund (hund.def)**: :math:`J_{ij}^{\rm Hund}` in + :math:`{\cal H}_H`, + + **Exchange (exchange.def)**: :math:`J_{ij}^{\rm Ex}` in + :math:`{\cal H}_E`, + + **PairHop**: :math:`J_{ij}^{\rm Pair}` in :math:`{\cal H}_P`, + + **InterAll**: :math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}` in + :math:`{\cal H}_I`. + +(4) Variational parameters to be optimized: + + The variational parameters to be optimized are specified by using + this categorized files. In mVMC, the variational wave function is + given as + + .. math:: + + \begin{aligned} + |\psi \rangle &= {\cal P}_G{\cal P}_J{\cal P}_{d-h}^{(2)}{\cal P}_{d-h}^{(4)}{\cal L}^S{\cal L}^K{\cal L}^P |\phi_{\rm pair} \rangle,\\ + {\cal P}_G&=\exp\left[ \sum_i g_i n_{i\uparrow} n_{i\downarrow} \right],\\ + {\cal P}_J&=\exp\left[\frac{1}{2} \sum_{i\neq j} v_{ij} (n_i-1)(n_j-1)\right],\\ + {\cal P}_{d-h}^{(2)}&= \exp \left[ \sum_t \sum_{n=0}^2 (\alpha_{2nt}^d \sum_{i}\xi_{i2nt}^d+\alpha_{2nt}^h \sum_{i}\xi_{i2nt}^h)\right],\\ + {\cal P}_{d-h}^{(4)}&= \exp \left[ \sum_t \sum_{n=0}^4 (\alpha_{4nt}^d \sum_{i}\xi_{i4nt}^d+\alpha_{4nt}^h \sum_{i}\xi_{i4nt}^h)\right],\\ + {\cal L}_S&=\frac{2S+1}{8 \pi^2}\int d\Omega P_s(\cos \beta) \hat{R}(\Omega),\\ + {\cal L}_K&=\frac{1}{N_s}\sum_{{\boldsymbol R}}e^{i {\boldsymbol K} \cdot{\boldsymbol R} } \hat{T}_{\boldsymbol R},\\ + {\cal L}_P&=\sum_{\alpha}p_{\alpha} \hat{G}_{\alpha},\end{aligned} + + where :math:`\Omega=(\alpha, \beta, \gamma)` is the Euler angle, + :math:`\hat{R}(\Omega)` is the rotational operator, :math:`P_S(x)` + is the :math:`S`-th polynomial, :math:`{\boldsymbol K}` is the momentum + operator of the whole system and :math:`\hat{T}_{\boldsymbol R}` is the + translational operators corresponding to the translational vector + :math:`{\boldsymbol R}`, :math:`\hat{G}_{\alpha}` is the point group + operator, and :math:`p_\alpha` is the parity operator, + respectively. The details of :math:`{\cal P}_{d-h}^{(2)}` and + :math:`{\cal P}_{d-h}^{(4)}` are shown in + [Tahara2008_ ]. The one body part of the + wavefunction is represented as the pair function of the real + space: + + .. math:: + + |\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} + \sum_{\sigma_1, \sigma_2}f_{i\sigma_1j \sigma_2} + c_{i\sigma_1}^{\dagger}c_{j\sigma_2}^{\dagger} \right]^{N/2}|0 \rangle, + + where :math:`N` is the number of electrons and :math:`N_s` is the + number of sites. The setting for optimizing variational parameters + or not is given by the following files (the parameters for + :math:`{\cal L}_S` are specified in the **ModPara** file). + + **Gutzwiller (gutzwilleridx.def)**: Set the target parameters + :math:`g_i` in :math:`{\cal P}_G` to be optimized. + + **Jastrow (jastrowidx.def)**: Set the target parameters + :math:`v_{ij}` in :math:`{\cal P}_J` to be optimized. + + **DH2**: Set the target 2-site doublon-holon correlation factor + :math:`\alpha_{2nt}^{d(h)}` in :math:`{\cal P}_{d-h}^{(2)}` to be + optimized. + + **DH4**: Set the target 4-site doublon-holon correlation factor + :math:`\alpha_{4nt}^{d(h)}` in :math:`{\cal P}_{d-h}^{(4)}` to be + optimized. + + **Orbital/OrbitalAntiParallel (orbitalidx.def)**: Set the pair + orbital with anti-parallel spins :math:`f_{i\uparrow j\downarrow}` + in :math:`|\phi_{\rm pair} \rangle` to be optimized. + + **OrbitalParallel**: Set the pair orbital with anti-parallel spins + :math:`f_{i\sigma j\sigma}` in :math:`|\phi_{\rm pair} \rangle` to + be optimized. + + **OrbitalGeneral**: Set the pair orbital with anti-parallel spins + :math:`f_{i\sigma j\sigma'}` in :math:`|\phi_{\rm pair} \rangle` + to be optimized. + + **TransSym (qptransidx.def)**: Set the the momentum projection + operators :math:`{\cal L}_K` and the lattice translational + projection operators :math:`{\cal L}_P`. + +(5) Initial variational parameters: + + Set the initial values of the variational parameters. When the + keyword is not setting, the corresponding parameters are given by + random values as default values. + + **InGutzwiller**: Set the initial values of :math:`g_i` in + :math:`{\cal P}_G`. + + **InJastrow**: Set the initial values of :math:`v_{ij}` in + :math:`{\cal P}_J`. + + **InDH2**: Set the initial values of :math:`\alpha_{2nt}^{d(h)}` + in :math:`{\cal P}_{d-h}^{(2)}`. + + **InDH4**: Set the initial values of :math:`\alpha_{4nt}^{d(h)}` + in :math:`{\cal P}_{d-h}^{(4)}`. + + **InOrbital /InOrbitalAntiParallel**: Set the initial values of + :math:`f_{i\uparrow j\downarrow}` in + :math:`|\phi_{\rm pair} \rangle`. + + **InOrbitalParallel**: Set the initial values of + :math:`f_{i\sigma j\sigma}` in :math:`|\phi_{\rm pair} \rangle`. + + **InOrbitalGeneral**: Set the initial values of + :math:`f_{i\sigma j\sigma'}` in :math:`|\phi_{\rm pair} \rangle`. + +(6) Output: + + **OneBodyG (greenone.def)**: Set the components of one-body green + functions to output. + + **TwoBodyG (greentwo.def)**: Set the components of two-body green + functions to output. + +.. _InputFileList: + +List file for Input files (namelist.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file determines input filenames correlated with keywords. An +example of the file format is shown as follows. + +:: + + ModPara modpara.def + LocSpin zlocspn.def + Trans ztransfer.def + InterAll zinterall.def + Orbital orbitalidx.def + OneBodyG zcisajs.def + TwoBodyG zcisajscktaltdc.def + +File format +^^^^^^^^^^^ + +[string01] [string02] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type + + **Description :** Select a word from keywords. + +- [ string02 ] + + **Type :** string-type + + **Description :** An input filename which is correlated with + keywords. + +User rules +^^^^^^^^^^ + +- After setting keywords at [string 01], half-width state is needed for + writing a filename. You can set the filename freely. + +- Keywords for input files are shown in Table [Table:Defs]. + +- Essential keywords are "CalcMod", "ModPara" , "LocSpin", "Orbital" + and "TransSym". + +- Keywords can be set in random order. + +- If keywords or filenames are incorrect, the program is terminated. + +- When the head of line is ``#``, the line is skipped. + +===================== =================================================================================== +Keywords Details for corresponding files +===================== =================================================================================== +ModPara :math:`^*` Parameters for calculation. +LocSpin :math:`^*` Configurations of the local spins for Hamiltonian. +Trans Transfer and chemical potential for Hamiltonian. +InterAll Two-body interactions for Hamiltonian. +CoulombIntra CoulombIntra interactions. +CoulombInter CoulombInter interactions. +Hund Hund couplings. +PairHop Pair hopping couplings. +Exchange Exchange couplings. +Gutzwiller Gutzwiller factors. +Jastrow Charge Jastrow factors. +DH2 2-site doublon-holon correlation factors. +DH4 4-site doublon-holon correlation factors. +Orbital :math:`^*` Pair orbital factors with anti-parallel spins :math:`f_{i\uparrow j\downarrow}`. +OrbitalAntiParallel Pair orbital factors with anti-parallel spins :math:`f_{i\uparrow j\downarrow}`. +OrbitalParallel Pair orbital factors with parallel spins :math:`f_{i\sigma j\sigma}`. +OrbitalGeneral Pair orbital factors :math:`f_{i\sigma_1 j\sigma_2}`. +TransSym :math:`^*` Translational and lattice symmetry operation. +InGutzwiller Initial values of Gutzwiller factors. +InJastrow Initial values of charge Jastrow factors. +InDH2 Initial values of 2-site doublon-holon correlation factors. +InDH4 Initial values of 4-site doublon-holon correlation factors. +InOrbital Initial values of pair orbital factors :math:`f_{i\uparrow j\downarrow}`. +InOrbitalAntiParallel Initial values of pair orbital factors :math:`f_{i\uparrow j\downarrow}`. +InOrbitalParallel Initial values of pair orbital factors :math:`f_{i\sigma j\sigma}`. +InOrbitalGeneral Initial values of pair orbital factors :math:`f_{i\sigma_1 j\sigma_2}`. +OneBodyG Output components for Green functions + :math:`\langle c_{i\sigma}^{\dagger}c_{j\sigma}\rangle` +TwoBodyG Output components for Correlation functions + :math:`\langle c_{i\sigma}^{\dagger}c_{j\sigma}c_{k\tau}^{\dagger}c_{l\tau}\rangle` +===================== =================================================================================== + +ModPara file (modpara.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file determines parameters for calculation. An example of the +file format is shown as follows. + +:: + + -------------------- + Model_Parameters 0 + -------------------- + VMC_Cal_Parameters + -------------------- + CDataFileHead zvo + CParaFileHead zqp + -------------------- + NVMCCalMode 0 + NLanczosMode 0 + -------------------- + NDataIdxStart 1 + NDataQtySmp 1 + -------------------- + Nsite 16 + Nelectron 8 + NSPGaussLeg 1 + NSPStot 0 + NMPTrans 1 + NSROptItrStep 1200 + NSROptItrSmp 100 + DSROptRedCut 0.001 + DSROptStaDel 0.02 + DSROptStepDt 0.02 + NVMCWarmUp 10 + NVMCInterval 1 + NVMCSample 1000 + NExUpdatePath 0 + RndSeed 11272 + NSplitSize 1 + NStore 1 + +File format +^^^^^^^^^^^ + +- Lines 1 - 5: Header + +- Line 6: [string01] [string02] + +- Line 7: [string03] [string04] + +- Line 8: Header + +- Lines 9 - : [string05] [int01] (or [double01]) + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** Set a keyword for header of output files. + +- [ string02 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** Set a header of output files. For example, the + output file of one-body green’s functions are named as + **xxx\_cisajs.dat**, where **xxx** is [ string02 ]. + +- [ string03 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** Set a keyword for header of output files for + variational parameters. + +- [ string04 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** Set a header of output files for variational + parameters. For example, the output file of optimized variational + parameters are named as **xxx\_opt.dat**, where **xxx** is + [ string04 ]. + +- [ string05 ] + + **Type :** string-type + + **Description :** Select a word from keywords. + +- [ int01 ] ([double01]) + + **Type :** int (double)-type (blank parameter not allowed) + + **Description :** A parameter which is correlated with a keyword. + +User rules +^^^^^^^^^^ + +- From Line 9: After setting keywords at [string 01], a half-width + blank is needed for setting a parameter. + +- From Line 9: When the first character of the line is "-", the line is + not read and skipped. + +Keywords and parameters +^^^^^^^^^^^^^^^^^^^^^^^ + +- ``NVMCCalMode`` + + **Type :** int-type (default value: 0) + + **Description :** [0] Optimization of variational parameters, [1] + Calculation of one body and two body Green’s functions. + +- ``NLanczosMode`` + + **Type :** int-type (default value: 0) + + **Description :** [0] Not using single Lanczos step, [1] Calculating + energy by using Single Lanczos Step, [2] Calculating one body and two + body Green’s functions by using Single Lanczos Step (Condition: The + options 1 and 2 can be selected when ``NVMCCalMode`` = 1). + +- ``NDataIdxStart`` + + **Type :** int-type (default value: 0) + + **Description :** An integer for numbering of output files. For + ``NVMCCalMode`` = 0 , ``NDataIdxStart`` is added at the end of the + output files. For ``NVMCCalMode`` = 1, the files are outputted with + the number from ``NDataIdxStart`` to + ``NDataIdxStart`` + ``NDataQtySmp``-1. + +- ``NDataQtySmp`` + + **Type :** int-type (default value: 1) + + **Description :** The set number for outputted files (only used for + ``NVMCCalMode`` = 1). + +- ``Nsite`` + + **Type :** int-type (Positive integer) + + **Description :** The number of sites. + +- ``Nelectron`` + + **Type :** int-type (Positive integer) + + **Description :** The number of electron pairs (the electron number + is given by 2 ``Nelectron``). + +- ``Ncond`` + + **Type :** int-type (greater than 0) + + **Description :** The number of conduction electrons. + +- ``2Sz`` + + **Type :** int-type + + **Description :** The value of :math:`2S_z`. Since the electrons form + pair, :math:`2S_z` must be even number. + +- ``NSPGaussLeg`` + + **Type :** int-type (Positive integer, default value: 8) + + **Description :** The mesh number for the Gauss-legendre quadrature + about :math:`\beta` integration (:math:`S_y` rotation) for the spin + quantum-number projection in actual numerical calculation. + +- ``NSPStot`` + + **Type :** int-type ( greater than 0, default value: 0) + + **Description :** The spin quantum-number. + +- ``NMPTrans`` + + **Type :** int-type (default value: 1) + + **Description :** The absolute value gives the number of the momentum + and lattice translational quantum-number projection. When the value + is negative, the mode of anti-periodic condition turns on. The + quantum-number projection is used from the top to ``NMPTrans`` with + the specified weight indicated in ``TransSym`` file. In the case of + not applying the projection, this value must be equal to 1. + +- ``NSROptItrStep`` + + **Type :** int-type (Positive integer, default value: 1000) + + **Description :** The whole step number to optimize variational + parameters by SR method. Only used for ``NVMCCalMode`` =0. + +- ``NSROptItrSmp`` + + **Type :** int-type (Positive integer, default value: + ``NSROptItrStep``/10) + + **Description :** In the ``NSROptItrStep`` step, the average values + of the each variational parameters at the ``NSROptItrStep`` step are + adopted as the optimized values. Only used for ``NVMCCalMode`` =0. + +- ``DSROptRedCut`` + + **Type :** double-type (default value: 0.001) + + **Description :** The stabilized factor for the SR method by + truncation of redundant directions corresponding to + :math:`\varepsilon_{\rm wf}` in the ref. + [Tahara2008_ ]. + +- ``DSROptStaDel`` + + **Type :** double-type (default value: 0.02) + + **Description :** The stabilized factor for the SR method by + modifying diagonal elements in the overwrap matrix corresponding to + :math:`\varepsilon` in the ref. [Tahara2008_ ]. + +- ``DSROptStepDt`` + + **Type :** double-type + + **Description :** The time step using in the SR method. + +- ``NSROptCGMaxIter`` + + **Type :** int-type (default value: 0) + + **Description :** The maximum number of CG steps for the SR method. + If this is zero or negative, CG steps will be run as many as the size + of :math:`S` matrix at maximum. Only used for ``NSRCG``!=0. + +- ``DSROptCGTol`` + + **Type :** double-type (default value: 1.0e-10) + + **Description :** The convergence condition of a CG step in the SR + method. CG method runs until the root mean square of the residues + becomes below this value. Only used for ``NSRCG``!=0. + +- ``NVMCWarmUp`` + + **Type :** int-type (Positive integer, default value: 10) + + **Description :** Idling number for the Malkov chain Montecarlo + Methods. + +- ``NVMCInterval`` + + **Type :** int-type (Positive integer, default value: 1) + + **Description :** The interval step between samples. The local update + will be performed ``Nsite`` × ``NVMCInterval`` times. + +- ``NVMCSample`` + + **Type :** int-type (Positive integer, default value: 1000) + + **Description :** The sample numbers to calculate the expected + values. + +- ``NExUpdatePath`` + + **Type :** int-type (Positive integer) + + **Description :** The option for local update about exchange terms. + 0: not update, 1: update for electron system. For Spin system, the + value must be 2. + +- ``RndSeed`` + + **Type :** int-type + + **Description :** The initial seed of generating random number. For + MPI parallelization, the initial seeds are given by ``RndSeed`` +my + rank+1 at each ranks. + +- ``NSplitSize`` + + **Type :** int-type (Positive integer, default value: 1) + + **Description :** The number of processes of MPI parallelization. + +- ``NStore`` + + **Type :** int-type (0 or 1, default value: 1) + + **Description :** The option of applying matrix-matrix product to + calculate expected values :math:`\langle O_k O_l \rangle` (0: off, 1: + on). This speeds up calculation but increases the amount of memory + usage from :math:`O(N_\text{p}^2)` to + :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})`, where + :math:`N_\text{p}` is the number of the variational parameters and + :math:`N_\text{MCS}` is the number of Monte Carlo sampling. + +- ``NSRCG`` + + **Type :** int-type (0 or 1, default value: 0) + + **Description :** The option of solving :math:`Sx=g` in the SR method + without construting :math:`S` + matrix [NeuscammanUmrigarChan_ ]. (0: off, 1: on). + This reduces the amount of memory usage from + :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})` to + :math:`O(N_\text{p}) + O(N_\text{p}N_\text{MCS})` when + :math:`N_\text{p} > N_\text{MCS}`. + +LocSpin file (locspn.def) +~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file determines sites with localized spins. An example of the +file format is shown as follows. + +:: + + ================================ + NlocalSpin 6 + ================================ + ========i_0LocSpn_1IteElc ====== + ================================ + 0 1 + 1 0 + 2 1 + 3 0 + 4 1 + 5 0 + 6 1 + 7 0 + 8 1 + 9 0 + 10 1 + 11 0 + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 -: [int02] [int03] + +Parameters +^^^^^^^^^^ + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of localized spins. You + can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of localized spins. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ] :math:`<` ``Nsite``). + +- [ int03 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer for selecting an electron state whether + localized spin or itinerant electron states (0: Itinerant electron + state, 1: localized spin state with :math:`S=1/2`). + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of localized spins indicated by + [ int03 ]. + +- A program is terminated, when [ int02 ] is + different from the total number of sites. + +- A program is terminated under the condition + [ int02 ] :math:`<0` or + ``Nsite`` :math:`\leq` [ int02 ]. + +Trans file (trans.def) +~~~~~~~~~~~~~~~~~~~~~~ + +The Hamiltonian for general one-body interactions + +.. math:: + + \begin{aligned} + {\cal H}_{T} =-\sum_{ij\sigma_1\sigma2} + t_{ij\sigma_1\sigma2}c_{i\sigma_1}^{\dagger}c_{j\sigma_2},\end{aligned} + +is added to the whole Hamiltonian by setting the parameters +:math:`t_{ij\sigma_1\sigma2}`. An example of the file format is shown +as follows. + +:: + + ======================== + NTransfer 24 + ======================== + ========i_j_s_tijs====== + ======================== + 0 0 2 0 1.000000 0.000000 + 2 0 0 0 1.000000 0.000000 + 0 1 2 1 1.000000 0.000000 + 2 1 0 1 1.000000 0.000000 + 2 0 4 0 1.000000 0.000000 + 4 0 2 0 1.000000 0.000000 + 2 1 4 1 1.000000 0.000000 + 4 1 2 1 1.000000 0.000000 + 4 0 6 0 1.000000 0.000000 + 6 0 4 0 1.000000 0.000000 + 4 1 6 1 1.000000 0.000000 + 6 1 4 1 1.000000 0.000000 + 6 0 8 0 1.000000 0.000000 + 8 0 6 0 1.000000 0.000000 + … + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3-5: Header + +- Lines 6-: [int02] [int03] [int04] [int05] [double01] [double02] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of transfer integrals. + You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of transfer + integrals. + +- [ int02 ], [ int04 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ], [ int04 ] :math:`<` ``Nsite``). + +- [ int03 ], [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a spin index, + + 0: up-spin, + + 1: down-spin. + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for a real part of + :math:`t_{ij\sigma_1\sigma_2}`. + +- [ double02 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for an imaginary part of + :math:`t_{ij\sigma_1\sigma_2}`. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- Blank line is not allowed. + +- A program is terminated, when [ int01 ] is + different from the total number of transfer integrals defined in this + file. + +- A program is terminated, when + [ int02 ]-[ int05 ] are out of + range from the defined values. + +- Since Hamiltonian must be Hermitian, the following relation must be + satisfied, + :math:`t_{ij\sigma_1\sigma_2}=t_{ji\sigma_2\sigma_1}^{\dagger}`. + +InterAll file +~~~~~~~~~~~~~ + +The Hamiltonian for general two-body interactions + +.. math:: + + \begin{aligned} + {\cal H}_I =\sum_{i,j,k,l}\sum_{\sigma_1,\sigma_2, \sigma_3, \sigma_4} + I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4} + c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}. + \end{aligned} + +is added to the whole Hamiltonian by setting the parameters +:math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}`. An example of file +format is shown as follows. + +:: + + ====================== + NInterAll 36 + ====================== + ========zInterAll===== + ====================== + 0 0 0 1 1 1 1 0 0.50 0.0 + 0 1 0 0 1 0 1 1 0.50 0.0 + 0 0 0 0 1 0 1 0 0.25 0.0 + 0 0 0 0 1 1 1 1 -0.25 0.0 + 0 1 0 1 1 0 1 0 -0.25 0.0 + 0 1 0 1 1 1 1 1 0.25 0.0 + 2 0 2 1 3 1 3 0 0.50 0.0 + 2 1 2 0 3 0 3 1 0.50 0.0 + 2 0 2 0 3 0 3 0 0.25 0.0 + 2 0 2 0 3 1 3 1 -0.25 0.0 + 2 1 2 1 3 0 3 0 -0.25 0.0 + 2 1 2 1 3 1 3 1 0.25 0.0 + 4 0 4 1 5 1 5 0 0.50 0.0 + 4 1 4 0 5 0 5 1 0.50 0.0 + 4 0 4 0 5 0 5 0 0.25 0.0 + 4 0 4 0 5 1 5 1 -0.25 0.0 + 4 1 4 1 5 0 5 0 -0.25 0.0 + 4 1 4 1 5 1 5 1 0.25 0.0 + ... + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 -: + [int02] [int03] [int04] [int05] [int06] [int07] [int08] [int09] [double01] [double02] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of generalized two body + interactions. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of generalized two + body interactions. + +- [ int02 ], [ int04 ], + [ int06 ], [ int08 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 :math:`], [` int04 ], [ int06 ], [ int08 ] :math:`<` ``Nsite``). + +- [ int03 ], [ int05 ], + [ int07 ], [ int09 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a spin index, + + 0: up-spin, + + 1: down-spin. + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for a real part of + :math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}`. + +- [ double02 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for an imaginary part of + :math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}`. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- Since Hamiltonian must be Hermitian, the following relation must be + satisfied, + :math:`I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}=I_{lkji\sigma_4\sigma_3\sigma_2\sigma_1}^{\dagger}`. + +- A program is terminated, when [ int01 ] is + different from the total number of generalized two body interactions + defined in this file. + +- A program is terminated, when + [ int02 ]-[ int09 ] are out of + range from the defined values. + +CoulombIntra file (coulombintra.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The Hamiltonian for the coulombintra interactions + +.. math:: + + {\cal H}_U =\sum_{i}U_i n_ {i \uparrow}n_{i \downarrow} + +is added to the whole Hamiltonian by setting :math:`U_i`. An example of +the file format is shown as follows. + +:: + + ====================== + NCoulombIntra 6 + ====================== + ========i_0LocSpn_1IteElc ====== + ====================== + 0 4.000000 + 1 4.000000 + 2 4.000000 + 3 4.000000 + 4 4.000000 + 5 4.000000 + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 -: [int02] [double01] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of on-site interactions. + You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of on-site + interactions. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ] :math:`<` ``Nsite``). + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for :math:`U_i`. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of on-site interactions defined in + this file. + +- A program is terminated, when [ int02 ] is out of + range from the defined values. + +CoulombInter file (coulombinter.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The Hamiltonian for the coulombintrer interactions + +.. math:: + + {\cal H}_V = \sum_{i,j}V_{ij} n_ {i} n_{j} + +is added to the whole Hamiltonian by setting :math:`V_{ij}`. An example +of the file format is shown as follows. + +:: + + ====================== + NCoulombInter 6 + ====================== + ========CoulombInter ====== + ====================== + 0 1 1.0000 + 1 2 1.0000 + 2 3 1.0000 + 3 4 1.0000 + 4 5 1.0000 + 5 0 1.0000 + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 -: [int02] [int03] [double01] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of off-site + interactions. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of off-site + interactions. + +- [ int02 ], [ int03 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ], [ int03 ] :math:`<` ``Nsite``). + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for :math:`V_{ij}`. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of off-site interactions defined in + this file. + +- A program is terminated, when either [ int02 ] or + [ int03 ] are out of range from the defined values. + +Hund file (hund.def) +~~~~~~~~~~~~~~~~~~~~ + +The Hamiltonian for Hund couplings + +.. math:: + + {\cal H}_H =-\sum_{i,j}J_{ij}^{\rm Hund} (n_{i\uparrow}n_{j\uparrow}+n_{i\downarrow}n_{j\downarrow}) + +is added to the whole Hamiltonian by setting the parameters +:math:`J_{ij}^{\rm Hund}`. An example of the file format is shown as +follows. + +:: + + ====================== + NHund 6 + ====================== + ========Hund ====== + ====================== + 0 1 -0.250000 + 1 2 -0.250000 + 2 3 -0.250000 + 3 4 -0.250000 + 4 5 -0.250000 + 5 0 -0.250000 + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 -: [int02] [int03] [double01] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of Hund couplings. You + can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of Hund couplings. + +- [ int02 ], [ int03 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ], [ int03 ] :math:`<` ``Nsite``). + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for :math:`J_{ij}^{\rm Hund}`. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of Hund couplings defined in this + file. + +- A program is terminated, when either [ int02 ] or + [ int03 ] are out of range from the defined values. + +PairHop file +~~~~~~~~~~~~ + +The Hamiltonian for PairHop couplings + +.. math:: + + {\cal H}_P=\sum_{i,j}J_{ij}^{\rm Pair} (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{i \downarrow}^{\dagger}c_{j \downarrow} + +c_{j \downarrow}^{\dagger}c_{i \downarrow}c_ {j \uparrow}^{\dagger}c_{i\uparrow}) + +is added to the whole Hamiltonian by setting the parameters +:math:`J_{ij}^{\rm Pair}`. An example of the file format is shown as +follows. + +:: + + ====================== + NPairhop 6 + ====================== + ========Pairhop ====== + ====================== + 0 1 0.50000 + 1 2 0.50000 + 2 3 0.50000 + 3 4 0.50000 + 4 5 0.50000 + 5 0 0.50000 + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 -: [int02] [int03] [double01] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of PairHop couplings. + You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of PairHop + couplings. + +- [ int02 ], [ int03 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ], [ int03 ] :math:`<` ``Nsite``). + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for :math:`J_{ij}^{\rm Pair}`. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of PairHop couplings defined in this + file. + +- A program is terminated, when either [ int02 ] or + [ int03 ] are out of range from the defined values. + +Exchange file (exchange.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The Hamiltonian for exchange couplings + +.. math:: + + {\cal H}_E =\sum_{i,j}J_{ij}^{\rm Ex} + (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow} + +c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow}) + +is added to the whole Hamiltonian by setting :math:`J_{ij}^{\rm Ex}`. +An example of the file format is shown as follows. + +:: + + ====================== + NExchange 6 + ====================== + ========Exchange ====== + ====================== + 0 1 0.50000 + 1 2 0.50000 + 2 3 0.50000 + 3 4 0.50000 + 4 5 0.50000 + 5 0 0.50000 + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3-5: Header + +- Lines 6-: [int02] [int03] [double01] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of Exchange couplings. + You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of Exchange + couplings. + +- [ int02 ], [ int03 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ], [ int03 ] :math:`<` ``Nsite``). + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** A value for :math:`J_{ij}^{\rm Ex}`. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of Exchange couplings defined in this + file. + +- A program is terminated, when either [ int02 ] or + [ int03 ] are out of range from the defined values. + +Gutzwiller file (gutzwiller.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file sets the calculation conditions of Gutzwiller factors + +.. math:: + + {\cal P}_G=\exp\left[ \sum_i g_i n_{i\uparrow} n_{i\downarrow} \right]. + +A site number :math:`i` and the variational parameters :math:`g_i` are +specified. An example of the file format is shown as follows. + +:: + + ====================== + NGutzwillerIdx 2 + ComplexType 0 + ====================== + ====================== + 0 0 + 1 0 + 2 0 + 3 1 + (continue...) + 12 1 + 13 0 + 14 0 + 15 0 + 0 1 + 1 0 + +File format +^^^^^^^^^^^ + +In the following, we define the whole number of sites as :math:`N_s` and +variational parameters as :math:`N_g`, respectively. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Line 3: [string02] [int02] + +- Lines 4 - 5: Header + +- Lines 6 - (5+ :math:`N_s`): [int03] [int04] + +- Lines (6+ :math:`N_s`) - (5+ :math:`N_s` + :math:`N_g`): + [int05] [int06] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of variational + parameters :math:`g_i`. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of variational + parameters :math:`g_i`. + +- [ string02 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for indicating the double or complex type + of variational parameters :math:`g_i`. You can freely give a name of + the keyword. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer indicates the double or complex type of + variational parameters :math:`g_i` (0: double, 1: complex). + +- [ int03 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int03 ] :math:`<` ``Nsite``). + +- [ int04 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer setting kinds of variational parameters + :math:`g_i` (0 :math:`\leq` [ int04 ] :math:`<` [ int01]). + +- [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving kinds of variational parameters + (0 :math:`\leq` [ int05 ] :math:`<` [ int01]). + +- [ int06 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer to select the target of variational + parameters indicated at [int05] to be optimized or not (0: not + optimize, 1: optimize). + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when components of variational parameters + are double counted. + +- A program is terminated, when [ int01 ] is + different from the total number of variational parameters defined in + this file. + +- A program is terminated, when [ int02 ] - + [ int06 ] are out of range from the defined values. + +Jastrow file (jastrow.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file sets the calculation conditions of Jastrow factors + +.. math:: + + {\cal P}_J=\exp\left[\frac{1}{2} \sum_{i\neq j} v_{ij} (n_i-1)(n_j-1)\right] + +Site numbers :math:`i` :math:`j`, and the variational parameters +:math:`v_{ij}` are specified. An example of the file format is shown as +follows. + +:: + + ====================== + NJastrowIdx 5 + ComplexType 0 + ====================== + ====================== + 0 1 0 + 0 2 1 + 0 3 0 + (continue...) + 0 1 + 1 1 + 2 1 + 3 1 + 4 1 + +File format +^^^^^^^^^^^ + +In the following, we define the total number of sites as :math:`N_s` and +variational parameters as :math:`N_j`, respectively. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Line 3: [string02] [int02] + +- Lines 4 - 5: Header + +- Lines 6 - (5+ :math:`N_s\times (N_s-1))`: [int03] [int04] [int05] + +- Lines (6+ :math:`N_s\times (N_s-1)`) - + (5+ :math:`N_s\times (N_s-1)` + :math:`N_j`): [int06] [int07] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of variational + parameters :math:`v_{ij}`. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of variational + parameters :math:`v_{ij}`. + +- [ string02 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for indicating the double or complex type + of variational parameters :math:`v_{ij}`. You can freely give a name + of the keyword. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer indicates the double or complex type of + variational parameters :math:`v_{ij}` (0: double, 1: complex). + +- [ int03 ], [ int04 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int03 ], [ int04 ] :math:`<` ``Nsite``). + +- [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer setting kinds of variational parameters + :math:`v_{ij}` (0 :math:`\leq` [ int05 ] :math:`<` [ int01]). + +- [ int06 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving kinds of variational parameters + (0 :math:`\leq` [ int06 ] :math:`<` [ int01]). + +- [ int07 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer to select the target of variational + parameters indicated at [int06] to be optimized or not (0: not + optimize, 1: optimize). + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of variational parameters defined in + this file. + +- A program is terminated, when [ int02 ] - + [ int07 ] are out of range from the defined values. + +DH2 file +~~~~~~~~ + +This file sets the calculation conditions of 2-site doublon-holon +correlation factors + +.. math:: + + {\cal P}_{d-h}^{(2)}= \exp \left[ \sum_t \sum_{n=0}^2 + (\alpha_{2nt}^d \sum_{i}\xi_{i2nt}^d+\alpha_{2nt}^h \sum_{i}\xi_{i2nt}^h)\right]. + +A site number :math:`i`, the two sites around :math:`i` site and the +variational parameters :math:`\alpha_{2nt}^{d(h)}` which have :math:`t` +kinds at each sites are specified. The details of the parameters +:math:`\alpha_{2nt}^{d(h)}` and the operator :math:`\xi_{i2nt}^{d(h)}` +are shown in ref. [Tahara2008_ ]. An example of the file +format is shown as follows. + +:: + + ==================================== + NDoublonHolon2siteIdx 2 + ComplexType 0 + ==================================== + ==================================== + 0 5 15 0 + 0 13 7 1 + (continue...) + 15 8 2 1 + 0 1 + (continue...) + 11 1 + +File format +^^^^^^^^^^^ + +In the following, we define the total number of sites as :math:`N_s` and +variational parameters as :math:`N_{\rm dh2}`, respectively. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Line 3: [string02] [int02] + +- Lines 4 - 5: Header + +- Lines 6 - (5+ :math:`N_s\times N_{\rm dh2})`: + [int03] [int04] [int05] [int06] + +- Lines (6+ :math:`N_s\times N_{\rm dh2}`) - + (5+ :math:`(N_s+6) \times N_{\rm dh2})`: [int07] [int08] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of variational + parameters. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of variational + parameters. + +- [ string02 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for indicating the double or complex type + of variational parameters. You can freely give a name of the keyword. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer indicates the double or complex type of + variational parameters (0: double, 1: complex). + +- [ int03 ], [ int04 ], + [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int03 ], [ int04 ], [ int05 ] :math:`<` ``Nsite``). + +- [ int06 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer setting kinds of variational parameters + (0 :math:`\leq` [ int06 ] :math:`<` [ int01]). + +- [ int07 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving kinds of variational parameters. + The value is :math:`(2n+s)\times` [int01]:math:`+t`, where + :math:`n`, :math:`s` and :math:`t` are given by the following + relation: + + - :math:`n`: The number of doublon (holon) around the center site + (0, 1, 2), + + - :math:`s`: When the center is doublon (holon), s=0 (1), + + - :math:`t`: The kind of variational parameters (0, :math:`\cdots` + [int1]-1). + +- [ int08 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer to select the target of variational + parameters indicated at [int07] to be optimized or not (0: not + optimize, 1: optimize). + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of variational parameters defined in + this file. + +- A program is terminated, when [ int02 ] - + [ int08 ] are out of range from the defined values. + +DH4 file +~~~~~~~~ + +This file sets the calculation conditions of 4-site doublon-holon +correlation factors + +.. math:: + + {\cal P}_{d-h}^{(4)}= \exp \left[ \sum_t \sum_{n=0}^4 + (\alpha_{4nt}^d \sum_{i}\xi_{i4nt}^d+\alpha_{4nt}^h \sum_{i}\xi_{i4nt}^h)\right] + +A site number :math:`i`, the four sites around :math:`i` site and the +variational parameters :math:`\alpha_{4nt}^{d(h)}` which have :math:`t` +kinds at each sites are specified. The details of the parameters +:math:`\alpha_{4nt}^{d(h)}` and the operator :math:`\xi_{i4nt}^{d(h)}` +are shown in ref. [Tahara2008_ ]. An example of the file +format is shown as follows. + +:: + + ==================================== + NDoublonHolon4siteIdx 1 + ComplexType 0 + ==================================== + ==================================== + 0 1 3 4 12 0 + 1 2 0 5 13 0 + (continue...) + 15 12 14 3 11 0 + 0 1 + (continue...) + 9 1 + +File format +^^^^^^^^^^^ + +In the following, we define the total number of sites as :math:`N_s` and +variational parameters as :math:`N_{\rm dh4}`, respectively. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Line 3: [string02] [int02] + +- Lines 4 - 5: Header + +- Lines 6 - (5+ :math:`N_s\times N_{\rm dh4}`): + [int03] [int04] [int05] [int06] [int07] [int08] + +- Lines (6+ :math:`N_s\times N_{\rm dh4}`) - + (5+ :math:`(N_s+10) \times N_{\rm dh4}`): [int09] [int10] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of variational + parameters. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of variational + parameters. + +- [ string02 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for indicating the double or complex type + of variational parameters. You can freely give a name of the keyword. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer indicates the double or complex type of + variational parameters (0: double, 1: complex). + +- [ int03 ], [ int04 ], + [ int05 ], [ int06 ], + [ int07 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int03 :math:`], \cdots, [` int07 ] :math:`<` ``Nsite``). + +- [ int08 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer setting kinds of variational parameters + (0 :math:`\leq` [ int08 ] :math:`<` [ int01]). + +- [ int09 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving kinds of variational parameters. + The value is :math:`(2n+s)\times` [int01]:math:`+t`, where + :math:`n`, :math:`s` and :math:`t` are given by the following + relation: + + - :math:`n`: The number of doublon (holon) around the center site + (0, 1, 2, 3, 4), + + - :math:`s`: When the center is doublon (holon), s=0 (1), + + - :math:`t`: The kind of variational parameters (0, :math:`\cdots` + [int1]-1). + +- [ int10 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer to select the target of variational + parameters indicated at [int09] to be optimized or not (0: not + optimize, 1: optimize). + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when components of variational parameters + are double counted. + +- A program is terminated, when [ int01 ] is + different from the total number of variational parameters defined in + this file. + +- A program is terminated, when [ int02 ] - + [ int10 ] are out of range from the defined values. + +Orbital/OrbitalAntiParallel file (orbitalidx.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file sets the calculation conditions of pair orbitals + +.. math:: + + |\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} + f_{ij}c_{i\uparrow}^{\dagger}c_{j\downarrow}^{\dagger} \right]^{N/2}|0 \rangle. + +Site numbers :math:`i, j` and the variational parameters :math:`f_{ij}` +are indicated. An example of the file format is shown as follows. + +:: + + ==================================== + NOrbitalIdx 64 + ComplexType 0 + ==================================== + ==================================== + 0 0 0 + 0 1 1 + 0 2 2 + 0 3 3 + (continue...) + 15 9 62 + 15 10 63 + 0 1 + 1 1 + (continue...) + 62 1 + 63 1 + +File format +^^^^^^^^^^^ + +In the following, we define the total number of sites as :math:`N_s` and +variational parameters as :math:`N_{\rm o}`, respectively. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Line 3: [string02] [int02] + +- Lines 4 - 5: Header + +- Lines 6 - (5+ :math:`N_s^2`): [int03] [int04] [int05] [int06] + +- Lines (6+ :math:`N_s^2` )- (5+ :math:`N_s^2+N_{\rm o}`): + [int06] [int07] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of variational + parameters. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of variational + parameters. + +- [ string02 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for indicating the double or complex type + of variational parameters. You can freely give a name of the keyword. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer indicates the double or complex type of + variational parameters (0: double, 1: complex). + +- [ int03 ], [ int04 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int03 ], [ int04 ] :math:`<` ``Nsite``). + +- [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer setting kinds of variational parameters + (0 :math:`\leq` [ int05 ] :math:`<` [ int01]). + +- [ int06 ] + + **Type :** int-type + + **Description :** When the mode of the anti-periodic condition turns + on (the mode turns on when the value of ``NMPTrans`` in ``ModPara`` + file is negative), the sign of :math:`f_{ij}` is specified by setting + [ int06 :math:`]=\pm1`. This term can be omitted when the + mode of the anti-periodic condition is off. + +- [ int07 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving kinds of variational parameters + (0 :math:`\leq` [ int06 ] :math:`<` [ int01]). + +- [ int08 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer to select the target of variational + parameters indicated at [int06] to be optimized or not (0: not + optimize, 1: optimize). + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of variational parameters defined in + this file. + +- A program is terminated, when [ int02 ] - + [ int09 ] are out of range from the defined values. + +OrbitalParallel file +~~~~~~~~~~~~~~~~~~~~ + +This file sets the calculation conditions of pair orbitals + +.. math:: + + |\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} \sum_{\sigma} + f_{i\sigma j\sigma}c_{i\sigma}^{\dagger}c_{j\sigma}^{\dagger} \right]^{N/2}|0 \rangle. + +Site numbers :math:`i, j`, the spin index :math:`\sigma` and the +variational parameters :math:`f_{i\sigma j\sigma}` are indicated. The +indexes of :math:`f_{i\sigma j\sigma}` must satisfy the condition +:math:`i < j `, where :math:`\sigma = 0` or :math:`1` and process will +terminate when the condition is broken. An example of the file format is +shown as follows. + +:: + + ==================================== + NOrbitalIdx 120 + ComplexType 0 + ==================================== + ==================================== + 0 1 0 + 0 2 1 + 0 3 2 + (continue...) + 15 13 118 + 15 14 119 + 0 1 + 1 1 + (continue...) + 118 1 + 119 1 + +File format +^^^^^^^^^^^ + +In the following, we define the total number of sites as :math:`N_s` and +variational parameters as :math:`N_{\rm o}`, respectively. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Line 3: [string02] [int02] + +- Lines 4 - 5: Header + +- Lines 6 - (5+ :math:`N_s*(N_s-1)/2`): [int03] [int04] [int05] [int06] + +- Lines (6+ :math:`N_s*(N_s-1)/2` )- + (5+ :math:`N_s*(N_s-1)/2+N_{\rm o}`): [int06] [int07] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of variational + parameters. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of variational + parameters. + +- [ string02 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for indicating the double or complex type + of variational parameters. You can freely give a name of the keyword. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer indicates the double or complex type of + variational parameters (0: double, 1: complex). + +- [ int03 ], [ int04 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int03 ], [ int04 ] :math:`<` ``Nsite``). + +- [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer setting kinds of variational parameters + (0 :math:`\leq` [ int05 ] :math:`<` [ int01]). + +- [ int06 ] + + **Type :** int-type + + **Description :** When the mode of the anti-periodic condition turns + on (the mode turns on when the value of ``NMPTrans`` in ``ModPara`` + file is negative), the sign of :math:`f_{ij}` is specified by setting + [ int06 :math:`]=\pm1`. This term can be omitted when the + mode of the anti-periodic condition is off. + +- [ int07 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving kinds of variational parameters + (0 :math:`\leq` [ int06 ] :math:`<` [ int01]). + +- [ int08 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer to select the target of variational + parameters indicated at [int06] to be optimized or not (0: not + optimize, 1: optimize). + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of variational parameters defined in + this file. + +- A program is terminated, when [ int02 ] - + [ int09 ] are out of range from the defined values. + +OrbitalGeneral file +~~~~~~~~~~~~~~~~~~~ + +This file sets the calculation conditions of pair orbitals + +.. math:: + + |\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} \sum_{\sigma_1, \sigma_2} + f_{i\sigma_1j\sigma_2}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}^{\dagger} \right]^{N/2}|0 \rangle. + +Site numbers :math:`i, j`, spin indexes :math:`\sigma_1, \sigma_2` and +the variational parameters :math:`f_{i\sigma_1j\sigma_2}` are indicated. +The indexes of :math:`f_{i\sigma_1j\sigma_2}` must satisfy the condition +:math:`i+\sigma_1 N_s < j+\sigma_2 N_s`, where :math:`\sigma_i = 0` or +:math:`1` and process will terminate when the condition is broken. An +example of the file format is shown as follows. + +12.5cm + +:: + + ==================================== + NOrbitalIdx 255 + ComplexType 0 + ==================================== + ==================================== + 0 0 0 1 0 + 0 0 1 1 1 + (continue...) + 14 0 15 1 253 + 15 0 15 1 254 + 0 1 + 1 1 + (continue...) + 253 1 + 254 1 + +File format +^^^^^^^^^^^ + +In the following, we define the total number of sites as :math:`N_s` and +variational parameters as :math:`N_{\rm o}`, respectively. A total +number of variational parameters :math:`N_p` is given by :math:`N_s^2`, +:math:`2 N_s^2 -N_s` in :math:`Sz` conserved and :math:`S_z` +unconserved system, respectively. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Line 3: [string02] [int02] + +- Lines 4 - 5: Header + +- Lines 6 - (5+ :math:`N_p`): + [int03] [int04] [int05] [int06] [int07] [int08] + +- Lines (6+ :math:`N_p`) - (5+ :math:`N_p+N_{\rm o}`): [int09] [int10] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of variational + parameters. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of variational + parameters. + +- [ string02 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for indicating the double or complex type + of variational parameters. You can freely give a name of the keyword. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer indicates the double or complex type of + variational parameters (0: double, 1: complex). + +- [ int03 ], [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int03 ], [ int04 ] :math:`<` ``Nsite``). + +- [ int04 ], [ int06 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a spin index (:math:`0:\uparrow` + spin, :math:`1:\downarrow` spin). + +- [ int07 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer setting kinds of variational parameters + (0 :math:`\leq` [ int07 ] :math:`<` [ int01]). + +- [ int08 ] + + **Type :** int-type + + **Description :** When the mode of the anti-periodic condition turns + on (the mode turns on when the value of ``NMPTrans`` in ``ModPara`` + file is negative), the sign of :math:`f_{i\sigma_1j\sigma_2}` is + specified by setting [ int08 :math:`]=\pm1`. This term can + be omitted when the mode of the anti-periodic condition is off. + +- [ int09 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving kinds of variational parameters + (0 :math:`\leq` [ int09 ] :math:`<` [ int01]). + +- [ int10 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer to select the target of variational + parameters indicated at [int09] to be optimized or not (0: not + optimize, 1: optimize). + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of variational parameters defined in + this file. + +- A program is terminated, when [ int02 ] - + [ int10 ] are out of range from the defined values. + +TransSym file (qptransidx.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file sets the weight and corresponding site numbers of momentum +projection +:math:`{\cal L}_K=\frac{1}{N_s}\sum_{{\boldsymbol R}}e^{i {\boldsymbol K} \cdot{\boldsymbol R} } \hat{T}_{\boldsymbol R}` +and lattice translational projection +:math:`{\cal L}_P=\sum_{\alpha}p_{\alpha} \hat{G}_{\alpha}`. The +patterns of projection are indicated by :math:`(\alpha, {\boldsymbol R})`. We +note that the weight must be equal to :math:`1.0` when the projection is +not done. An example of the file format is shown as follows. + +12.5cm + +:: + + ==================================== + NQPTrans 4 + ==================================== + == TrIdx_TrWeight_and_TrIdx_i_xi == + ==================================== + 0 1.000000 + 1 1.000000 + 2 1.000000 + 3 1.000000 + 0 0 0 + (continue...) + 3 12 1 + 3 13 2 + +File format +^^^^^^^^^^^ + +In the following, we define the total number of sites as :math:`N_s` and +projection patterns as :math:`N_{\rm TS}`, respectively. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 - (5+ :math:`N_{\rm TS})`: [int02] [double01] + +- Lines (6+ :math:`N_{\rm TS}`) - (5+ :math:`(N_s+1) \times N_{\rm TS}`): + [int03] [int04] [int05] [int06] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of projection patterns. + You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of projection + patterns. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving the projection pattern + :math:`(\alpha, {\boldsymbol R})` + (0 :math:`\leq` [ int02 ] :math:`<` [ int01]). + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** The weight + :math:`p_{\alpha}\cos ({\boldsymbol K}\cdot {\boldsymbol R})` of the projection + pattern :math:`(\alpha, {\boldsymbol R})`. + +- [ int03 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving kinds of the projection pattern + :math:`(\alpha, {\boldsymbol R})` + (0 :math:`\leq` [ int03 ] :math:`<` [ int01]). + +- [ int04 ], [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int04 ], [ int05 ] :math:`<` ``Nsite``). + The site number [ int05 ] is given by applying the + translation and point group transformation indicated by + [ int03 ] to the site [ int04 ]. + +- [ int06 ] + + **Type :** int-type + + **Description :** When the mode of the anti-periodic condition turns + on (the mode turns on when the value of ``NMPTrans`` in ``ModPara`` + file is negative), the sign of the translational operator is + specified by setting [ int06 ] :math:`=\pm1`. This term can + be omitted when the mode of the anti-periodic condition is off. + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of projection patterns defined in + this file. + +- A program is terminated, when [ int02 ] - + [ int06 ] are out of range from the defined values. + +.. _InputParam: + +Files to set initial values of variational parameters +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file sets the initial values of variational parameters. The kinds +of variational parameters are specified by setting the following +keywords in ``List`` file (namelist.def): +``InGutzwiller``, ``InJastrow``, ``InDH2``, ``InDH4``, ``InOrbital``, +``InOrbitalAntiParallel``, ``InOrbitalParallel``, +``InOrbitalGeneral``. +The file format is common and an example of the ``InJastrow`` file is +shown as follows. + +:: + + ====================== + NJastrowIdx 28 + ====================== + == i_j_JastrowIdx === + ====================== + 0 -8.909963465082626488e-02 0.000000000000000000e+00 + 1 5.521681211878626955e-02 0.000000000000000000e+00 + (continue...) + 27 -9.017586139930480749e-02 0.000000000000000000e+00 + +File format +^^^^^^^^^^^ + +In the following, we define the total number of variational parameters +as :math:`N_v`. + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 - (5+ :math:`N_v`): [int03] [double01] [double02] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of variational + parameters. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of variational + parameters. + +- [ int02 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer setting kinds of variational parameters + (0 :math:`\leq` [ int02 ] :math:`<` [ int01]). + +- [ double01 ] + + **Type :** double-type (blank parameter not allowed) + + **Description :** The real part of the variational parameter + indicated by [int01]. + +- [ double02 ] + + **Type :** double-type + + **Description :** The imaginary part of the variational parameter + indicated by [int01]. + +User rules +^^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of variational parameters defined in + this file. + +OneBodyG file (greenone.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file determines the target components to calculate and output +one-body Green’s function +:math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle`. An example +of file format is shown as follows. + +:: + + =============================== + NCisAjs 24 + =============================== + ======== Green functions ====== + =============================== + 0 0 0 0 + 0 1 0 1 + 1 0 1 0 + 1 1 1 1 + 2 0 2 0 + 2 1 2 1 + 3 0 3 0 + 3 1 3 1 + 4 0 4 0 + 4 1 4 1 + 5 0 5 0 + 5 1 5 1 + 6 0 6 0 + 6 1 6 1 + 7 0 7 0 + 7 1 7 1 + 8 0 8 0 + 8 1 8 1 + 9 0 9 0 + 9 1 9 1 + 10 0 10 0 + 10 1 10 1 + 11 0 11 0 + 11 1 11 1 + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 -: [int02] [int03] [int04] [int05] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of one-body Green’s + functions. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of one-body Green’s + functions. + +- [ int02 ], [ int04 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ], [ int04 ] :math:`<` ``Nsite``). + +- [ int03 ], [ int05 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a spin index, + + 0: up-spin, + + 1: down-spin. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of one-body Green’s functions defined + in this file. + +- A program is terminated, when + [ int02 ]-[ int05 ] are out of + range from the defined values. + +TwoBodyG file (greentwo.def) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file determines the target components to calculate and output +two-body Green’s function +:math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle`. +For Spin, the condition :math:`i=j` and :math:`k=l` must be satisfied. +An example of file format is shown as follows. + +:: + + ============================================= + NCisAjsCktAltDC 576 + ============================================= + ======== Green functions for Sq AND Nq ====== + ============================================= + 0 0 0 0 0 0 0 0 + 0 0 0 0 0 1 0 1 + 0 0 0 0 1 0 1 0 + 0 0 0 0 1 1 1 1 + 0 0 0 0 2 0 2 0 + 0 0 0 0 2 1 2 1 + 0 0 0 0 3 0 3 0 + 0 0 0 0 3 1 3 1 + 0 0 0 0 4 0 4 0 + 0 0 0 0 4 1 4 1 + 0 0 0 0 5 0 5 0 + 0 0 0 0 5 1 5 1 + 0 0 0 0 6 0 6 0 + 0 0 0 0 6 1 6 1 + 0 0 0 0 7 0 7 0 + 0 0 0 0 7 1 7 1 + 0 0 0 0 8 0 8 0 + 0 0 0 0 8 1 8 1 + 0 0 0 0 9 0 9 0 + 0 0 0 0 9 1 9 1 + 0 0 0 0 10 0 10 0 + 0 0 0 0 10 1 10 1 + 0 0 0 0 11 0 11 0 + 0 0 0 0 11 1 11 1 + 0 1 0 1 0 0 0 0 + ... + +File format +^^^^^^^^^^^ + +- Line 1: Header + +- Line 2: [string01] [int01] + +- Lines 3 - 5: Header + +- Lines 6 -: + [int02] [int03] [int04] [int05] [int06] [int07] [int08] [int09] + +Parameters +^^^^^^^^^^ + +- [ string01 ] + + **Type :** string-type (blank parameter not allowed) + + **Description :** A keyword for total number of two-body Green’s + functions. You can freely give a name of the keyword. + +- [ int01 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving total number of two-body Green’s + functions. + +- [ int02 ], + [ int04 ], [ int06 ], + [ int08 ] + + **Type :** int-type (blank parameter not allowed) + + **Description :** An integer giving a site index + (0 :math:`\leq` [ int02 ], [ int04 ], [ int06 ], [ int08 ] :math:`<` ``Nsite``). + +- [ int03 ], + [ int05 ], [ int07 ], + [ int09 ] + + **Type :** int-type (blank parameter not allowed) + + | **Description :** An integer giving a spin index, + | 0: up-spin, + | 1: down-spin. + +Use rules +^^^^^^^^^ + +- Headers cannot be omitted. + +- A program is terminated, when [ int01 ] is + different from the total number of two-body Green’s functions defined + in this file. + +- A program is terminated, when + [ int02 ]-[ int09 ] are out of + range from the defined values. diff --git a/doc/en/fourier/fourier_contact_en.rst b/doc/en/fourier/fourier_contact_en.rst new file mode 100644 index 00000000..9404d730 --- /dev/null +++ b/doc/en/fourier/fourier_contact_en.rst @@ -0,0 +1,12 @@ +Contact +======= + +If you have any comments, questions, bug reports etc. about this utility, +please contact to the main developer (Mitsuaki Kawamura) by +sending the e-mail (the address is shown below). + +:: + + mkawamura_at_issp.u-tokyo.ac.jp + +Please change ``_at_`` into ``@``, when you will send the e-mail. diff --git a/doc/en/fourier/fourier_format_en.rst b/doc/en/fourier/fourier_format_en.rst new file mode 100644 index 00000000..df29ac48 --- /dev/null +++ b/doc/en/fourier/fourier_format_en.rst @@ -0,0 +1,252 @@ +.. _fileformat: + +File format +=========== + +.. _geometry: + +Geometry +-------- + +The file name in the :ref:`tutorial` is ``geometry.dat``. +When we use Standard mode of mVMC/:math:`{\mathcal H}\Phi`, +this file is generated automatically. +Therefore we do not have to care it. + +:: + + 1.000000 0.000000 0.000000 (1) + 0.000000 1.000000 0.000000 (1) + 0.000000 0.000000 1.000000 (1) + 0.000000 0.000000 0.000000 (2) + 4 0 0 (3) + 0 4 0 (3) + 0 0 1 (3) + 0.000000 0.000000 0.000000 (4) + 1.000000 0.000000 0.000000 (4) + 2.000000 0.000000 0.000000 (4) + 3.000000 0.000000 0.000000 (4) + 0.000000 1.000000 0.000000 (4) + 1.000000 1.000000 0.000000 (4) + 2.000000 1.000000 0.000000 (4) + 3.000000 1.000000 0.000000 (4) + 0.000000 2.000000 0.000000 (4) + 1.000000 2.000000 0.000000 (4) + 2.000000 2.000000 0.000000 (4) + 3.000000 2.000000 0.000000 (4) + 0.000000 3.000000 0.000000 (4) + 1.000000 3.000000 0.000000 (4) + 2.000000 3.000000 0.000000 (4) + 3.000000 3.000000 0.000000 (4) + +#. The unit lattice vectors. Arbitrary unit. +#. The phase for the one-body term across boundaries of the simulation cell (degree unit). +#. Three integer vector specifying the shape of the simulation cell. + They are the same as the input parameters ``a0W``, ``a0L``, ``a0H``, ``a1W``... + in Standard mode. +#. The position of each site. The fractional coordinate is used. + + +One- and Two-body correlation function in the site representation +----------------------------------------------------------------- + +.. _greenindex: + +Specify the index of correlation function to be computed +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Specify the index of correlation functions +computed with mVMC/:math:`{\mathcal H}\Phi`. +When we use the standard mode, this file is generated automatically. +The general description is written in the manuals for mVMC/:math:`{\mathcal H}\Phi`. +The file names in the :ref:`tutorial` are ``greenone.def`` (one body) and ``greentwo.def`` (two body). + +For calculating correlation functions in :ref:`supported`, +indices must be specified as follows: + +- :math:`\langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle` + + :math:`\langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle` + with :math:`(i, j)` ranging on the whole site. + +- :math:`\langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle` + + :math:`\langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle` + with :math:`(i, j)` ranging on the whole site. + +- :math:`\langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle` and + :math:`\langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle` + + :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i \sigma} {\hat c}_{j \sigma'}^{\dagger} {\hat c}_{j \sigma'}\rangle` + with :math:`(i, j)` ranging on the whole site and + :math:`(\sigma, \sigma')` ranging from :math:`\uparrow` to :math:`\downarrow`. + +- :math:`\langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle` and + :math:`\langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle` + + For :math:`{\mathcal H}\Phi`, + :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i -\sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{j \sigma}\rangle` + with :math:`(i, j)` ranging on the whole site and + :math:`\sigma` ranging from :math:`\uparrow` to :math:`\downarrow`. + For mVMC, + :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{j \sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{i -\sigma}\rangle` + with :math:`(i, j)` ranging on the whole site and + :math:`\sigma` ranging from :math:`\uparrow` to :math:`\downarrow`. + In the both cases, please care the order of operators. + +In the default settings of Standard mode (``outputmode="corr"``), +the above indices are specified automatically. +Therefore we do not have to care it. + +.. _zvocisajs: + +Results of correlation function in the site representation +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The correlation functions having the indices specified in :ref:`greenindex` +are computed by mVMC/:math:`{\mathcal H}\Phi`, +and written to files. +The general description of this file is written in the manuals of mVMC/:math:`{\mathcal H}\Phi`. +File names in the :ref:`tutorial` are +``output/zvo_cisajs_001.dat`` and ``output/zvo_cisajscktalt_001.dat`` (mVMC), or +``output/zvo_cisajs.dat`` and ``output/zvo_cisajscktalt.dat`` (:math:`{\mathcal H}\Phi`). + +The utility ``fourier`` reads these files before the calculation. +If some of the correlation functions with indices written in :ref:`greenindex` are lacking +(for example, because Standard mode was not used), +this utility assume them as 0. + +.. _zvocorr: + +Correlation functions in the primitive Brillouin zone +----------------------------------------------------- + +This file contains the Fourier-transformed correlation function and +generated by the utility ``fourier``. +The file name in the :ref:`tutorial` is ``output/zvo_corr.dat``. + +:: + + #HPhi 16 (1) + # kx[1] ky[2] kz[3](Cart.) UpUp[4,5] (Re. Im.) DownDown[6,7] (2) + # Density[8,9] SzSz[10,11] S+S-[12,13] S-S+[14,15] (2) + #k-offset 0.0000000 0.0000000 0.0000000 (3) + 0.00000E+00 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) + 0.15708E+01 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) + : : + +#. ``"#HPhi"`` for the output of ``HPhi``, + ``"#mVMC"`` for the output of ``vmc.out`` + The subsequent integer indicate the number of :math:`k` points in the primitive Brillouine zone. +#. The description of the quantities in each column. +#. The :math:`k` offset for the one-body correlation function. + That is to say, the one-body correlation function in the 4-7 columns are those + at the :math:`k` point shifted from that point in the 1-3 column. +#. The :math:`k` point (Cartesian) and correlation functions. + The real- and the imaginary-part of each correlation function are written. + +.. _kpoint: + +*k*\-point file for corplot +--------------------------- + +This file is generated by ``fourier`` and +read by ``corplot`` when the correlation function is plotted. +The file name is ``kpoint.dat``. + +:: + + 81 9 (1) + 0.62832E+01 0.00000E+00 0.00000E+00 (2) + 0.00000E+00 0.62832E+01 0.00000E+00 (2) + 0.00000E+00 0.00000E+00 0.62832E+01 (2) + -0.62832E+01 -0.62832E+01 0.00000E+00 1 (3) + -0.47124E+01 -0.62832E+01 0.00000E+00 2 (3) + -0.31416E+01 -0.62832E+01 0.00000E+00 3 + -0.15708E+01 -0.62832E+01 0.00000E+00 4 + 0.00000E+00 -0.62832E+01 0.00000E+00 1 + 0.15708E+01 -0.62832E+01 0.00000E+00 2 + 0.31416E+01 -0.62832E+01 0.00000E+00 3 + 0.47124E+01 -0.62832E+01 0.00000E+00 4 + +#. The total number of :math:`k` points plotted by ``corplot`` and + the number of columns for displaying by splot of gnuplot. +#. Reciprocal lattice vectors (Cartesian coordinate). +#. The :math:`k` vector (Cartesian) and + the index of the equivalent :math:`k` point in the primitive Brillouin zone. + This number is the same as that in :ref:`zvocorr` + +.. _gnuplot: + +gnuplot script +-------------- + +This file is generated by ``corplot``, +and read from gnuplot launched automatically. +We also can launch gnuplot independently and ``load`` this script. +The file name is ``correlation.gp``. + +.. code-block:: gnuplot + + #set terminal pdf color enhanced \ (1) + #dashed dl 1.0 size 20.0cm, 20.0cm (1) + #set output 'correlation.pdf' (1) + #set view 60.0, 30.0 (1) + + set view equal xy + set ticslevel 0 + set hidden3d + set xlabel 'kx' + set ylabel 'ky' + set zrange [ 0.25000E-10: 0.18435E+00] + + set pm3d + set pm3d interpolate 5, 5 + set view 0.0, 0.0 + + ##### Set Brillouin-Zone Boundary ##### + + set arrow from -0.31416E+01, -0.31416E+01, ... + set arrow from -0.31416E+01, 0.31416E+01, ... + : + ##### End Set Brillouin-Zone Boundary ##### + + splot \ + 'correlation.dat' u 1:2:3 w l tit '1' (2) + pause -1 + +#. When we want to write the figure to a file, + this line is uncommented. + For pasting this figure on the paper etc., + we write the setting of font, line-color, and so on. + For more details, please see the manual of gnuplot. +#. Plotting the file in :ref:`correlation`. + +.. _correlation: + +Correlation function at wide range of *k* +----------------------------------------- + +This file is generated by ``corplot``, and +read from gnuplot through :ref:`gnuplot`. +The file name is ``correlation.dat``. + +:: + + -0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 + -0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 + -0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 + -0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 + 0.00000E+00 -0.62832E+01 0.18435E+00 0.00000E+00 + 0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 + 0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 + 0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 + 0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 + + -0.62832E+01 -0.47124E+01 0.36159E-01 0.00000E+00 + -0.47124E+01 -0.47124E+01 0.20921E-01 0.00000E+00 + -0.31416E+01 -0.47124E+01 0.11372E-01 0.00000E+00 + : + +The 1st and the 2nd column contains the :math:`k` vector (Cartesian). +3rd and the 4th column contains the correlation function and its standard error, respectively. diff --git a/doc/en/fourier/fourier_overview_en.rst b/doc/en/fourier/fourier_overview_en.rst new file mode 100644 index 00000000..63c2bc91 --- /dev/null +++ b/doc/en/fourier/fourier_overview_en.rst @@ -0,0 +1,63 @@ +Overview +======== + +This document is the manual for the utility +to perform the Fourier transformation of the correlation function +in the site representation generated by mVMC or :math:`{\mathcal H}\Phi`. + +Prerequisite +------------ + +The prerequisite of this utility is the same as that of mVMC or :math:`{\mathcal H}\Phi`. + +.. _supported: + +Supported quantities +-------------------- + +This utility supports the Fourier transformation of the following quantities: + +One-body correlations + +.. math:: + :nowrap: + + \begin{align} + \langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle + &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle + \\ + \langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle + &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle + \end{align} + +Density-density correlation + +.. math:: + + \begin{align} + \langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle + \equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat \rho}_{i} {\hat \rho}_{j}\rangle + \end{align} + +Spin-Spin correlations + +.. math:: + :nowrap: + + \begin{align} + \langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat S}_{i}^{z} {\hat S}_{j}^{z} \rangle + \\ + \langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat S}_{i}^{+} {\hat S}_{j}^{-} \rangle + \\ + \langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle + &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} + \langle {\hat {\bf S}}_{i} \cdot {\hat {\bf S}}_{j} \rangle + \end{align} + diff --git a/doc/en/fourier/fourier_tutorial_en.rst b/doc/en/fourier/fourier_tutorial_en.rst new file mode 100644 index 00000000..7fd36760 --- /dev/null +++ b/doc/en/fourier/fourier_tutorial_en.rst @@ -0,0 +1,116 @@ +.. _tutorial: + +Tutorial +======== + +This tutorial is done by using the input file +in ``sample/Standard/Spin/HeisenbergSquare/``. + +Run HPhi/vmc.out +---------------- + +- For :math:`{\mathcal H}\Phi` + + Calculate the ground state and the correlation function at that state. + + .. code-block:: bash + + $ ../../../../src/HPhi -s StdFace.def + +- For mVMC + + Optimize the trial wavefunction. + + .. code-block:: bash + + $ ../../../../src/vmc.out -s StdFace.def + + Add the following line in ``StdFace.def`` to compute the correlation function. + + :: + + NVMCCalMode = 1 + + Compute the correlation function. + + .. code-block:: bash + + $ ../../../../src/vmc.out -s StdFace.def output/zqp_opt.dat + +Then the one- and two-body correlation function are written to files +in the ``output/`` directory. + +Related files + +- StdFace.def (See the manuals for mVMC/:math:`{\mathcal H}\Phi`) +- zqp_opt.dat (See the manual for mVMC) +- greenone.def (:ref:`greenindex`) +- greentwo.def (:ref:`greenindex`) + +Fourier transformation of correlation functions +----------------------------------------------- + +Perform the Fourier transformation of the correlation function +by using the utility ``fourier``. + +.. code-block:: bash + + $ ../../../../tool/fourier namelist.def geometry.dat + +Then the Fourier-transformed correlation functions are +written to a file in ``output/``. + +Related files + +- output/zvo_cisajs_001.dat (:ref:`zvocisajs`) +- output/zvo_cisajs.dat (:ref:`zvocisajs`) +- output/zvo_cisajscktalt_001.dat (:ref:`zvocisajs`) +- output/zvo_cisajscktalt.dat (:ref:`zvocisajs`) +- geometry.dat (:ref:`geometry`) +- output/zvo_corr.dat (:ref:`zvocorr`) + +Display correlation functions +----------------------------- + +Plot the correlation function in the :math:`k` space +by using the utility ``corplot``. + +.. code-block:: bash + + $ ../../../../tool/corplot output/zvo_corr.dat + +Then the following message appears in the terminal. + +:: + + ##### Plot Start ##### + + Please specify target number from below (0 or Ctrl-C to exit): + + Real Part Without ErrorBar + [ 1] Up-Up [ 2] Down-Down [ 3] Density-Density [ 4] SzSz [ 5] S+S- [ 6] S-S+ + Imaginary Part Without ErrorBar + [11] Up-Up [12] Down-Down [13] Density-Density [14] SzSz [15] S+S- [16] S-S+ + Real Part With ErrorBar + [21] Up-Up [22] Down-Down [23] Density-Density [24] SzSz [25] S+S- [26] S-S+ + Imaginary Part With ErrorBar + [31] Up-Up [32] Down-Down [33] Density-Density [34] SzSz [35] S+S- [36] S-S+ + + Target : + +Type a number corresponding to the quantity to be plotted (for example ``4``) +and press ``Enter``, +then gnuplot is launched and the 3D figure is displayed (Fig. :num:`corplotpng`). + +.. _corplotpng: + +.. figure:: ../../figs/corplot.png + + The 3D picture when ``Target : 4``. + The solid black lines indicate the Brillouin zone. + +Related files + +- kpoint.dat (:ref:`kpoint`) +- correlation.gp (:ref:`gnuplot`) +- correlation.dat (:ref:`correlation`) diff --git a/doc/en/fourier/fourier_util_en.rst b/doc/en/fourier/fourier_util_en.rst new file mode 100644 index 00000000..858e5418 --- /dev/null +++ b/doc/en/fourier/fourier_util_en.rst @@ -0,0 +1,94 @@ +Behavior of each utility +======================== + +Utility ``fourier`` +------------------- + +This utility is used as follows: + +.. code-block:: bash + + $ ${PATH}/fourier ${NAMELIST} ${GEOMETRY} + +where ``${PATH}`` is the path to the directory where +the executable ``fourier`` exists, +${NAMELIST} is the NameList input-file name of :math:`{\mathcal H}\Phi`/mVMC, and +${GEOMETRY} is the path to the :ref:`geometry` file. + +The behavior of this utility is slightly different between the correlation functions from +each mode of :math:`{\mathcal H}\Phi` (Lanczos, TPQ, Full diagonalization, LOBCG) +and mVMC. +In the following cases, we assume that +``CDataFileHead`` in the ModPara input file is ``"zvo"`` (default). + +HPhi-Lanczos +~~~~~~~~~~~~ + +In this case, ``HPhi`` writes correlation functions to the files +``zvo_cisajs.dat`` (one body) and ``zvo_cisajscktalt.dat`` (two body) +in ``output/`` directory. +``fourier`` utility reads this files, performs the Fourier transformation, and +generate single file ``zvo_corr.dat`` in ``output/`` directory. + +HPhi-TPQ +~~~~~~~~ + +``HPhi`` writes correlation functions to files +``zvo_cisajs_run*step*.dat`` (one body), ``zvo_cisajscktalt_run*step*.dat`` (two body) +at each trial and TPQ step to the ``output/`` directory. +``fourier`` utility reads the one- and the two-body correlation function at each trial/TPQ-step, +and performs Fourier transformation, and +write to a file ``zvo_corr_run*step*.dat`` in ``output/`` directory. + +HPhi-Full diagonalization and LOBCG +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +``HPhi`` writes correlation functions to files +``zvo_cisajs_eigen*.dat`` (one body) and ``zvo_cisajscktalt_eigen*.dat`` (two body) +for each wavefunction to the ``output/`` directory. +``fourier`` utility reads the one- and the two-body correlation function at each state +and performs Fourier transformation, and +write to a file ``zvo_corr_eigen*.dat`` in ``output/``. + +mVMC +~~~~ + +``vmc.out`` performs calculations according to the input parameters ``NDataIdxStart`` and ``NDataQtySmp`` +in ``ModPara`` file, and it generates +``zvo_cisajs_???.dat`` (one body) and ``zvo_cisajscktalt_???.dat`` (two body) +in ``output/`` directory. +``fourier`` utility reads all of these files, performs Fourier transformation, +computes the average + +.. math:: + + \begin{align} + \langle A \rangle = \frac{1}{N_{\rm Try}} \sum_{i=1}^{N_{\rm Try}} A_i + \end{align} + +and the standard error + +.. math:: + + \begin{align} + \delta A = \frac{1}{N_{\rm Try} - 1} + \sqrt{\frac{1}{N_{\rm Try}} \sum_{i=1}^{N_{\rm Try}} (A_i - \langle A \rangle)^2} + \end{align} + +of the real- and imaginary-part of each correlation function, and +writes them to a file ``zvo_corr_eigen*.dat`` in ``output/`` directory. + +Utility ``corplot`` +------------------- + +This utility is used as follows: + +.. code-block:: bash + + $ ${PATH}/corplot ${CORR1} ${CORR2} ${CORR3} ... + +where ``${PATH}`` is the path to the directory which contains the executable ``corplot``, +${CORR1}, ${CORR2}, ${CORR3}, ... are :ref:`zvocorr` files +generated by the utility ``fourier``. +Therefore, this utility can plot multiple files simultaneously +(for example, to study the temperature dependence in the TPQ calculation). diff --git a/doc/en/fourier/index.rst b/doc/en/fourier/index.rst new file mode 100644 index 00000000..e1c957d5 --- /dev/null +++ b/doc/en/fourier/index.rst @@ -0,0 +1,26 @@ +.. test documentation master file, created by + sphinx-quickstart on Sat Jan 7 22:10:04 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +.. _fourier: + +HPhi/mVMC Fourie-Transformation utility +======================================= + +.. toctree:: + :maxdepth: 3 + + fourier_overview_en.rst + fourier_tutorial_en.rst + fourier_format_en.rst + fourier_util_en.rst + fourier_contact_en.rst + +.. Indices and tables +.. ================== + +.. * :ref:`genindex` +.. * :ref:`modindex` +.. * :ref:`search` + diff --git a/doc/en/index.rst b/doc/en/index.rst new file mode 100644 index 00000000..7b909b8f --- /dev/null +++ b/doc/en/index.rst @@ -0,0 +1,29 @@ +.. test documentation master file, created by + sphinx-quickstart on Sat Jan 7 22:10:04 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +Manual for mVMC +=============== + +.. toctree:: + :maxdepth: 2 + + intro.rst + start.rst + tutorial.rst + standard.rst + expert.rst + output.rst + algorithm.rst + appendix.rst + fourier/index + acknowledge.rst + +.. Indices and tables +.. ================== + +.. * :ref:`genindex` +.. * :ref:`modindex` +.. * :ref:`search` + diff --git a/doc/en/intro.rst b/doc/en/intro.rst new file mode 100644 index 00000000..16d8a083 --- /dev/null +++ b/doc/en/intro.rst @@ -0,0 +1,161 @@ +.. include:: ../bib/ref.txt + +What is mVMC? +============= + +High-accuracy analyses of theoretical models for quantum many-body +systems are expected to play important role for clarifying the nature of +novel quantum phases such as high-temperature superconductivities and +quantum spin liquids. Furthermore, recent theoretical progress enables +us to obtain low-energy effective models for real materials with +non-empirical way [ImadaMiyake_ ]. To clarify the +electronic structures of real materials and control the physical +properties, it is important to perform the high-accuracy analyses for +the low-energy effective models. One of the most reliable theoretical +tools for treating the strongly correlated electron systems is the exact +diagonalization method. However, applicable range of system size is +strongly limited in the exact diagonalization method. Variational Monte +Carlo method [Gros_ ] is one of promising way to perform +the high-accuracy calculations for the larger system sizes beyond exact +diagonalization method. Although the strong limitation of the +variational wave function is the origin of the poor accuracy of the +variational Monte Carlo method, recent development of the theoretical +method and computers relaxes the limitation of the variational wave +functions and enable us to perform the highly-accurate +calculations [Tahara2008_ , Misawa2014_ , Morita2015_ ]. + +mVMC (many-variable Variational Monte Carlo method) is a software for +performing the highly-accurate variational Monte Carlo calculations with +the simple and flexible user interface. mVMC also supports the +large-scale parallelization. For the conventional models in strongly +correlated electron systems such as the Hubbard model, the Heisenberg +model, and the Kondo-lattice model, users can perform the calculation by +preparing the one input files whose length is shorter than ten lines. By +using the same input file, users can perform the exact diagonalization +through HPhi [HPhi_ ]. Thus, it is easy to examine the accuracy of the +variational calculation for small system sizes and to perform the +calculations for large system sizes that can not be treated by the exact +diagonalization. A broad spectrum of users including experimental +scientists is cordially welcome. + +Overview of mVMC +---------------- + +By using mVMC, the following calculation can be done: + +- The variational wave function which gives the minimum value of the + expected value of energy in the range of the degree of freedoms of + variational parameters is numerically generated. The calculation + limited to the partial space divided by quantum numbers is also + possible. + +- The expected values of the physical quantities such as correlation + functions can be calculated by using the generated variational wave + functions. + +The calculation flow in mVMC is shown as follows: + +#. Read input files (\*.def) + +#. Optimize variational parameters :math:`\vec{\alpha}` to minimize + :math:`\langle {\cal H} \rangle` + +#. Calculate one body and two body Green functions + +#. Output variational parameters and expected values + +In calculation, the simple parallelization for the generation of the +real space arrangement :math:`|x\rangle` and the collecting samples and +the calculation result of expected energies is implemented. Following +the procedure for each cluster computers, the parallelized calculation +using MPI is automatically done by indicating the parallel number. +However, mVMC cannot execute under the environment where the MPI job is +forbidden such as the front-end of system B at ISSP. In mVMC, we use +PFAPACK [PFAPACK_ ] to compute the Pfaffian matrix. + +License +------- + +The distribution of the program package and the source codes for mVMC +follows GNU General Public License version 3 (GPL v3). + +We hope that you cite the following URL, +https://github.com/issp-center-dev/mVMC, when you publish the results +using mVMC (after writing the paper for mVMC, we will replace the URL to +the paper’s reference). + +Copyright +--------- + + *©2016- The University of Tokyo.* *All rights reserved.* + +This software is developed under the support of “\ *Project for +advancement of software usability in materials science* " by The +Institute for Solid State Physics, The University of Tokyo. + +Contributors +------------ + +This software is developed by following contributors. + +- ver.1.0.1 (released at 2017/6/8) + +- ver.1.0.0 (released at 2017/5/23) + +- ver.0.2.0 (released at 2017/3/16) + +- ver.0.1.1 (released at 2016/12/16) + +- ver.0.1.0 (released at 2016/10/26) + + - Developers + + - Takahiro Misawa + (The Institute for Solid State Physics, The University of + Tokyo) + + - Satoshi Morita + (The Institute for Solid State Physics, The University of + Tokyo) + + - Takahiro Ogoe + (Department of Applied Physics, The University of Tokyo) + + - Kota Ido + (Department of Applied Physics, The University of Tokyo) + + - Masatoshi Imada + (Department of Applied Physics, The University of Tokyo) + + - Yuichi Motoyama + (The Institute for Solid State Physics, The University of + Tokyo) + + - Mitsuaki Kawamura + (The Institute for Solid State Physics, The University of + Tokyo) + + - Kazusyohi Yoshimi + (The Institute for Solid State Physics, The University of + Tokyo) + + - Project coordinator + + - Takeo Kato + (The Institute for Solid State Physics, The University of + Tokyo) + +Operating environment +--------------------- + +mVMC is tested in the following platform: + +- The supercomputer system-B “sekirei”S in ISSP + +- K computer + +- OpenMPI + Intel Compiler + MKL + +- MPICH + Intel Compiler + MKL + +- MPICH + GNU Compiler + MKL diff --git a/doc/en/output.rst b/doc/en/output.rst new file mode 100644 index 00000000..2df1d30b --- /dev/null +++ b/doc/en/output.rst @@ -0,0 +1,349 @@ +.. include:: ../bib/ref.txt + +.. _OutputFile: + +Output files +============ + +The list of output files are shown in Table [Table:Output], where \*\*\* +and xxx are the header indicated by +``CParaFileHead``,``CDataFileHead`` in ``ModPara`` file, respectively. +yyy is a number given by +``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp``, +where both ``NDataIdxStart`` and ``NDataQtySmp`` are defined in +``ModPara`` file and zzz is a number given by ``NDataIdxStart`` in +``ModPara``. + ++--------------------------------------+---------------------------------------------------------------+ +| Name | Details for corresponding files | ++======================================+===============================================================+ +| \*\*\*\_opt.dat | All optimized parameters. | ++--------------------------------------+---------------------------------------------------------------+ +| \*\*\*\_gutzwiller\_opt.dat | Optimized gutzwiller factors. | ++--------------------------------------+---------------------------------------------------------------+ +| \*\*\*\_jastrow\_opt.dat | Optimized jastrow factors. | ++--------------------------------------+---------------------------------------------------------------+ +| \*\*\*\_doublonHolon2site\_opt.dat | Optimized 2-site doublon-holon correlation factors. | ++--------------------------------------+---------------------------------------------------------------+ +| \*\*\*\_doublonHolon4site\_opt.dat | Optimized 4-site doublon-holon correlation factors. | ++--------------------------------------+---------------------------------------------------------------+ +| \*\*\*\_orbital\_opt.dat | Optimized pair orbital factors. | ++--------------------------------------+---------------------------------------------------------------+ +| xxx\_out\_yyy.dat | Energy and deviation. | ++--------------------------------------+---------------------------------------------------------------+ +| xxx\_var\_yyy.dat | Progress information for optimizing variational parameters. | ++--------------------------------------+---------------------------------------------------------------+ +| xxx\_CalcTimer.dat | Computation time for each processes. | ++--------------------------------------+---------------------------------------------------------------+ +| xxx\_time\_zzz.dat | Progress information for MonteCalro samplings. | ++--------------------------------------+---------------------------------------------------------------+ +| xxx\_cisajs\_yyy.dat | One body Green’s functions. | ++--------------------------------------+---------------------------------------------------------------+ +| xxx\_cisajscktalt\_yyy.dat | Correlation functions. | ++--------------------------------------+---------------------------------------------------------------+ + +Output file for variational parameters (\*\*\*\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The average and deviation values of variational parameters and the +energy optimized by the SR method are outputted in the following order: + +.. math:: + + \langle H \rangle, \langle H^2 \rangle, g_i, v_{ij}, + \alpha_{2nt}^{d(h)}, \alpha_{4nt}^{d(h)}, f_{ij} \nonumber. + +The type of average values is a complex number, while that of the +deviation is a real number. Since the initial values of all variational +parameters are specified at the beginning of the calculation, the +calculation of physical quantities is done by using this file file. +Here, \*\*\* is the header indicated by ``CParaFileHead`` in ``ModPara`` +file. + +Output files for variational parameters at each steps (xxx\_var\_yyy.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The average and deviation values of variational parameters and the +energy optimized by the SR method are postscripted by the order same as +$$$\_opt.dat file (the deviation is always outputted as 0). Here, xxx is +the header indicated by ``CDataFileHead`` in ``ModPara`` file and yyy is +a number given by +``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp``, +where both ``NDataIdxStart`` and ``NDataQtySmp`` are defined in +``ModPara`` file. + +Output file for gutzwiller factors +(\*\*\*\_gutzwiller\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The optimized Gutzwiller factors by SR method are outputted. The file +format is same as the ``InGutzwiller`` file defined in Sec. +:ref:`InputParam`. + +Output file for jastrow factors +(\*\*\*\_jastrow\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The optimized Jastrow factors by SR method are outputted. The file +format is same as the ``InJastrow`` file defined in Sec. +:ref:`InputParam`. + +Output file for doublonHolon 2-site factors +(\*\*\*\_doublonHolon2site\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The optimized 2-site doublon-holon crrelation factors by SR method are +outputted. The file format is same as the ``InDH2`` file defined in Sec. +:ref:`InputParam`. + +Output file for doublonHolon 4-site factors +(\*\*\*\_doublonHolon4site\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The optimized 4-site doublon-holon crrelation factors by SR method are +outputted. The file format is same as the ``InDH4`` file defined in Sec. +:ref:`InputParam`. + +Output file for pair orbitals +(\*\*\*\_orbital\_opt.dat) +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The optimized pair orbitals by SR method are outputted. The file format +is same as the ``InOrbital`` file defined in Sec. :ref:`InputParam`. + +xxx\_out\_yyy.dat +~~~~~~~~~~~~~~~~~ + +The calculation information at each bins are outputted in the order: + +.. math:: + + \langle H \rangle, \langle H^2 \rangle, + \frac{\langle H^2 \rangle- \langle H \rangle^2 }{\langle H \rangle^2}, + \langle S^z \rangle, \langle (S^z)^2 \rangle + \nonumber. + +The type of :math:`\langle H \rangle` is a complex number, and that of +the others is a real number. Here, xxx is the header indicated by +``CDataFileHead`` in ``ModPara`` file and yyy is a number given by +``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp``, +where both ``NDataIdxStart`` and ``NDataQtySmp`` are defined in +``ModPara`` file. An example of outputted file is shown as follows. + +:: + + 1.151983765704212992e+01 8.124622418360909482e-01 \ + 1.619082955438887268e+02 2.019905203939084959e-01 + 1.288482613817423150e+01 5.006903733262847433e-01 + 1.972000325276957824e+02 1.824505193695792893e-01 + 1.308897206011880421e+01 5.701244886956570168e-01 \ + 2.072610167083121837e+02 2.029162857569105916e-01 + ... + +xxx\_CalcTimer.dat +~~~~~~~~~~~~~~~~~~~ + +After finishing calculation, the processing time is outputted in the +order of the name, the number assigned by the process and the seconds at +each processes. An example of outputted file is shown as follows. + +:: + + All [0] 15.90724 + Initialization [1] 0.04357 + read options [10] 0.00012 + ReadDefFile [11] 0.00082 + SetMemory [12] 0.00002 + InitParameter [13] 0.03026 + VMCParaOpt [2] 15.86367 + VMCMakeSample [3] 12.85650 + ... + +xxx\_time\_zzz.dat +~~~~~~~~~~~~~~~~~~~ + +The calculation information at each bins are outputted in the order of +the sampling number, the acceptance ratio for hopping and exchange term +(acc\_hopp, acc\_ex), trial numbers to update for hopping and exchange +term (n\_hopp, n\_ex) and the time stamp. Here, xxx is the header +indicated by ``CDataFileHead`` in ``ModPara`` file and zzz is a number +given by ``NDataIdxStart`` in ``ModPara``. An example of outputted file +is shown as follows. + +:: + + 00000 acc_hop acc_ex n_hop n_ex : Mon Jul 25 14:03:29 2016 + 00001 0.59688 0.00000 320 0 : Mon Jul 25 14:03:30 2016 + 00002 0.47727 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + 00003 0.50000 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + 00004 0.49432 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + 00005 0.57386 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + 00006 0.55114 0.00000 176 0 : Mon Jul 25 14:03:30 2016 + … + +xxx\_cisajs\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~ + +This file is the outputted files for one-body Green’s function +:math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle`. The target +components are set in the input file with the keyword "OneBodyG". Here, +xxx is the header indicated by ``CDataFileHead`` in ``ModPara`` file and +yyy is a number given by +``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp``, +where both ``NDataIdxStart`` and ``NDataQtySmp`` are defined in +``ModPara`` file. + +An example of the file format is as follows. + +:: + + 0 0 0 0 0.4452776740 0.0000000000 + 0 1 0 1 0.4452776740 0.0000000000 + 1 0 1 0 0.5000000000 0.0000000000 + 1 1 1 1 0.5000000000 0.0000000000 + 2 0 2 0 0.4452776740 0.0000000000 + 2 1 2 1 0.4452776740 0.0000000000 + 3 0 3 0 0.5000000000 0.0000000000 + 3 1 3 1 0.5000000000 0.0000000000 + ... + +File format +^^^^^^^^^^^ + +- [int01]  [int02]  [int03]  [int04]  [double01]  [double02] + +Parameters +^^^^^^^^^^ + +- [int01], [int03] + + **Type :** Int + + **Description :** The integer of the site number. + [int01] and [int03] show the + :math:`i` and :math:`j` site numbers, respectively. + +- [int02], [int04] + + **Type :** Int + + | **Description :** The integer of the spin index: + | 0: Up-spin + | 1: Down-spin. + | [int02] and [int04] show + :math:`\sigma_1` and :math:`\sigma_2`, respectively. + +- [double01], [double02] + + **Type :** Double + + | **Description :** The value of + :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle`. + | [double01] and [double02] + show the real and imaginary part of + :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle`, + respectively. + +xxx\_cisajscktalt\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file is the outputted files for the two-body Green’s function +:math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle`. +The target components are set in the input file with the keyword +"TwoBodyG". Here, xxx is the header indicated by ``CDataFileHead`` in +``ModPara`` file and yyy is a number given by +``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp``, +where both ``NDataIdxStart`` and ``NDataQtySmp`` are defined in +``ModPara`` file. An example of the file format is as follows. + +:: + + 0 0 0 0 0 0 0 0 0.4452776740 0.0000000000 + 0 0 0 0 0 1 0 1 0.1843355815 0.0000000000 + 0 0 0 0 1 0 1 0 0.1812412105 0.0000000000 + 0 0 0 0 1 1 1 1 0.2640364635 0.0000000000 + 0 0 0 0 2 0 2 0 0.0279690007 0.0000000000 + 0 0 0 0 2 1 2 1 0.2009271524 0.0000000000 + 0 0 0 0 3 0 3 0 0.2512810778 0.0000000000 + 0 0 0 0 3 1 3 1 0.1939965962 0.0000000000 + ... + +File format +^^^^^^^^^^^ + +- [int01]  [int02]  [int03]  [int04]  [int05]  [int06]  [int07]  [int08]  [double01]  [double02]. + +Parameters +^^^^^^^^^^ + +- [int01], + [int03],[int05], + [int07] + + **Type :** Int + + **Description :** The integer of the site number. + [int01], [int03], + [int05], and [int07] show the + :math:`i`, :math:`j`, :math:`k`, and :math:`l` site numbers, + respectively. + +- [int02], + [int04],[int06], + [int08] + + **Type :** Int + + **Description :** The integer of the spin index: + + 0: Up-spin + + 1: Down-spin. + + [int02], [int04], + [int06], and [int08] show + :math:`\sigma_1`, :math:`\sigma_2`, :math:`\sigma_3`, and + :math:`\sigma_4`, respectively. + +- [double01], [double02] + + **Type :** Double + + **Description :** The value of + :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle`. + [double01] and [double02] + show the real and imaginary part of + :math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle`, + respectively. + +xxx\_ls\_out\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~~ + +This file is the outputted files for :math:`\langle H \rangle`, +:math:`\langle H^2\rangle`, and the optimized parameter :math:`\alpha` +obtained by Power Lanczos method. This file is outputted when +``NVMCCalMode`` = 1, ``NLanczosmode`` = 1 or 2 are set in ``ModPara`` +file. Here, xxx is the header indicated by ``CDataFileHead`` in +``ModPara`` file and yyy is a number given by +``NDataIdxStart`` :math:`\cdots` ``NDataIdxStart`` + ``NDataQtySmp``, +where both ``NDataIdxStart`` and ``NDataQtySmp`` are defined in +``ModPara`` file. + +xxx\_ls\_cisajs\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file is the outputted files for one-body Green’s function +:math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle` obtained by +Power Lanczos method. The file format is same as the +xxx\_cisajs\_yyy.dat file. This file is outputted when ``NVMCCalMode`` = +1, ``NLanczosmode`` = 2 are set in ``ModPara`` file. + +xxx\_ls\_cisajscktalt\_yyy.dat +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This file is the outputted files for the two-body Green’s function +:math:`\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle` +obtained by Power Lanczos method. The file format is same as the +xxx\_cisajscktalt\_yyy.dat file. This file is outputted when +``NVMCCalMode`` = 1, ``NLanczosmode`` = 2 are set in ``ModPara`` file. + diff --git a/doc/en/standard.rst b/doc/en/standard.rst new file mode 100644 index 00000000..75d9061a --- /dev/null +++ b/doc/en/standard.rst @@ -0,0 +1,742 @@ +.. include:: ../bib/ref.txt + +.. _HOwToStandard: + +Input files for Standard mode +============================= + +An example of input file for the standard mode is shown below: + +:: + + W = 2 + L = 4 + model = "spin" + + lattice = "triangular lattice" + //mu = 1.0 + // t = -1.0 + // t' = -0.5 + // U = 8.0 + //V = 4.0 + //V'=2.0 + J = -1.0 + J'=-0.5 + // nelec = 8 + +**Basic rules for input files** + +- In each line, there is a set of a keyword (before an " ``=``") and a + parameter(after an " ``=``"); they are separated by " ``=``". + +- You can describe keywords in a random order. + +- Empty lines and lines beginning in a "``//``"(comment outs) are + skipped. + +- Upper- and lowercase are not distinguished. Double quotes and blanks + are ignored. + +- There are three kinds of parameters. + + 1. Parameters that must be specified (if not, ``vmcdry.out`` will + stop with error messages), + + 2. Parameters that is not necessary be specified (if not, default + values are used), + + 3. Parameters that must not be specified (if specified, + ``vmcdry.out`` will stop with error messages). + + An example of 3 is transfer :math:`t` for the Heisenberg spin + system. If you choose "model=spin", you should not specify + ":math:`t`". + +We explain each keywords as follows: + +Parameters about the kind of a calculation +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +- ``model`` + + **Type :** String (Choose from ``"Fermion Hubbard"``, ``"Spin"``, + ``"Kondo Lattice"`` , ``"Fermion HubbardGC"``, ``"SpinGC"``, + ``"Kondo LatticeGC"`` ) [1]_ + + **Description :** The target model is specified with this parameter; + ``"Fermion Hubbard"`` denotes the canonical ensemble of the Fermion + in the Hubbard model + + .. math:: + :label: hubbard + + \begin{aligned} + H = -\mu \sum_{i \sigma} c^\dagger_{i \sigma} c_{i \sigma} + - \sum_{i \neq j \sigma} t_{i j} c^\dagger_{i \sigma} c_{j \sigma} + + \sum_{i} U n_{i \uparrow} n_{i \downarrow} + + \sum_{i \neq j} V_{i j} n_{i} n_{j}, + \end{aligned} + + ``"Spin"`` denotes canonical ensemble in the Spin + model( :math:`\{\sigma_1, \sigma_2\}={x, y, z}`) + + .. math:: + :label: spin + + \begin{aligned} + H &= -h \sum_{i} S_{i z} - \Gamma \sum_{i} S_{i x} + D \sum_{i} S_{i z} S_{i z} + \nonumber \\ + &+ \sum_{i j, \sigma_1}J_{i j \sigma_1} S_{i \sigma_1} S_{j \sigma_1}+ \sum_{i j, \sigma_1 \neq \sigma_2} J_{i j \sigma_1 \sigma_2} S_{i \sigma_1} S_{j \sigma_2} , + \end{aligned} + + ``"Kondo Lattice"`` denotes canonical ensemble in the Kondo lattice + model + + .. math:: + :label: kondo + + \begin{aligned} + H = - \mu \sum_{i \sigma} c^\dagger_{i \sigma} c_{i \sigma} + - t \sum_{\langle i j \rangle \sigma} c^\dagger_{i \sigma} c_{j \sigma} + + \frac{J}{2} \sum_{i} \left\{ + S_{i}^{+} c_{i \downarrow}^\dagger c_{i \uparrow} + + S_{i}^{-} c_{i \uparrow}^\dagger c_{i \downarrow} + + S_{i z} (n_{i \uparrow} - n_{i \downarrow}) + \right\}. + \end{aligned} + + ``"Fermion HubbardGC"``, ``"SpinGC"``, and ``"Kondo LatticeGC"`` + indicate the :math:`S_z`-unconserved Fermion in the Hubbard model + [Eqn. :eq:`hubbard` ], the :math:`S_z`-unconserved Spin model + [Eqn. :eq:`spin` ], and the :math:`S_z`-unconserved Kondo + lattice model [Eqn. :eq:`kondo` ], respectively. Note: Although + these flags has a word "GC"(=grandcanonical), the number of electrons + are conserved in these system. + +- ``lattice`` + + **Type :** String (Choose from ``"Chain Lattice"``, + ``"Square Lattice"``, ``"Triangular Lattice"``, + ``"Honeycomb Lattice"``, ``"Kagome"``, ``"Ladder"``) + + **Description :** The lattice shape is specified with this parameter; + above words denote the one dimensional chain lattice (Fig. + :num:`latticepng` (a)), the two dimensional square lattice + (Fig. :num:`latticepng` (b)), the two dimensional triangular + lattice (Fig. :num:`latticepng` (c)), the two dimensional + anisotropic honeycomb lattice (Fig. :num:`honeycombpng` ), the + Kagome Lattice(Fig. :num:`kagomepng` ), and the ladder lattice (Fig. + :num:`ladderpng` ), respectively. + + .. _latticepng: + + .. figure:: ../figs/chap04_1_lattice.png + :width: 15.00000cm + + Schematic illustration of (a) one dimensional chain lattice, (b) + two dimensional square lattice, and (c) two dimensional triangular + lattice. They have :math:`t`, :math:`V`, and :math:`J` as a + nearest neighbor hopping, an offsite Coulomb integral, and a + spin-coupling constant, respectively (magenta solid lines); They + also have :math:`t'`, :math:`V'`, and :math:`J'` as a next nearest + neighbor hopping, offsite Coulomb integral, and spin-coupling + constant, respectively (green dashed line). + + .. _honeycombpng: + + .. figure:: ../figs/chap04_1_honeycomb.png + :width: 15.00000cm + + Schematic illustration of the anisotropic honeycomb lattice. The + nearest neighbor hopping integral, spin coupling, offsite Coulomb + integral depend on the bond direction. Those between second + nearest neighbor sites are not supported. + + .. _kagomepng: + + .. figure:: ../figs/kagome.png + :width: 10.00000cm + + Schematic illustration of the Kagome lattice. + + .. _ladderpng: + + .. figure:: ../figs/ladder.png + :width: 10.00000cm + + Schematic illustration of the ladder lattice. + +Parameters for the lattice +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Chain lattice +^^^^^^^^^^^^^ + +Fig. :num:`latticepng` (a) + +- ``L`` + + **Type :** Integer + + **Description :** The length of the chain is specified with this + parameter. + +Ladder lattice +^^^^^^^^^^^^^^ + +Fig. :num:`ladderpng` + +- ``L`` + + **Type :** Integer + + **Description :** The length of the ladder is specified with this + parameter. + +- ``W`` + + **Type :** Integer + + **Description :** The number of the ladder is specified with this + parameter. + + .. _unitlatticepng: + + .. figure:: ../figs/chap04_1_unitlattice.png + :width: 15.00000cm + + The shape of the numerical cell when + :math:`{\vec a}_0 = (6, 2), {\vec a}_1 = (2, 4)` in the triangular + lattice. The region surrounded by :math:`{\vec a}_0` (Magenta dashed + arrow) and :math:`{\vec a}_1` (Green dashed arrow) becomes the cell + to be calculated (20 sites). + +Square lattice , Triangular lattice, Honeycomb lattice, Kagome lattice +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Square lattice [Fig. :num:`latticepng` (b)], Triangular lattice[Fig. :num:`latticepng` (c)], Honeycomb lattice(Fig. :num:`honeycombpng` ), Kagome lattice(Fig. :num:`kagomepng` ) + +In these lattices, we can specify the shape of the numerical cell by +using the following two methods. + +- ``W``, ``L`` + + **Type :** Integer + + **Description :** The alignment of original unit cells (dashed black + lines in Figs. :num:`latticepng` - :num:`kagomepng` ) is + specified with these parameter. + +- ``a0W``, ``a0L``, ``a1W``, ``a1L`` + + **Type :** Integer + + **Description :** We can specify two vectors + (:math:`{\vec a}_0, {\vec a}_1`) that surrounds the numerical cell + (Fig. :num:`unitlatticepng` ). These vectors should be + specified in the Fractional coordinate. + +If we use both of these method, ``vmcdry.out`` stops. + +We can check the shape of the numerical cell by using a file +``lattice.gp`` (only for square, trianguler, honeycomb, and kagome +lattice) which is written in the Standard mode. This file can be read by +``gnuplot`` as follows: + +.. code-block:: bash + + $ gnuplot lattice.gp + +Sublattice +~~~~~~~~~~ + +By using the following parameters, we can force the pair-orbital +symmetrical to the translation of the sublattice. + +- ``a0Wsub``, ``a0Lsub``, ``a1Wsub``, ``a1Lsub``, ``Wsub``, ``Lsub`` + + **Type :** Positive integer. In the default setting, ``a0Wsub=a0W``, + ``a0Lsub=a0L``, ``a1Wsub=a1W``, ``a1Lsub=a1L``, ``Wsub=W``, and + ``Lsub=L``. Namely, there is no sublattice. + + **Description :** We can specify these parameter as we specify + ``a0W``, ``a0L``, ``a1W``, ``a1L``, ``W``, ``L``. If the sublattice + is incommensurate with the original lattice, ``vmcdry.out`` stops. + +Parameters for the Hamiltonian +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A default value is set as :math:`0` unless a specific value is not +defined in a description. Table [table\_interactions] shows the +parameters for each models. In the case of a complex type, a file format +is " *a real part, an imaginary part* " while in the case of a real +type, only " *a real part* ". + +Local terms +^^^^^^^^^^^ + +- ``mu`` + + **Type :** Real + + **Description :** (Hubbard and Kondo lattice model) The chemical + potential :math:`\mu` (including the site potential) is specified + with this parameter. + +- ``U`` + + **Type :** Real + + **Description :** (Hubbard and Kondo lattice model) The onsite + Coulomb integral :math:`U` is specified with this parameter. + +- ``Jx``, ``Jy``, ``Jz``, ``Jxy``, ``Jyx``, ``Jxz``, ``Jzx``, ``Jyz``, + ``Jzy`` + + **Type :** Real + + **Description :** (Kondo lattice model) The spin-coupling constant + between the valence and the local electrons is specified with this + parameter. If the exchange coupling ``J`` is specified in the input + file, instead of ``Jx, Jy, Jz``, the diagonal exchange couplings, + ``Jx, Jy, Jz``, are set as ``Jx = Jy = Jz = J``. When both the set of + exchange couplings (``Jx``, ``Jy``, ``Jz``) and the exchange coupling + ``J`` are specified in the input file, ``vmcdry.out`` will stop. + +- ``h``, ``Gamma``, ``D`` + + **Type :** Real + + **Description :** (Spin model) The longitudinal magnetic field, + transverse magnetic field, and the single-site anisotropy parameter + are specified with these parameters. The single-site anisotropy + parameter is not available for ``model=SpinGCBoost``. + +The non-local terms described below should be specified in different +ways depending on the lattice structure: For ``lattice=Ladder``, the +non-local terms are specified in the different way from +``lattice=Chain Lattice``, ``Square Lattice``, ``Triangular Lattice``, +``Honeycomb Lattice``, ``Kagome``. Below, the available parameters for +each lattice are shown in Table [table\_interactions]. + +================================ ======== ========= ============= ========= ====== ====== +Interactions 1D chain 2D square 2D triangular Honeycomb Kagome Ladder +================================ ======== ========= ============= ========= ====== ====== +``J``, ``t``, ``V`` (simplified) OK OK OK OK OK NG +``J'``, ``t'``, ``V'`` OK OK OK OK OK NG +``J0``, ``t0``, ``V0`` OK OK OK OK OK OK +``J1``, ``t1``, ``V1`` NG OK OK OK OK OK +``J2``, ``t2``, ``V2`` NG NG OK OK OK OK +``J1'``, ``t1'``, ``V1'`` NG NG NG NG NG OK +``J2'``, ``t2'``, ``V2'`` NG NG NG NG NG OK +================================ ======== ========= ============= ========= ====== ====== + +Table: Interactions for each models defined in an input file. We can +define spin couplings as matrix format. + +Non-local terms for Ladder lattice +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Fig. :num:`ladderpng` + +- ``t0``, ``t1``, ``t1'``, ``t2``, ``t2'`` + + **Type :** Complex + + **Description :** (Hubbard and Kondo lattice model) Hopping integrals + in the ladder lattice (See Fig. :num:`ladderpng` ) is specified with this + parameter. + +- ``V0``, ``V1``, ``V1'``, ``V2``, ``V2'`` + + **Type :** Real + + **Description :** (Hubbard and Kondo lattice model) Offsite Coulomb + integrals on the ladder lattice (Fig. :num:`honeycombpng` are + specified with these parameters. + +- ``J0x``, ``J0y``, ``J0z``, ``J0xy``, ``J0yx``, ``J0xz``, ``J0zx``, + ``J0yz``, ``J0zy`` + +- ``J1x``, ``J1y``, ``J1z``, ``J1xy``, ``J1yx``, ``J1xz``, ``J1zx``, + ``J1yz``, ``J1zy`` + +- ``J1'x``, ``J1'y``, ``J1'z``, ``J1'xy``, ``J1'yx``, ``J1'xz``, + ``J1'zx``, ``J1'yz``, ``J1'zy`` + +- ``J2x``, ``J2y``, ``J2z``, ``J2xy``, ``J2yx``, ``J2xz``, ``J2zx``, + ``J2yz``, ``J2zy`` + +- ``J2'x``, ``J2'y``, ``J2'z``, ``J2'xy``, ``J2'yx``, ``J2'xz``, + ``J2'zx``, ``J2'yz``, ``J2'zy`` + + **Type :** Real + + **Description :** (Spin model) Spin-coupling constants in the ladder + lattice (See Fig. :num:`ladderpng` ) are specified with these parameter. + If the simplified parameter ``J0`` is specified in the input file + instead of the diagonal couplings, ``J0x, J0y, J0z``, these diagonal + couplings are set as ``J0x = J0y = J0z = J0``. If both ``J0`` and the + set of the couplings (``J0x, J0y, J0z``) are specified, + ``vmcdry.out`` will stop. The above rules are also valid for the + simplified parameters, ``J1``, ``J1'``, ``J2``, and ``J2'``. + +Non-local terms for other than Ladder +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Figs. :num:`latticepng` , :num:`honeycombpng` , :num:`kagomepng` + +- ``t0``, ``t1``, ``t2`` + + **Type :** Complex + + **Description :** (Hubbard and Kondo lattice model) Nearest neighbor + hoppings for each direction (See Figs. + :num:`latticepng` -:num:`kagomepng` . These bonds are depicted + with different line styles.) are specified with these parameter. If + there is no bond dependence of the nearest-neighbor hoppings, the + simplified parameter ``t`` is available to specify ``t0``, ``t1``, + and ``t2`` as ``t0 = t1 = t2 = t``. If both ``t`` and the set of the + hoppings (``t0``, ``t1``, ``t2``) are specified, ``vmcdry.out`` will + stop. + +- ``V0``, ``V1``, ``V2`` + + **Type :** Real + + **Description :** (Hubbard and Kondo lattice model) Nearest-neighbor + offsite Coulomb integrals :math:`V` for each direction (See Figs. + :num:`latticepng` -:num:`kagomepng` . These bonds are depicted + with different line styles.) are specified with these parameters. If + there is no bond dependence of the nearest-neighbor offsite Coulomb + integrals, the simplified parameter ``V`` is available to specify + ``V0``, ``V1``, and ``V2`` as ``V0 = V1 = V2 = V``. If both ``V`` and + the set of the Coulomb integrals (``V0``, ``V1``, ``V2``) are + specified, ``vmcdry.out`` will stop. + +- ``J0x``, ``J0y``, ``J0z``, ``J0xy``, ``J0yx``, ``J0xz``, ``J0zx``, + ``J0yz``, ``J0zy`` + +- ``J1x``, ``J1y``, ``J1z``, ``J1xy``, ``J1yx``, ``J1xz``, ``J1zx``, + ``J1yz``, ``J1zy`` + +- ``J2x``, ``J2y``, ``J2z``, ``J2xy``, ``J2yx``, ``J2xz``, ``J2zx``, + ``J2yz``, ``J2zy`` + + **Type :** Real + + **Description :** (Spin model) Nearest-neighbor exchange couplings + for each direction are specified with thees parameters. If the + simplified parameter ``J0`` is specified, instead of + ``J0x, J0y, J0z``, the exchange couplings, ``J0x, J0y, J0z``, are set + as ``J0x = J0y = J0z = J0``. If both ``J0`` and the set of the + exchange couplings (``J0x, J0y, J0z``) are specified, ``vmcdry.out`` + will stop. The above rules are valid for ``J1`` and ``J2``. + + If there is no bond dependence of the nearest-neighbor exchange + couplings, the simplified parameters, ``Jx``, ``Jy``, ``Jz``, + ``Jxy``, ``Jyx``, ``Jxz``, ``Jzx``, ``Jyz``, ``Jzy``, are available + to specify the exchange couplings for every bond as + ``J0x = J1x = J2x = Jx``. If any simplified parameter + (``Jx`` :math:`\sim` ``Jzy``) is specified in addition to its + counter parts (``J0x`` :math:`\sim` ``J2zy``), ``vmcdry.out`` will + stop. Below, examples of parameter sets for nearest-neighbor exchange + couplings are shown. + + - If there are no bond-dependent, no anisotropic and offdiagonal + exchange couplings (such as :math:`J_{x y}`), please specify ``J`` + in the input file. + + - If there are no bond-dependent and offdiagonal exchange couplings + but are anisotropic couplings, please specify the non-zero + couplings in the diagonal parameters, ``Jx, Jy, Jz``. + + - If there are no bond-dependent exchange couplings but are + anisotropic and offdiagonal exchange couplings, please specify the + non-zero couplings in the nine parameters, + ``Jx, Jy, Jz, Jxy, Jyz, Jxz, Jyx, Jzy, Jzx``. + + - If there are no anisotropic and offdiagonal exchange couplings, + but are bond-dependent couplings, please specify the non-zero + couplings in the three parameters, ``J0, J1, J2``. + + - If there are no anisotropic exchange couplings, but are + bond-dependent and offdiagonal couplings, please specify the + non-zero couplings in the nine parameters, + ``J0x, J0y, J0z, J1x, J1y, J1z, J2x, J2y, J2z``. + + - If there are bond-dependent, anisotropic and offdiagonal exchange + couplings, please specify the non-zero couplings in the + twenty-seven parameters from ``J0x`` to ``J2zy``. + +- ``t'`` + + **Type :** Complex + + **Description :** (Hubbard and Kondo lattice model) Nearest neighbor + hoppings for each direction (See Figs. + :num:`latticepng` -:num:`kagomepng` ) are specified with these + parameter. + +- ``V'`` + + **Type :** Real + + **Description :** (Hubbard and Kondo lattice model) Nearest + neighbor-offsite Coulomb integrals :math:`V` for each direction (See + Figs. :num:`latticepng` -:num:`kagomepng` ) are specified with + these parameters. + +- ``J'x``, ``J'y``, ``J'z``, ``J'xy``, ``J'yx``, ``J'xz``, ``J'zx``, + ``J'yz``, ``J'zy`` + + **Type :** Real + + **Description :** (Spin model) Second nearest-neighbor exchange + couplings are specified. However, for ``lattice = Honeycomb Lattice`` + and ``lattice = Kagome`` with ``model=SpinGCBoost``, the second + nearest-neighbor exchange couplings are not available in the + :math:`Standard` mode. If the simplified parameter ``J'`` is + specified, instead of ``J'x, J'y, J'z``, the exchange couplings are + set as ``J'x = J'y = J'z = J'``. If both ``J'`` and the set of the + couplings (``J'x, J'y, J'z``), ``vmcdry.out`` will stop. + +- ``phase0``, ``phase1`` + + **Type :** Double (``0.0`` as defaults) + + **Description :** We can specify the phase for the hopping through + the cell boundary with these parameter (unit: degree). These fuctor + for the :math:`\vec{a}_0` direction and the :math:`\vec{a}_1` + direction can be specified independently. For the one-dimensional + system, only ``phase0`` can be used. For example, a fopping from + :math:`i`-th site to :math:`j`-th site through the cell boundary with + the positive direction becomes as + + .. math:: + + \begin{aligned} + \exp(i \times {\rm phase0}\times\pi/180) \times t {\hat c}_{j \sigma}^\dagger {\hat c}_{i \sigma} + + \exp(-i \times {\rm phase0}\times\pi/180) \times t^* {\hat c}_{i \sigma}^\dagger {\hat c}_{j \sigma} + \end{aligned} + +Parameters for the numerical condition +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +- ``nelec`` + + **Type :** int-type (must be specified) + + **Description :** The number of itenerant electrons. It is the sum of + the :math:`\uparrow` and :math:`\downarrow` electrons. + +- ``NVMCCalMode`` + + **Type :** int-type (default value: 0) + + **Description :** [0] Optimization of variational parameters, [1] + Calculation of one body and two body Green’s functions. + +- ``NDataIdxStart`` + + **Type :** int-type (default value: 1) + + **Description :** An integer for numbering of output files. For + ``NVMCCalMode`` = 0 , ``NDataIdxStart`` is added at the end of the + output files. For ``NVMCCalMode`` = 1, the files are outputted with + the number from ``NDataIdxStart`` to + ``NDataIdxStart`` + ``NDataQtySmp``-1. + +- ``NDataQtySmp`` + + **Type :** int-type (default value: 1) + + **Description :** The set number for outputted files (only used for + ``NVMCCalMode`` = 1). + +- ``NSPGaussLeg`` + + **Type :** int-type (Positive integer, default value is 8 for + ``2Sz=0``) + + **Description :** The mesh number for the Gauss-legendre quadrature + about :math:`\beta` integration (:math:`S_y` rotation) for the spin + quantum-number projection in actual numerical calculation. + +- ``NSPStot`` + + **Type :** int-type ( greater equal 0, default value is 0 for + ``2Sz=0``) + + **Description :** The total spin quantum-number. + +- ``2Sz`` + + **Type :** int-type ( greater equal 0, default value is 0) + + **Description :** The spin quantum-number :math:`S_z`. + +- ``NMPTrans`` + + **Type :** int-type (Positive integer. Default ``1``) + + **Description :** The number of the momentum and lattice + translational quantum-number projection. In the case of not to apply + the projection, this value must be set as 1. + +- ``NSROptItrStep`` + + **Type :** int-type (Positive integer, default value: 1000) + + **Description :** The whole step number to optimize variational + parameters by SR method. Only used for ``NVMCCalMode`` =0. + +- ``NSROptItrSmp`` + + **Type :** int-type (Positive integer, default value: + ``NSROptItrStep``/10) + + **Description :** In the ``NSROptItrStep`` step, the average values + of the each variational parameters at the ``NSROptItrStep`` step are + adopted as the optimized values. Only used for ``NVMCCalMode`` =0. + +- ``DSROptRedCut`` + + **Type :** double-type (default value: 0.001) + + **Description :** The stabilized factor for the SR method by + truncation of redundant directions corresponding to + :math:`\varepsilon_{\rm wf}` in the ref. + [Tahara2008_ ]. + +- ``DSROptStaDel`` + + **Type :** double-type (default value: 0.02) + + **Description :** The stabilized factor for the SR method by + modifying diagonal elements in the overwrap matrix corresponding to + :math:`\varepsilon` in the ref. [Tahara2008_ ]. + +- ``DSROptStepDt`` + + **Type :** double-type (default value: 0.02) + + **Description :** The time step using in the SR method. + +- ``NVMCWarmUp`` + + **Type :** int-type (Positive integer, default value: 10) + + **Description :** Idling number for the Malkov chain Montecarlo + Methods. + +- ``NVMCInterval`` + + **Type :** int-type (Positive integer, default value: 1) + + **Description :** The interval step between samples. The local update + will be performed ``Nsite`` × ``NVMCInterval`` times. + +- ``NVMCSample`` + + **Type :** int-type (Positive integer, default value: 1000) + + **Description :** The sample numbers to calculate the expected + values. + +- ``NExUpdatePath`` + + **Type :** int-type (Positive integer) + + **Description :** The option for local update about exchange terms. + 0: not update, 1: update. The default value is set as 1 when the + local spin exists, otherwise 0. + +- ``RndSeed`` + + **Type :** int-type (default value: 123456789) + + **Description :** The initial seed of generating random number. For + MPI parallelization, the initial seeds are given by ``RndSeed`` +my + rank+1 at each ranks. + +- ``NSplitSize`` + + **Type :** int-type (Positive integer, default value: 1) + + **Description :** The number of processes of MPI parallelization. + +- ``NStore`` + + **Type :** int-type (0 or 1, default value: 1) + + **Description :** The option of applying matrix-matrix product to + calculate expected values :math:`\langle O_k O_l \rangle` (0: off, 1: + on). This speeds up calculation but increases the amount of memory + usage from :math:`O(N_\text{p}^2)` to + :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})`, where + :math:`N_\text{p}` is the number of the variational parameters and + :math:`N_\text{MCS}` is the number of Monte Carlo sampling. + +- ``NSRCG`` + + **Type :** int-type (0 or 1, default value: 0) + + **Description :** The option of solving :math:`Sx=g` in the SR method + without construting :math:`S` + matrix [NeuscammanUmrigarChan_ ]. (0: off, 1: on). + This reduces the amount of memory usage from + :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})` to + :math:`O(N_\text{p}) + O(N_\text{p}N_\text{MCS})` when + :math:`N_\text{p} > N_\text{MCS}`. + +- ``ComplexType`` + + **Type :** int-type (``0`` or ``1``. Default value is ``0`` for the + :math:`S_z`-conserved system and ``1`` for the + :math:`S_z`-unconserved system.) + + **Description :** If it is ``0``, only the real part of the + variational parameters are optimized. And the real and the imaginary + part of them are optimized if this parameter is ``1``. + +- ``OutputMode`` + + **Type :** Choose from ``"none"``, ``"correlation"``, and ``"full"`` + (``correlation`` as a default) + + **Description :** Indices of correlation functions are specified with + this keyword. ``"none"`` indicates correlation functions will not + calculated. When ``outputmode="correlation"``, the correlation + function supported by the utility ``fourier`` is computed. For more + details, see the document in ``doc/fourier/``. If ``"full"`` is + selected, :math:`\langle c_{i \sigma}^{\dagger}c_{j \sigma'} \rangle` + is computed at all :math:`i, j, \sigma, \sigma'`, and + :math:`\langle c_{i_1 \sigma}^{\dagger}c_{i_2 \sigma} c_{i_3 \sigma'}^{\dagger}c_{i_4 \sigma'} \rangle` + is computed at all :math:`i_1, i_2, i_3, i_4, \sigma, \sigma'`. + + In spin system, indices are specified as those on the Bogoliubov + representation (See [sec\_bogoliubov\_rep]). + +- ``CDataFileHead`` + + **Type :** string-type (default : ``"zvo"``) + + **Description :** A header for output files. For example, the output + filename for one body Green’s function becomes + " **xxx\_cisajs\_yyy.dat**" (xxx are characters set by + ``CDataFileHead`` and yyy are numbers given by numbers from + ``NDataIdxStart`` to ``NDataIdxStart`` + ``NDataQtySmp``). + +- ``CParaFileHead`` + + **Type :** string-type (default : ``"zqp"``) + + **Description :** A header for output files of the optimized + variational parameters. For example, the optimized variational + parameters are outputted as **zzz\_opt\_yyy.dat** (zzz are characters + set by ``CParaFileHead`` and yyy are numbers given by numbers from + ``NDataIdxStart`` to ``NDataIdxStart`` + ``NDataQtySmp`` -1). + +.. [1] + GC=Grand Canonical diff --git a/doc/en/start.rst b/doc/en/start.rst new file mode 100644 index 00000000..b7b8c5c9 --- /dev/null +++ b/doc/en/start.rst @@ -0,0 +1,353 @@ +How to use mVMC? +================ + +Prerequisite +------------ + +mVMC requires the following packages: + +- C compiler (intel, Fujitsu, GNU, etc. ) + +- MPI library + +- Option: ScaLAPACK library (intel MKL, Fujitsu, ATLAS, etc.) + +.. note:: + + **Settings of intel compiler** + + When you use the intel compiler, you can use easily scripts attached to + the compiler. In the case of the bash in 64 bit OS, write the following + in your ``~/.bashrc``: + + .. code-block:: bash + + $ source /opt/intel/bin/compilervars.sh intel64 + + or + + .. code-block:: bash + + $ source /opt/intel/bin/iccvars.sh intel64 + $ source /opt/intel/mkl/bin/mklvars.sh + + Please read manuals of your compiler/library for more information. + +Installation +------------ + +You can download mVMC in the following place. +https://github.com/issp-center-dev/mVMC/releases + +You can obtain the mVMC directory by typing + +.. code-block:: bash + + $ tar xzvf mVMC-xxx.tar.gz + +There are two kind of procedures to install mVMC. + +Using ``mVMCconfig.sh`` +~~~~~~~~~~~~~~~~~~~~~~~ + +Please run ``mVMCconfig.sh`` script in the mVMC directory as follow (for +ISSP system-B "sekirei"): + +.. code-block:: bash + + $ bash mVMCconfig.sh sekirei + +Then environmental configuration file ``make.sys`` is generated in +``src/`` directory. The command-line argument of ``mVMCconfig.sh`` is as +follows: + +- ``sekirei`` : ISSP system-B "sekirei" + +- ``kei`` : K computer and ISSP system-C "maki" + +- ``intel-openmpi`` : Intel compiler + OpenMPI + +- ``intel-mpich`` : Intel compiler + MPICH2 + +- ``intel-intelmpi`` : Intel compiler + IntelMPI + +- ``gcc-openmpi`` : GCC + OpenMPI + +- ``gcc-mpich-mkl`` : GCC + MPICH + MKL + +``make.sys`` is as follows (for ISSP-system-B "sekirei"): + +.. code-block:: makefile + + CC = mpicc + F90 = mpif90 + CFLAGS = -O3 -no-prec-div -xHost -qopenmp -Wno-unknown-pragmas + FFLAGS = -O3 -implicitnone -xHost + LIBS = -L $(MKLROOT)/lib/intel64 -lmkl_scalapack_lp64 -lmkl_intel_lp64 \ + -lmkl_intel_thread -lmkl_core -lmkl_blacs_sgimpt_lp64 -lpthread -lm + SFMTFLAGS = -no-ansi-alias -DHAVE_SSE2 + +We explain macros of this file as: + +- ``CC`` : C compiler (``mpicc``, ``mpifccpx``) + +- ``F90`` : fortran compiler (``ifort``, ``frtpx``) + +- ``Libs`` : Linker option + +- ``CFLAGS`` : C compile option + +- ``FFLAGS`` : fortran compile option + +Then you are ready to compile mVMC. Please type + +.. code-block:: bash + + $ make mvmc + +and obtain ``vmc.out`` and ``vmcdry.out`` in ``src/`` directory; you +should add this directory to the ``$PATH``. + +You can make a PATH to mVMC as follows: +``$ export PATH=${PATH}:``\ *mVMC\_top\_directory*\ ``/src/`` +If you keep this PATH, you should write above in ``~/.bashrc`` (for +``bash`` as a login shell) + +Using ``cmake`` +~~~~~~~~~~~~~~~ + +We can compile mVMC as + +.. code-block:: bash + + cd $HOME/build/mvmc + cmake -DCONFIG=gcc $PathTomvmc + make + +Here, we set a path to mVMC as ``$PathTomvmc`` and to a build directory +as `` $HOME/build/mvmc``. After compilation, ``src`` directory is +constructed below a ``$HOME/build/mvmc`` directory and we obtain an +executable ``vmc.out`` in ``src/`` directory. + +In the above example, we compile mVMC by using a gcc compiler. We can +select a compiler by using the following options: + +- ``sekirei`` : ISSP system-B "sekirei" + +- ``fujitsu`` : Fujitsu compiler + +- ``intel`` : Intel compiler + Linux PC + +- ``gcc`` : GCC compiler + Linux PC. + +An example of compiling mVMC by using the Intel compiler is shown as +follows: + +.. code-block:: bash + + mkdir ./build + cd ./build + cmake -DCONFIG=intel ../ + make + +After compilation, ``src/`` directory is created below the ``build/`` directory +and an execute ``vmc.out`` in the ``src/`` directory. We can select +ScaLAPACK instead of LAPACK for vmc calculation by adding the following +as the cmake option + +:: + + -DUSE_SCALAPACK=ON -DSCALAPACK_LIBRARIES="xxx". + +Here, xxx is the libraries to use ScaLAPACK. Please note that we must +delete the ``build/`` directory and repeat the above operations when we +change the compiler. + +.. note:: + + Before using cmake for sekirei, you must type + + .. code-block:: bash + + $ source /home/issp/materiapps/tool/env.sh + + When we type the following in sekirei, + + .. code-block:: bash + + $ cmake -DCONFIG=sekirei ../ -DUSE_SCALAPACK=ON , + + ``-DSCALAPACK_LIBRARIES`` is automatically set as + + :: + + -DSCALAPACK_LIBRARIES="\${MKLROOT}/lib/intel64 -lmkl_scalapack_lp64 + -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core + -lmkl_blacs_sgimpt_lp64". + + When the path to libraries for ScaLAPACK is different in your + circumstance, please set ``-DSCALAPACK_LIBRARIES`` as the correct path. + +Directory structure +------------------- + +| When mVMC-xxx.tar.gz is unzipped, the following directory structure is + composed. +| ├──COPYING +| ├──mVMCconfig.sh +| ├──doc/ +| │      ├──bib/ +| │      │      ├──elsart-num\_mod.bst +| │      │      └──userguide.bib +| │      ├──figs/ +| │      │      ├──\*.pdf +| │      │      └──\*.xbb +| │      ├──fourier/ +| │      │      ├──en/ +| │      │      ├──figs/ +| │      │      └──ja/ +| │      ├──jp/ +| │      │      └──\*.tex +| │      └──en/ +| │             └──\*.tex +| ├──sample/ +| │      └──Standard/ +| │                  ├──Hubbard/ +| │                  │      ├─square/ +| │                  │      │      ├──StdFace.def +| │                  │      │      └──reference/ +| │                  │      │                 └──\*\*.dat +| │                  │      └─triangular/ +| │                  │            └──\ :math:`\cdots` +| │                  ├──Kondo/ +| │                  │      └─chain/ +| │                  │            └──\ :math:`\cdots` +| │                  └──Spin/ +| │                              ├─HeisenbergChain/ +| │                              │      └──\ :math:`\cdots` +| │                              ├─HeisenbergSquare/ +| │                              │      └──\ :math:`\cdots` +| │                              └─Kagome/ +| │                                     └──\ :math:`\cdots` +| ├──src/ +| │          ├──mVMC/ +| │          │      ├─ \*\*.c +| │          │      └──include/ +| │          │              └──\*\*.h +| │          ├──ComplexUHF/ +| │          │      ├─ \*\*.c +| │          │      └──include/ +| │          │              └──\*\*.h +| │          ├──StdFace/ +| │          │       ├──\*\*.c +| │          │       └──\*\*.h +| │          ├──pfapack/ +| │          │       ├──makefile\_pfapack +| │          │       └──\*\*.f +| │          └──sfmt/ +| │                  ├──makefkie\_sfmt +| │                  ├──\*\*.c +| │                  └──\*\*.h +| └──tool/ +|            ├──\*\*.f90 +|            └──makefile\_tool + +Basic usage +----------- + +mVMC works as whether the following two modes: + +- Expert mode + + mVMC supports the arbitrary fermion-/spin-lattice system; we can + specify the hopping, etc. at each site independently. Although this + makes us able to specify flexibly the target this requires many + input-files, and the setup of the calculation is complicated. + +- Standard mode + + For some typical models (such as the Heisenberg model on the square + lattice), we can start calculation with a few parameters (for + example, the size of the simulation cell, the common coupling + parameter). In this case, the input-files for Expert mode are + automatically generated. Although the number of available systems is + smaller than that number of Expert mode, the setup of the calculation + is easier than in Expert mode. + +We can calculate by using these modes as follows: + +#. Prepare a minimal input file + + You can choose a model (the Heisenberg model, the Hubbard model, + etc.) and a lattice (the square lattice, the triangular lattice, + etc.) from ones provided; you can specify some parameters (such as + the first/second nearest neighbor hopping integrals, the on-site + Coulomb integral, etc.) for them. The input file format is described + in :ref:`HowToStandard`. + +#. Run + + Run a executable ``vmc.out`` in terminal by specifying the name of + input file written in previous step (option ``-s`` is required). + + .. code-block:: bash + + $ mpiexec -np number-of-processes Path/vmc.out -s Input-file-name + + When you use a queuing system in workstations or super computers, + sometimes the number of processes is specified as an argument for the + job-submitting command. If you need more information, please refer + manuals for your system. + +#. Watch calculation logs + + Log files are outputted in the ``output/`` directory which is + automatically made in the directory for a calculation scenario. The + details of output files are shown in :ref:`OutputFile`. + +#. Results + + If the calculation is finished normally, the result files are + outputted in the ``output/`` directory. The details of output files + are shown in :ref:`OutputFile`. + +#. Prepare and run Expert mode + + In the above case, the calculation starts as soon as input files for + Expert mode are generated. If we only generate files without starting + the calculation, we can use a executable ``vmcdry.out`` as follows + (MPI is not used in this step): + + .. code-block:: bash + + $ Path/vmcdry.out Input-file-name + + Then, we can edit generated files by hand and run a executable + ``vmc.out`` with ``namelist.def`` as an argument (option ``-e`` is + required) as follows: + + .. code-block:: bash + + $ mpiexec -np number-of-processes Path/vmc.out -e namelist.def + +.. note:: + + **The number of threads for OpenMP** + + If you specify the number of OpenMP threads for mVMC, you should set it + as follows (in case of 16 threads) before the running: + + .. code-block:: bash + + $ export OMP_NUM_THREADS=16 + +Printing version ID +------------------- + +By using ``-v`` option as follows, you can check which version of mVMC +you are using. + +.. code-block:: bash + + $ PATH/vmcdry.out -v + $ PATH/vmc.out -v diff --git a/doc/en/tutorial.rst b/doc/en/tutorial.rst new file mode 100644 index 00000000..aee96ec7 --- /dev/null +++ b/doc/en/tutorial.rst @@ -0,0 +1,341 @@ +Tutorial +======== + +List of sample files +-------------------- + +There are following tutorials in ``samples/Standard/``. + +- The Hubbard model on the two dimensional square lattice + + (``samples/Standard/Hubbard/square/``) + +- The Hubbard model on the two dimensional triangular lattice + + (``samples/Standard/Hubbard/triangular/``) + +- The one dimensional Kondo chain + + (``samples/Standard/Kondo/chain/``) + +- The one dimensional antiferromagnetic Heisenberg chain + + (``samples/Standard/Spin/HeisenbergChain/HeisenbergChain/``) + +- The antiferromagnetic Heisenberg model on the two dimensional square + lattice + + (``samples/Standard/Spin/HeisenbergSquare/``) + +- The antiferromagnetic Heisenberg model on the two dimensional Kagome + lattice + + (``samples/Standard/Spin/Kagome/``) + +We can perform these tutorials in the same way. In the following, the +tutorial of the one dimensional antiferromagnetic Heisenberg chain is +shown. + +Heisenberg model +---------------- + +This tutorial should be performed in + +:: + + sample/Standard/Spin/HeisenbergChain/. + +This directory contains the following things: + +The input file: StdFace.def + +reference outputs: reference/ + +In this case, we treat the one dimensional antiferromagnetic Heisenberg +chain which has a nearest neighbor spin coupling. + +.. math:: + + \begin{aligned} + {\hat H} = J \sum_{i=1}^{L} {\hat {\boldsymbol S}}_i \cdot {\hat {\boldsymbol S}}_{i+1} + \end{aligned} + +The input file is as follows: + +:: + + L = 16 + Lsub=4 + model = "Spin" + lattice = "chain lattice" + J = 1.0 + 2Sz = 0 + NMPtrans=1 + +In this tutorial, J and the number of sites are set to 1 (arbitrary +unit) and 16 respectively. + +Running +^^^^^^^ + +We execute the following command. + +.. code-block:: bash + + $ mpiexec -np number-of-processes Path/vmcdry.out -s StdFace.def + +The MPI command depends on your system (such as ``mpiexec``, ``mpirun``, +``mpijob``, ``poe``, etc.). Then, the calculation starts and the +following standard message is outputted in the terminal. + +:: + + ###### Standard Intarface Mode STARTS ###### + + Open Standard-Mode Inputfile StdFace.def + + KEYWORD : l | VALUE : 16 + KEYWORD : lsub | VALUE : 4 + KEYWORD : model | VALUE : spin + KEYWORD : lattice | VALUE : chain + KEYWORD : j | VALUE : 1.0 + KEYWORD : nmptrans | VALUE : 1 + + ####### Parameter Summary ####### + + @ Lattice Size & Shape + + L = 16 + Lsub = 4 + L = 16 + W = 1 + phase0 = 0.00000 ###### DEFAULT VALUE IS USED ###### + + @ Hamiltonian + + 2S = 1 ###### DEFAULT VALUE IS USED ###### + h = 0.00000 ###### DEFAULT VALUE IS USED ###### + Gamma = 0.00000 ###### DEFAULT VALUE IS USED ###### + D = 0.00000 ###### DEFAULT VALUE IS USED ###### + J0x = 1.00000 + J0y = 1.00000 + J0z = 1.00000 + + @ Numerical conditions + + Lsub = 4 + Wsub = 1 + ioutputmode = 1 ###### DEFAULT VALUE IS USED ###### + + ###### Print Expert input files ###### + + qptransidx.def is written. + filehead = zvo ###### DEFAULT VALUE IS USED ###### + filehead = zqp ###### DEFAULT VALUE IS USED ###### + NVMCCalMode = 0 ###### DEFAULT VALUE IS USED ###### + NLanczosMode = 0 ###### DEFAULT VALUE IS USED ###### + NDataIdxStart = 1 ###### DEFAULT VALUE IS USED ###### + NDataQtySmp = 1 ###### DEFAULT VALUE IS USED ###### + NSPGaussLeg = 8 ###### DEFAULT VALUE IS USED ###### + NMPTrans = 1 + NSROptItrStep = 1000 ###### DEFAULT VALUE IS USED ###### + NSROptItrSmp = 100 ###### DEFAULT VALUE IS USED ###### + NVMCWarmUp = 10 ###### DEFAULT VALUE IS USED ###### + NVMCInterval = 1 ###### DEFAULT VALUE IS USED ###### + NVMCSample = 1000 ###### DEFAULT VALUE IS USED ###### + NExUpdatePath = 2 + RndSeed = 123456789 ###### DEFAULT VALUE IS USED ###### + NSplitSize = 1 ###### DEFAULT VALUE IS USED ###### + NStore = 0 ###### DEFAULT VALUE IS USED ###### + DSROptRedCut = 0.00100 ###### DEFAULT VALUE IS USED ###### + DSROptStaDel = 0.02000 ###### DEFAULT VALUE IS USED ###### + DSROptStepDt = 0.02000 ###### DEFAULT VALUE IS USED ###### + NSPStot = 0 ###### DEFAULT VALUE IS USED ###### + ComplexType = 0 ###### DEFAULT VALUE IS USED ###### + locspn.def is written. + trans.def is written. + interall.def is written. + jastrowidx.def is written. + coulombintra.def is written. + coulombinter.def is written. + hund.def is written. + exchange.def is written. + orbitalidx.def is written. + gutzwilleridx.def is written. + namelist.def is written. + modpara.def is written. + greenone.def is written. + greentwo.def is written. + + ###### Input files are generated. ###### + ----------- + Start: Read *def files. + Read File namelist.def . + Read File 'modpara.def' for ModPara. + Read File 'locspn.def' for LocSpin. + Read File 'trans.def' for Trans. + Read File 'coulombintra.def' for CoulombIntra. + Read File 'coulombinter.def' for CoulombInter. + Read File 'hund.def' for Hund. + Read File 'exchange.def' for Exchange. + Read File 'gutzwilleridx.def' for Gutzwiller. + Read File 'jastrowidx.def' for Jastrow. + Read File 'orbitalidx.def' for Orbital. + Read File 'qptransidx.def' for TransSym. + Read File 'greenone.def' for OneBodyG. + Read File 'greentwo.def' for TwoBodyG. + End : Read *def files. + Start: Read parameters from *def files. + End : Read parameters from *def files. + Start: Set memories. + End : Set memories. + Start: Initialize parameters. + End : Initialize parameters. + Start: Initialize variables for quantum projection. + End : Initialize variables for quantum projection. + Start: Optimize VMC parameters. + End : Optimize VMC parameters. + ----------- + +In the beginning of this run, files describing the detail of considered +Hamiltonian + +- ``locspin.def`` + +- ``trans.def`` + +- ``coulombinter.def`` + +- ``coulombintra.def`` + +- ``exchange.def`` + +- ``hund.def`` + +- ``namelist.def`` + +- ``modpara.def`` + +and files for setting variational parameters + +- ``gutzwilleridx.def`` + +- ``jastrowidx.def`` + +- ``orbitalidx.def`` + +- ``qptransidx.def`` + +and files specifying elements of correlation functions that will be +calculated + +- ``greenone.def`` + +- ``greentwo.def`` + +are generated. The details of these files are shown in :ref:`HowToExpert`. + +During the calculation, the following files are outputted in +``output`` directory: + +:: + + zvo_SRinfo.dat + zvo_out_001.dat + zvo_time_001.dat + zvo_var_001.dat + zvo_CalcTimer.dat + +In ``zvo_out_001.dat``, the following quantities are outputted at each +bins + +.. math:: + + \langle H \rangle, \langle H^2 \rangle, + \frac{\langle H^2 \rangle- \langle H \rangle^2 }{\langle H \rangle^2} \nonumber. + +By seeing these informations, the conversion of the calculation can be +judged. By using gnuplot, we can check the evolution of +:math:`\langle H \rangle` as follows: + +.. code-block:: gnuplot + + gnuplot> plot "zvo_out_001.dat" u 1 + +The details of these outputted files are shown in :ref:`OutputFile`. + +Output results +^^^^^^^^^^^^^^ + +After finishing calculation normally, the files for the energy, the +deviation, the optimized variational parameters and the time of +execution for each calculation steps are outputted in ``output/`` +directory. In the following, the outputted files are shown + +:: + + gutzwiller_opt.dat + jastrow_opt.dat + orbital_opt.dat + zqp_opt.dat + ClacTimer.dat + +The details of these outputted files are shown in :ref:`OutputFile`. + +Calculation of Green functions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +After changing the value of ``NVMCCalMode`` from 0 to 1 in +``modpara.def`` file, we execute the following command. When we add +``"zqp_opt.dat"`` after ``"namelist.dat"`` as a command-line argument as +follows, the calculation of Green functions is done by using the +optimized variational parameters. + +.. code-block:: bash + + $ Path/vmc.out -e namelist.def output/zqp_opt.dat + +After the calculation finishes, the following files are outputted in +``output/`` directory. + +:: + + zvo_cisajs_001.dat + zvo_cisajscktalt_001.dat + +The details of these outputted files are shown in :ref:`OutputFile`. + +Input files for Expert mode +--------------------------- + +In mVMC, the calculation is done by reading input files categorized by +the following six parts. + +(1) List: + Specify the kinds and names of input files. + +(2) Basic parameters: + Specify the basic parameters. + +(3) Set Hamiltonian: + Specify the Hamiltonian. + +(4) Set condition of variational parameters : + Specify the variational parameters to be optimized. + +(5) Initial variational parameters: + Specify the initial values of the variational parameters. + +(6) Output: + Specify the components of one-body and two-body Green’s functions to + be outputted. + +The calculation for complex models can be done by directly making above +input files. The details for each files are shown in :ref:`HowToExpert`. + +Fourier transformation of correlation functions +----------------------------------------------- + +This package has a utility which performs the Fourier transformation of +the correlation function and plots that function. +For more details, please see :ref:`fourier`. diff --git a/doc/jp/appendix.rst b/doc/jp/appendix.rst index 66bc9978..042e4d2d 100644 --- a/doc/jp/appendix.rst +++ b/doc/jp/appendix.rst @@ -21,9 +21,15 @@ UHF近似では揺らぎ :math:`\delta A \equiv A-\langle A \rangle` の一次 .. math:: \begin{aligned} - n_ {i}n_{j} &=& (\langle n_{i} \rangle +\delta n_i) (\langle n_{j} \rangle +\delta n_j) - \left[ \langle c_{i}^{\dag}c_j \rangle +\delta (c_{i}^{\dag}c_j ) \right] \left[ \langle c_{j}^{\dag}c_i \rangle +\delta (c_{j}^{\dag}c_i )\right] \nonumber\\ - &\sim&\langle n_{i} \rangle n_j+\langle n_{j} \rangle n_i - \langle c_{i}^{\dag}c_j \rangle c_{j}^{\dag}c_i - \langle c_{j}^{\dag}c_i \rangle c_{i}^{\dag}c_j - -\langle n_{i} \rangle \langle n_j \rangle + \langle c_{j}^{\dag}c_i \rangle \langle c_{i}^{\dag}c_j \rangle + n_ {i}n_{j} &= + (\langle n_{i} \rangle +\delta n_i) (\langle n_{j} \rangle +\delta n_j) + - \left[ \langle c_{i}^{\dagger}c_j \rangle +\delta (c_{i}^{\dagger}c_j ) \right] + \left[ \langle c_{j}^{\dagger}c_i \rangle +\delta (c_{j}^{\dagger}c_i )\right] + \nonumber\\ + &\sim + \langle n_{i} \rangle n_j+\langle n_{j} \rangle n_i + - \langle c_{i}^{\dagger}c_j \rangle c_{j}^{\dagger}c_i - \langle c_{j}^{\dagger}c_i \rangle c_{i}^{\dagger}c_j + -\langle n_{i} \rangle \langle n_j \rangle + \langle c_{j}^{\dagger}c_i \rangle \langle c_{i}^{\dagger}c_j \rangle \end{aligned} と近似されます。このような形式で、その他の相互作用についても近似を行うことで、一体問題に帰着させることができます。 @@ -39,9 +45,9 @@ UHF近似では揺らぎ :math:`\delta A \equiv A-\langle A \rangle` の一次 コンパイルはmVMCのコンパイルと同様にmVMCのフォルダ直下で -:: +.. code-block:: bash - $ make mvmc + $ make mvmc を実行することで行われます。コンパイルが終了すると、 ``src/ComplexUHF/src`` に実行ファイル ``UHF`` が作成されます。 @@ -52,8 +58,8 @@ UHF近似では揺らぎ :math:`\delta A \equiv A-\langle A \rangle` の一次 入力ファイル指定用ファイル (namelsit.def) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -| UHFで指定するファイルは以下のファイルです。 - ``namelist.def`` は :ref:`InputFileList` で定義されているファイルと同じ様式です。 +UHFで指定するファイルは以下のファイルです。 +``namelist.def`` は :ref:`InputFileList` で定義されているファイルと同じ様式です。 - ``ModPara`` @@ -105,23 +111,28 @@ UHFで指定するパラメータは以下のパラメータです。 ``Nsite``, ``Ne`` はmVMCと共通のパラメータで、以下の三つがUHF独特のパラメータです。 -- | ``Mix`` - | linear - mixingをdouble型で指定します。mix=1とすると完全に新しいGreen関数に置き換えられます。 +- ``Mix`` + + linear + mixingをdouble型で指定します。mix=1とすると完全に新しいGreen関数に置き換えられます。 -- | ``EPS`` - | 収束判定条件をint型で指定します。新しく計算されたGreen関数と一つ前のGreen関数の残差が :math:`10^{-\verb|eps|}` の場合に、計算が打ち切られます。 +- ``EPS`` + + 収束判定条件をint型で指定します。新しく計算されたGreen関数と一つ前のGreen関数の残差が + :math:`10^{-\verb|eps|}` の場合に、計算が打ち切られます。 -- | ``IterationMax`` - | ループの最大数をint型で指定します。 +- ``IterationMax`` + + ループの最大数をint型で指定します。 なお、mVMCで使用するその他パラメータが存在する場合はWarningが標準出力されます(計算は中断せずに実行されます)。 Initialファイル ^^^^^^^^^^^^^^^ -グリーン関数 :math:`G_{ij\sigma_1\sigma_2}\equiv \langle c_{i\sigma_1}^\dag c_{j\sigma_2}\rangle` の初期値を与えます。 -ファイル様式は ``Trans`` ファイルと同じで、 :math:`t_{ij\sigma_1\sigma_2}` の代わりに :math:`G_{ij\sigma_1\sigma_2}` の値を記述します。 +グリーン関数 :math:`G_{ij\sigma_1\sigma_2}\equiv \langle c_{i\sigma_1}^\dagger c_{j\sigma_2}\rangle` の初期値を与えます。 +ファイル様式は ``Trans`` ファイルと同じで、 :math:`t_{ij\sigma_1\sigma_2}` の代わりに +:math:`G_{ij\sigma_1\sigma_2}` の値を記述します。 なお、値を指定しないグリーン関数には０が入ります。 使用方法 @@ -129,7 +140,7 @@ Initialファイル UHF自体はmVMCと同じように -:: +.. code-block:: bash $ UHF namelist.def @@ -145,7 +156,9 @@ UHF自体はmVMCと同じように 計算後に出力されるファイルおよび出力例は以下の通りです。 -- | zvo\_result.dat: エネルギーと粒子数が出力されます。 +- zvo\_result.dat: + + エネルギーと粒子数が出力されます。 :: @@ -153,6 +166,7 @@ UHF自体はmVMCと同じように num 36.0000000000 - zvo\_check.dat: + イタレーションのステップ数、グリーン関数の残差の絶対値の平均、収束過程のエネルギー、粒子数を順に出力します。 :: @@ -163,9 +177,10 @@ UHF自体はmVMCと同じように 3 0.000681060599 -82.973664527606 36.000000 ... -- | zvo\_UHF\_cisajs.dat: - 収束した一体グリーン関数 :math:`G_{ij\sigma_1\sigma_2}\equiv\langle c_{i\sigma_1}^{\dag}c_{j\sigma_2}\rangle` 。 - | 全成分について :math:`i, \sigma_1, j, \sigma_2, {\rm Re}\left[G_{ij\sigma_1\sigma_2}\right], {\rm Im}\left[G_{ij\sigma_1\sigma_2}\right]` の順に出力されます。 +- zvo\_UHF\_cisajs.dat: + + 収束した一体グリーン関数 :math:`G_{ij\sigma_1\sigma_2}\equiv\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle` 。 + 全成分について :math:`i, \sigma_1, j, \sigma_2, {\rm Re}\left[G_{ij\sigma_1\sigma_2}\right], {\rm Im}\left[G_{ij\sigma_1\sigma_2}\right]` の順に出力されます。 :: @@ -173,10 +188,11 @@ UHF自体はmVMCと同じように 0 0 0 1 0.4610257618 0.0003115503 0 1 0 0 0.4610257618 -0.0003115503 0 1 0 1 0.4962444717 0.0000000000 - ... + ... + +- zvo\_eigen.dat: -- | zvo\_eigen.dat: - 収束したハミルトニアンの固有値が低エネルギー順に出力されます。 + 収束したハミルトニアンの固有値が低エネルギー順に出力されます。 :: @@ -186,6 +202,7 @@ UHF自体はmVMCと同じように ... - zvo\_gap.dat: + 全電子数を :math:`N_{\rm tot}` とした場合に、 :math:`\Delta E= E(N_{\rm tot}+1)-E(N_{\rm tot})` が出力されます。 :: @@ -193,7 +210,9 @@ UHF自体はmVMCと同じように 5.2208232631 - zvo\_orbital\_opt.dat: + スレータ行列式から生成した :math:`f_{ij}` 。 ``InOrbital``, ``InOrbitalAntiParallel``, ``InOrbitalParallel``, ``InOrbitalAntiGeneral`` ファイルと同じ形式のファイルが出力されます。 :math:`f_{ij}` が ``Orbital``, ``OrbitalAntiParallel``, - ``OrbitalParallel``, ``OrbitalAntiGeneral`` ファイルを参照し計算され、同種のパラメータについては平均化した値が採用されます。 + ``OrbitalParallel``, ``OrbitalAntiGeneral`` ファイルを参照し計算され、 + 同種のパラメータについては平均化した値が採用されます。 From cc5ead77cca3a158cb62d4f7c6f92a92b2210c86 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Fri, 16 Mar 2018 00:41:50 +0900 Subject: [PATCH 15/34] Manual (JP) for downfolding --- .../{fourier_contact_en.rst => contact.rst} | 0 .../{fourier_format_en.rst => format.rst} | 0 doc/en/fourier/index.rst | 10 +- .../{fourier_overview_en.rst => overview.rst} | 0 .../{fourier_tutorial_en.rst => tutorial.rst} | 0 .../fourier/{fourier_util_en.rst => util.rst} | 0 doc/fourier/en/Makefile | 177 --- doc/fourier/en/conf.py | 263 ----- doc/fourier/en/fourier_contact_en.rst | 12 - doc/fourier/en/fourier_format_en.rst | 252 ----- 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sample/Standard/Hubbard/square/UHF/locspn.def | 13 - .../Standard/Hubbard/square/UHF/modpara.def | 12 - .../Standard/Hubbard/square/UHF/namelist.def | 6 - .../Hubbard/square/UHF/orbitalidx.def | 101 -- sample/Standard/Hubbard/square/UHF/trans.def | 53 - .../Hubbard/square/reference/zqp_opt.dat | 1 - .../Hubbard/square/reference/zvo_out_001.dat | 500 --------- .../Hubbard/triangular/UHF/coulombintra.def | 13 - .../Hubbard/triangular/UHF/locspn.def | 13 - .../Hubbard/triangular/UHF/modpara.def | 12 - .../Hubbard/triangular/UHF/namelist.def | 6 - .../Hubbard/triangular/UHF/orbitalidx.def | 133 --- .../Standard/Hubbard/triangular/UHF/trans.def | 85 -- .../Hubbard/triangular/reference/zqp_opt.dat | 1 - .../triangular/reference/zvo_out_001.dat | 500 --------- .../Kondo/Chain/reference/zqp_opt.dat | 1 - .../Kondo/Chain/reference/zvo_out_001.dat | 300 ----- .../HeisenbergChain/reference/zqp_opt.dat | 1 - .../HeisenbergChain/reference/zvo_out_001.dat | 300 ----- .../HeisenbergSquare/reference/zqp_opt.dat | 1 - .../reference/zvo_out_001.dat | 200 ---- .../Spin/Kagome/reference/zqp_opt.dat | 1 - .../Spin/Kagome/reference/zvo_out_001.dat | 1000 ----------------- .../Spin/Kitaev/reference/zqp_opt.dat | 1 - .../Spin/Kitaev/reference/zvo_out_001.dat | 1000 ----------------- {sample => samples}/Standard/.gitignore | 0 .../Standard/Hubbard/square/StdFace.def | 0 .../Standard/Hubbard/square/UHF/initial.def | 0 .../UHF/reference/zqp_APOrbital_opt.dat | 0 .../square/UHF/reference/zvo_check.dat | 0 .../square/UHF/reference/zvo_eigen.dat | 0 .../Hubbard/square/UHF/reference/zvo_gap.dat | 0 .../square/UHF/reference/zvo_result.dat | 0 .../Standard/Hubbard/triangular/StdFace.def | 0 .../Hubbard/triangular/UHF/initial.def | 0 .../UHF/reference/zqp_APOrbital_opt.dat | 0 .../triangular/UHF/reference/zvo_check.dat | 0 .../triangular/UHF/reference/zvo_eigen.dat | 0 .../triangular/UHF/reference/zvo_gap.dat | 0 .../triangular/UHF/reference/zvo_result.dat | 0 .../Standard/Kondo/Chain/StdFace.def | 0 .../Standard/Spin/HeisenbergChain/StdFace.def | 0 .../Spin/HeisenbergSquare/StdFace.def | 0 .../Standard/Spin/Kagome/StdFace.def | 0 .../Standard/Spin/Kitaev/StdFace.def | 0 samples/Wannier/Sr2VO4/README.md | 44 + samples/Wannier/Sr2VO4/band.in | 82 ++ samples/Wannier/Sr2VO4/bands.in | 4 + samples/Wannier/Sr2VO4/nscf.in | 35 + samples/Wannier/Sr2VO4/respack.in | 50 + samples/Wannier/Sr2VO4/scf.in | 34 + samples/Wannier/Sr2VO4/stan.in | 18 + 88 files changed, 383 insertions(+), 6255 deletions(-) rename doc/en/fourier/{fourier_contact_en.rst => contact.rst} (100%) rename doc/en/fourier/{fourier_format_en.rst => format.rst} (100%) rename doc/en/fourier/{fourier_overview_en.rst => overview.rst} (100%) rename doc/en/fourier/{fourier_tutorial_en.rst => tutorial.rst} (100%) rename doc/en/fourier/{fourier_util_en.rst => util.rst} (100%) delete mode 100644 doc/fourier/en/Makefile delete mode 100644 doc/fourier/en/conf.py delete mode 100644 doc/fourier/en/fourier_contact_en.rst delete mode 100644 doc/fourier/en/fourier_format_en.rst delete mode 100644 doc/fourier/en/fourier_overview_en.rst delete mode 100644 doc/fourier/en/fourier_tutorial_en.rst delete mode 100644 doc/fourier/en/fourier_util_en.rst delete mode 100644 doc/fourier/figs/corplot.png delete mode 100644 doc/fourier/ja/Makefile delete mode 100644 doc/fourier/ja/conf.py delete mode 100644 doc/fourier/ja/fourier_tutorial_ja.rst delete mode 100644 doc/fourier/ja/index.rst rename doc/{fourier/ja/fourier_contact_ja.rst => jp/fourier/contact.rst} (100%) rename doc/{fourier/ja/fourier_format_ja.rst => jp/fourier/format.rst} (100%) delete mode 100644 doc/jp/fourier/fourier_format_ja.rst delete mode 100644 doc/jp/fourier/fourier_overview_ja.rst delete mode 100644 doc/jp/fourier/fourier_util_ja.rst rename doc/{fourier/ja/fourier_overview_ja.rst => jp/fourier/overview.rst} (100%) rename doc/jp/fourier/{fourier_tutorial_ja.rst => tutorial.rst} (100%) rename doc/{fourier/ja/fourier_util_ja.rst => jp/fourier/util.rst} (100%) rename doc/jp/{fourier/fourier_contact_ja.rst => wannier/contact.rst} (100%) create mode 100644 doc/jp/wannier/format.rst rename doc/{fourier/en => jp/wannier}/index.rst (57%) create mode 100644 doc/jp/wannier/overview.rst create mode 100644 doc/jp/wannier/parameter.rst create mode 100644 doc/jp/wannier/tutorial.rst delete mode 100644 sample/Standard/Hubbard/square/UHF/coulombintra.def delete mode 100644 sample/Standard/Hubbard/square/UHF/locspn.def delete mode 100644 sample/Standard/Hubbard/square/UHF/modpara.def delete mode 100644 sample/Standard/Hubbard/square/UHF/namelist.def delete mode 100644 sample/Standard/Hubbard/square/UHF/orbitalidx.def delete mode 100644 sample/Standard/Hubbard/square/UHF/trans.def delete mode 100644 sample/Standard/Hubbard/square/reference/zqp_opt.dat delete mode 100644 sample/Standard/Hubbard/square/reference/zvo_out_001.dat delete mode 100644 sample/Standard/Hubbard/triangular/UHF/coulombintra.def delete mode 100644 sample/Standard/Hubbard/triangular/UHF/locspn.def delete mode 100644 sample/Standard/Hubbard/triangular/UHF/modpara.def delete mode 100644 sample/Standard/Hubbard/triangular/UHF/namelist.def delete mode 100644 sample/Standard/Hubbard/triangular/UHF/orbitalidx.def delete mode 100644 sample/Standard/Hubbard/triangular/UHF/trans.def delete mode 100644 sample/Standard/Hubbard/triangular/reference/zqp_opt.dat delete mode 100644 sample/Standard/Hubbard/triangular/reference/zvo_out_001.dat delete mode 100644 sample/Standard/Kondo/Chain/reference/zqp_opt.dat delete mode 100644 sample/Standard/Kondo/Chain/reference/zvo_out_001.dat delete mode 100644 sample/Standard/Spin/HeisenbergChain/reference/zqp_opt.dat delete mode 100644 sample/Standard/Spin/HeisenbergChain/reference/zvo_out_001.dat delete mode 100644 sample/Standard/Spin/HeisenbergSquare/reference/zqp_opt.dat delete mode 100644 sample/Standard/Spin/HeisenbergSquare/reference/zvo_out_001.dat delete mode 100644 sample/Standard/Spin/Kagome/reference/zqp_opt.dat delete mode 100644 sample/Standard/Spin/Kagome/reference/zvo_out_001.dat delete mode 100644 sample/Standard/Spin/Kitaev/reference/zqp_opt.dat delete mode 100644 sample/Standard/Spin/Kitaev/reference/zvo_out_001.dat rename {sample => samples}/Standard/.gitignore (100%) rename {sample => samples}/Standard/Hubbard/square/StdFace.def (100%) rename {sample => samples}/Standard/Hubbard/square/UHF/initial.def (100%) rename {sample => samples}/Standard/Hubbard/square/UHF/reference/zqp_APOrbital_opt.dat (100%) rename {sample => samples}/Standard/Hubbard/square/UHF/reference/zvo_check.dat (100%) rename {sample => samples}/Standard/Hubbard/square/UHF/reference/zvo_eigen.dat (100%) rename {sample => samples}/Standard/Hubbard/square/UHF/reference/zvo_gap.dat (100%) rename {sample => samples}/Standard/Hubbard/square/UHF/reference/zvo_result.dat (100%) rename {sample => samples}/Standard/Hubbard/triangular/StdFace.def (100%) rename {sample => samples}/Standard/Hubbard/triangular/UHF/initial.def (100%) rename {sample => samples}/Standard/Hubbard/triangular/UHF/reference/zqp_APOrbital_opt.dat (100%) rename {sample => samples}/Standard/Hubbard/triangular/UHF/reference/zvo_check.dat (100%) rename {sample => samples}/Standard/Hubbard/triangular/UHF/reference/zvo_eigen.dat (100%) rename {sample => samples}/Standard/Hubbard/triangular/UHF/reference/zvo_gap.dat (100%) rename {sample => samples}/Standard/Hubbard/triangular/UHF/reference/zvo_result.dat (100%) rename {sample => samples}/Standard/Kondo/Chain/StdFace.def (100%) rename {sample => samples}/Standard/Spin/HeisenbergChain/StdFace.def (100%) rename {sample => samples}/Standard/Spin/HeisenbergSquare/StdFace.def (100%) rename {sample => samples}/Standard/Spin/Kagome/StdFace.def (100%) rename {sample => samples}/Standard/Spin/Kitaev/StdFace.def (100%) create mode 100644 samples/Wannier/Sr2VO4/README.md create mode 100644 samples/Wannier/Sr2VO4/band.in create mode 100644 samples/Wannier/Sr2VO4/bands.in create mode 100644 samples/Wannier/Sr2VO4/nscf.in create mode 100644 samples/Wannier/Sr2VO4/respack.in create mode 100644 samples/Wannier/Sr2VO4/scf.in create mode 100644 samples/Wannier/Sr2VO4/stan.in diff --git a/doc/en/fourier/fourier_contact_en.rst b/doc/en/fourier/contact.rst similarity index 100% rename from doc/en/fourier/fourier_contact_en.rst rename to doc/en/fourier/contact.rst diff --git a/doc/en/fourier/fourier_format_en.rst b/doc/en/fourier/format.rst similarity index 100% rename from doc/en/fourier/fourier_format_en.rst rename to doc/en/fourier/format.rst diff --git a/doc/en/fourier/index.rst b/doc/en/fourier/index.rst index e1c957d5..dc15bb4e 100644 --- a/doc/en/fourier/index.rst +++ b/doc/en/fourier/index.rst @@ -11,11 +11,11 @@ HPhi/mVMC Fourie-Transformation utility .. toctree:: :maxdepth: 3 - fourier_overview_en.rst - fourier_tutorial_en.rst - fourier_format_en.rst - fourier_util_en.rst - fourier_contact_en.rst + overview + tutorial + format + util + contact .. Indices and tables .. ================== diff --git a/doc/en/fourier/fourier_overview_en.rst b/doc/en/fourier/overview.rst similarity index 100% rename from doc/en/fourier/fourier_overview_en.rst rename to doc/en/fourier/overview.rst diff --git a/doc/en/fourier/fourier_tutorial_en.rst b/doc/en/fourier/tutorial.rst similarity index 100% rename from doc/en/fourier/fourier_tutorial_en.rst rename to doc/en/fourier/tutorial.rst diff --git a/doc/en/fourier/fourier_util_en.rst b/doc/en/fourier/util.rst similarity index 100% rename from doc/en/fourier/fourier_util_en.rst rename to doc/en/fourier/util.rst diff --git a/doc/fourier/en/Makefile b/doc/fourier/en/Makefile deleted file mode 100644 index c6b37e39..00000000 --- a/doc/fourier/en/Makefile +++ /dev/null @@ -1,177 +0,0 @@ -# Makefile for Sphinx documentation -# - -# You can set these variables from the command line. -SPHINXOPTS = -SPHINXBUILD = sphinx-build -PAPER = -BUILDDIR = _build - -# User-friendly check for sphinx-build -ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $$?), 1) -$(error The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/) -endif - -# Internal variables. -PAPEROPT_a4 = -D latex_paper_size=a4 -PAPEROPT_letter = -D latex_paper_size=letter -ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . -# the i18n builder cannot share the environment and doctrees with the others -I18NSPHINXOPTS = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . - -.PHONY: help clean html dirhtml singlehtml pickle json htmlhelp qthelp devhelp epub latex latexpdf text man changes linkcheck doctest gettext - -help: - @echo "Please use \`make ' where is one of" - @echo " html to make standalone HTML files" - @echo " dirhtml to make HTML files named index.html in directories" - @echo " singlehtml to make a single large HTML file" - @echo " pickle to make pickle files" - @echo " json to make JSON files" - @echo " htmlhelp to make HTML files and a HTML help project" - @echo " qthelp to make HTML files and a qthelp project" - @echo " devhelp to make HTML files and a Devhelp project" - @echo " epub to make an epub" - @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter" - @echo " latexpdf to make LaTeX files and run them through pdflatex" - @echo " latexpdfja to make LaTeX files and run them through platex/dvipdfmx" - @echo " text to make text files" - @echo " man to make manual pages" - @echo " texinfo to make Texinfo files" - @echo " info to make Texinfo files and run them through makeinfo" - @echo " gettext to make PO message catalogs" - @echo " changes to make an overview of all changed/added/deprecated items" - @echo " xml to make Docutils-native XML files" - @echo " pseudoxml to make pseudoxml-XML files for display purposes" - @echo " linkcheck to check all external links for integrity" - @echo " doctest to run all doctests embedded in the documentation (if enabled)" - -clean: - rm -rf $(BUILDDIR)/* - -html: - $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html - @echo - @echo "Build finished. The HTML pages are in $(BUILDDIR)/html." - -dirhtml: - $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml - @echo - @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml." - -singlehtml: - $(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml - @echo - @echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml." - -pickle: - $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle - @echo - @echo "Build finished; now you can process the pickle files." - -json: - $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json - @echo - @echo "Build finished; now you can process the JSON files." - -htmlhelp: - $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp - @echo - @echo "Build finished; now you can run HTML Help Workshop with the" \ - ".hhp project file in $(BUILDDIR)/htmlhelp." - -qthelp: - $(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp - @echo - @echo "Build finished; now you can run "qcollectiongenerator" with the" \ - ".qhcp project file in $(BUILDDIR)/qthelp, like this:" - @echo "# qcollectiongenerator $(BUILDDIR)/qthelp/fourier.qhcp" - @echo "To view the help file:" - @echo "# assistant -collectionFile $(BUILDDIR)/qthelp/fourier.qhc" - -devhelp: - $(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp - @echo - @echo "Build finished." - @echo "To view the help file:" - @echo "# mkdir -p $$HOME/.local/share/devhelp/fourier" - @echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/fourier" - @echo "# devhelp" - -epub: - $(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub - @echo - @echo "Build finished. The epub file is in $(BUILDDIR)/epub." - -latex: - $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex - @echo - @echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex." - @echo "Run \`make' in that directory to run these through (pdf)latex" \ - "(use \`make latexpdf' here to do that automatically)." - -latexpdf: - $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex - @echo "Running LaTeX files through pdflatex..." - $(MAKE) -C $(BUILDDIR)/latex all-pdf - @echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex." - -latexpdfja: - $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex - @echo "Running LaTeX files through platex and dvipdfmx..." - $(MAKE) -C $(BUILDDIR)/latex all-pdf-ja - @echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex." - -text: - $(SPHINXBUILD) -b text $(ALLSPHINXOPTS) $(BUILDDIR)/text - @echo - @echo "Build finished. The text files are in $(BUILDDIR)/text." - -man: - $(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man - @echo - @echo "Build finished. The manual pages are in $(BUILDDIR)/man." - -texinfo: - $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo - @echo - @echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo." - @echo "Run \`make' in that directory to run these through makeinfo" \ - "(use \`make info' here to do that automatically)." - -info: - $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo - @echo "Running Texinfo files through makeinfo..." - make -C $(BUILDDIR)/texinfo info - @echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo." - -gettext: - $(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale - @echo - @echo "Build finished. The message catalogs are in $(BUILDDIR)/locale." - -changes: - $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes - @echo - @echo "The overview file is in $(BUILDDIR)/changes." - -linkcheck: - $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck - @echo - @echo "Link check complete; look for any errors in the above output " \ - "or in $(BUILDDIR)/linkcheck/output.txt." - -doctest: - $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest - @echo "Testing of doctests in the sources finished, look at the " \ - "results in $(BUILDDIR)/doctest/output.txt." - -xml: - $(SPHINXBUILD) -b xml $(ALLSPHINXOPTS) $(BUILDDIR)/xml - @echo - @echo "Build finished. The XML files are in $(BUILDDIR)/xml." - -pseudoxml: - $(SPHINXBUILD) -b pseudoxml $(ALLSPHINXOPTS) $(BUILDDIR)/pseudoxml - @echo - @echo "Build finished. The pseudo-XML files are in $(BUILDDIR)/pseudoxml." diff --git a/doc/fourier/en/conf.py b/doc/fourier/en/conf.py deleted file mode 100644 index 923fbe37..00000000 --- a/doc/fourier/en/conf.py +++ /dev/null @@ -1,263 +0,0 @@ -# -*- coding: utf-8 -*- -# -# Fourier documentation build configuration file, created by -# sphinx-quickstart on Sat Jan 7 22:10:04 2017. -# -# This file is execfile()d with the current directory set to its -# containing dir. -# -# Note that not all possible configuration values are present in this -# autogenerated file. -# -# All configuration values have a default; values that are commented out -# serve to show the default. - -import sys -import os - -# If extensions (or modules to document with autodoc) are in another directory, -# add these directories to sys.path here. If the directory is relative to the -# documentation root, use os.path.abspath to make it absolute, like shown here. -#sys.path.insert(0, os.path.abspath('.')) - -# -- General configuration ------------------------------------------------ - -# If your documentation needs a minimal Sphinx version, state it here. -#needs_sphinx = '1.0' - -# Add any Sphinx extension module names here, as strings. They can be -# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom -# ones. -extensions = [ - 'sphinx.ext.mathjax', - 'sphinx_numfig' -] - -# Add any paths that contain templates here, relative to this directory. -templates_path = ['_templates'] - -# The suffix of source filenames. -source_suffix = '.rst' - -# The encoding of source files. -#source_encoding = 'utf-8-sig' - -# The master toctree document. -master_doc = 'index' - -# General information about the project. -project = u'fourier' -copyright = u'2017, kawamura' - -# The version info for the project you're documenting, acts as replacement for -# |version| and |release|, also used in various other places throughout the -# built documents. -# -# The short X.Y version. -version = '0.1' -# The full version, including alpha/beta/rc tags. -release = '0.1.1' - -# The language for content autogenerated by Sphinx. Refer to documentation -# for a list of supported languages. -language = 'en' - -# There are two options for replacing |today|: either, you set today to some -# non-false value, then it is used: -#today = '' -# Else, today_fmt is used as the format for a strftime call. -#today_fmt = '%B %d, %Y' - -# List of patterns, relative to source directory, that match files and -# directories to ignore when looking for source files. -exclude_patterns = ['_build'] - -# The reST default role (used for this markup: `text`) to use for all -# documents. -#default_role = None - -# If true, '()' will be appended to :func: etc. cross-reference text. -#add_function_parentheses = True - -# If true, the current module name will be prepended to all description -# unit titles (such as .. function::). -#add_module_names = True - -# If true, sectionauthor and moduleauthor directives will be shown in the -# output. They are ignored by default. -#show_authors = False - -# The name of the Pygments (syntax highlighting) style to use. -pygments_style = 'sphinx' - -# A list of ignored prefixes for module index sorting. -#modindex_common_prefix = [] - -# If true, keep warnings as "system message" paragraphs in the built documents. -#keep_warnings = False - - -# -- Options for HTML output ---------------------------------------------- - -# The theme to use for HTML and HTML Help pages. See the documentation for -# a list of builtin themes. -html_theme = 'default' - -# Theme options are theme-specific and customize the look and feel of a theme -# further. For a list of options available for each theme, see the -# documentation. -#html_theme_options = {} - -# Add any paths that contain custom themes here, relative to this directory. -#html_theme_path = [] - -# The name for this set of Sphinx documents. If None, it defaults to -# " v documentation". -#html_title = None - -# A shorter title for the navigation bar. Default is the same as html_title. -#html_short_title = None - -# The name of an image file (relative to this directory) to place at the top -# of the sidebar. -#html_logo = None - -# The name of an image file (within the static path) to use as favicon of the -# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 -# pixels large. -#html_favicon = None - -# Add any paths that contain custom static files (such as style sheets) here, -# relative to this directory. They are copied after the builtin static files, -# so a file named "default.css" will overwrite the builtin "default.css". -html_static_path = ['_static'] - -# Add any extra paths that contain custom files (such as robots.txt or -# .htaccess) here, relative to this directory. These files are copied -# directly to the root of the documentation. -#html_extra_path = [] - -# If not '', a 'Last updated on:' timestamp is inserted at every page bottom, -# using the given strftime format. -#html_last_updated_fmt = '%b %d, %Y' - -# If true, SmartyPants will be used to convert quotes and dashes to -# typographically correct entities. -#html_use_smartypants = True - -# Custom sidebar templates, maps document names to template names. -#html_sidebars = {} - -# Additional templates that should be rendered to pages, maps page names to -# template names. -#html_additional_pages = {} - -# If false, no module index is generated. -#html_domain_indices = True - -# If false, no index is generated. -#html_use_index = True - -# If true, the index is split into individual pages for each letter. -#html_split_index = False - -# If true, links to the reST sources are added to the pages. -#html_show_sourcelink = True - -# If true, "Created using Sphinx" is shown in the HTML footer. Default is True. -#html_show_sphinx = True - -# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. -#html_show_copyright = True - -# If true, an OpenSearch description file will be output, and all pages will -# contain a tag referring to it. The value of this option must be the -# base URL from which the finished HTML is served. -#html_use_opensearch = '' - -# This is the file name suffix for HTML files (e.g. ".xhtml"). -#html_file_suffix = None - -# Output file base name for HTML help builder. -htmlhelp_basename = 'testdoc' - - -# -- Options for LaTeX output --------------------------------------------- - -latex_elements = { -# The paper size ('letterpaper' or 'a4paper'). -#'papersize': 'letterpaper', - -# The font size ('10pt', '11pt' or '12pt'). -#'pointsize': '10pt', - -# Additional stuff for the LaTeX preamble. -#'preamble': '\usepackage{pxjahyper}', - 'babel': '\\usepackage[english]{babel}', - 'classoptions': ',dvipdfmx,openany' -} - -# Grouping the document tree into LaTeX files. List of tuples -# (source start file, target name, title, -# author, documentclass [howto, manual, or own class]). -latex_documents = [ - ('index', 'fourier.tex', u'Fourier Documentation', - u'kawamura', 'manual'), -] - -# The name of an image file (relative to this directory) to place at the top of -# the title page. -#latex_logo = None - -# For "manual" documents, if this is true, then toplevel headings are parts, -# not chapters. -#latex_use_parts = False - -# If true, show page references after internal links. -#latex_show_pagerefs = False - -# If true, show URL addresses after external links. -#latex_show_urls = False - -# Documents to append as an appendix to all manuals. -#latex_appendices = [] - -# If false, no module index is generated. -#latex_domain_indices = True - - -# -- Options for manual page output --------------------------------------- - -# One entry per manual page. List of tuples -# (source start file, name, description, authors, manual section). -man_pages = [ - ('index', 'fourier', u'fourier Documentation', - [u'kawamura'], 1) -] - -# If true, show URL addresses after external links. -#man_show_urls = False - - -# -- Options for Texinfo output ------------------------------------------- - -# Grouping the document tree into Texinfo files. List of tuples -# (source start file, target name, title, author, -# dir menu entry, description, category) -texinfo_documents = [ - ('index', 'fourier', u'Fourier Documentation', - u'kawamura', 'fourier', 'One line description of project.', - 'Miscellaneous'), -] - -# Documents to append as an appendix to all manuals. -#texinfo_appendices = [] - -# If false, no module index is generated. -#texinfo_domain_indices = True - -# How to display URL addresses: 'footnote', 'no', or 'inline'. -#texinfo_show_urls = 'footnote' - -# If true, do not generate a @detailmenu in the "Top" node's menu. -#texinfo_no_detailmenu = False diff --git a/doc/fourier/en/fourier_contact_en.rst b/doc/fourier/en/fourier_contact_en.rst deleted file mode 100644 index 9404d730..00000000 --- a/doc/fourier/en/fourier_contact_en.rst +++ /dev/null @@ -1,12 +0,0 @@ -Contact -======= - -If you have any comments, questions, bug reports etc. about this utility, -please contact to the main developer (Mitsuaki Kawamura) by -sending the e-mail (the address is shown below). - -:: - - mkawamura_at_issp.u-tokyo.ac.jp - -Please change ``_at_`` into ``@``, when you will send the e-mail. diff --git a/doc/fourier/en/fourier_format_en.rst b/doc/fourier/en/fourier_format_en.rst deleted file mode 100644 index df29ac48..00000000 --- a/doc/fourier/en/fourier_format_en.rst +++ /dev/null @@ -1,252 +0,0 @@ -.. _fileformat: - -File format -=========== - -.. _geometry: - -Geometry --------- - -The file name in the :ref:`tutorial` is ``geometry.dat``. -When we use Standard mode of mVMC/:math:`{\mathcal H}\Phi`, -this file is generated automatically. -Therefore we do not have to care it. - -:: - - 1.000000 0.000000 0.000000 (1) - 0.000000 1.000000 0.000000 (1) - 0.000000 0.000000 1.000000 (1) - 0.000000 0.000000 0.000000 (2) - 4 0 0 (3) - 0 4 0 (3) - 0 0 1 (3) - 0.000000 0.000000 0.000000 (4) - 1.000000 0.000000 0.000000 (4) - 2.000000 0.000000 0.000000 (4) - 3.000000 0.000000 0.000000 (4) - 0.000000 1.000000 0.000000 (4) - 1.000000 1.000000 0.000000 (4) - 2.000000 1.000000 0.000000 (4) - 3.000000 1.000000 0.000000 (4) - 0.000000 2.000000 0.000000 (4) - 1.000000 2.000000 0.000000 (4) - 2.000000 2.000000 0.000000 (4) - 3.000000 2.000000 0.000000 (4) - 0.000000 3.000000 0.000000 (4) - 1.000000 3.000000 0.000000 (4) - 2.000000 3.000000 0.000000 (4) - 3.000000 3.000000 0.000000 (4) - -#. The unit lattice vectors. Arbitrary unit. -#. The phase for the one-body term across boundaries of the simulation cell (degree unit). -#. Three integer vector specifying the shape of the simulation cell. - They are the same as the input parameters ``a0W``, ``a0L``, ``a0H``, ``a1W``... - in Standard mode. -#. The position of each site. The fractional coordinate is used. - - -One- and Two-body correlation function in the site representation ------------------------------------------------------------------ - -.. _greenindex: - -Specify the index of correlation function to be computed -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -Specify the index of correlation functions -computed with mVMC/:math:`{\mathcal H}\Phi`. -When we use the standard mode, this file is generated automatically. -The general description is written in the manuals for mVMC/:math:`{\mathcal H}\Phi`. -The file names in the :ref:`tutorial` are ``greenone.def`` (one body) and ``greentwo.def`` (two body). - -For calculating correlation functions in :ref:`supported`, -indices must be specified as follows: - -- :math:`\langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle` - - :math:`\langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle` - with :math:`(i, j)` ranging on the whole site. - -- :math:`\langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle` - - :math:`\langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle` - with :math:`(i, j)` ranging on the whole site. - -- :math:`\langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle` and - :math:`\langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle` - - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i \sigma} {\hat c}_{j \sigma'}^{\dagger} {\hat c}_{j \sigma'}\rangle` - with :math:`(i, j)` ranging on the whole site and - :math:`(\sigma, \sigma')` ranging from :math:`\uparrow` to :math:`\downarrow`. - -- :math:`\langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle` and - :math:`\langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle` - - For :math:`{\mathcal H}\Phi`, - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i -\sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{j \sigma}\rangle` - with :math:`(i, j)` ranging on the whole site and - :math:`\sigma` ranging from :math:`\uparrow` to :math:`\downarrow`. - For mVMC, - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{j \sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{i -\sigma}\rangle` - with :math:`(i, j)` ranging on the whole site and - :math:`\sigma` ranging from :math:`\uparrow` to :math:`\downarrow`. - In the both cases, please care the order of operators. - -In the default settings of Standard mode (``outputmode="corr"``), -the above indices are specified automatically. -Therefore we do not have to care it. - -.. _zvocisajs: - -Results of correlation function in the site representation -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -The correlation functions having the indices specified in :ref:`greenindex` -are computed by mVMC/:math:`{\mathcal H}\Phi`, -and written to files. -The general description of this file is written in the manuals of mVMC/:math:`{\mathcal H}\Phi`. -File names in the :ref:`tutorial` are -``output/zvo_cisajs_001.dat`` and ``output/zvo_cisajscktalt_001.dat`` (mVMC), or -``output/zvo_cisajs.dat`` and ``output/zvo_cisajscktalt.dat`` (:math:`{\mathcal H}\Phi`). - -The utility ``fourier`` reads these files before the calculation. -If some of the correlation functions with indices written in :ref:`greenindex` are lacking -(for example, because Standard mode was not used), -this utility assume them as 0. - -.. _zvocorr: - -Correlation functions in the primitive Brillouin zone ------------------------------------------------------ - -This file contains the Fourier-transformed correlation function and -generated by the utility ``fourier``. -The file name in the :ref:`tutorial` is ``output/zvo_corr.dat``. - -:: - - #HPhi 16 (1) - # kx[1] ky[2] kz[3](Cart.) UpUp[4,5] (Re. Im.) DownDown[6,7] (2) - # Density[8,9] SzSz[10,11] S+S-[12,13] S-S+[14,15] (2) - #k-offset 0.0000000 0.0000000 0.0000000 (3) - 0.00000E+00 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) - 0.15708E+01 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) - : : - -#. ``"#HPhi"`` for the output of ``HPhi``, - ``"#mVMC"`` for the output of ``vmc.out`` - The subsequent integer indicate the number of :math:`k` points in the primitive Brillouine zone. -#. The description of the quantities in each column. -#. The :math:`k` offset for the one-body correlation function. - That is to say, the one-body correlation function in the 4-7 columns are those - at the :math:`k` point shifted from that point in the 1-3 column. -#. The :math:`k` point (Cartesian) and correlation functions. - The real- and the imaginary-part of each correlation function are written. - -.. _kpoint: - -*k*\-point file for corplot ---------------------------- - -This file is generated by ``fourier`` and -read by ``corplot`` when the correlation function is plotted. -The file name is ``kpoint.dat``. - -:: - - 81 9 (1) - 0.62832E+01 0.00000E+00 0.00000E+00 (2) - 0.00000E+00 0.62832E+01 0.00000E+00 (2) - 0.00000E+00 0.00000E+00 0.62832E+01 (2) - -0.62832E+01 -0.62832E+01 0.00000E+00 1 (3) - -0.47124E+01 -0.62832E+01 0.00000E+00 2 (3) - -0.31416E+01 -0.62832E+01 0.00000E+00 3 - -0.15708E+01 -0.62832E+01 0.00000E+00 4 - 0.00000E+00 -0.62832E+01 0.00000E+00 1 - 0.15708E+01 -0.62832E+01 0.00000E+00 2 - 0.31416E+01 -0.62832E+01 0.00000E+00 3 - 0.47124E+01 -0.62832E+01 0.00000E+00 4 - -#. The total number of :math:`k` points plotted by ``corplot`` and - the number of columns for displaying by splot of gnuplot. -#. Reciprocal lattice vectors (Cartesian coordinate). -#. The :math:`k` vector (Cartesian) and - the index of the equivalent :math:`k` point in the primitive Brillouin zone. - This number is the same as that in :ref:`zvocorr` - -.. _gnuplot: - -gnuplot script --------------- - -This file is generated by ``corplot``, -and read from gnuplot launched automatically. -We also can launch gnuplot independently and ``load`` this script. -The file name is ``correlation.gp``. - -.. code-block:: gnuplot - - #set terminal pdf color enhanced \ (1) - #dashed dl 1.0 size 20.0cm, 20.0cm (1) - #set output 'correlation.pdf' (1) - #set view 60.0, 30.0 (1) - - set view equal xy - set ticslevel 0 - set hidden3d - set xlabel 'kx' - set ylabel 'ky' - set zrange [ 0.25000E-10: 0.18435E+00] - - set pm3d - set pm3d interpolate 5, 5 - set view 0.0, 0.0 - - ##### Set Brillouin-Zone Boundary ##### - - set arrow from -0.31416E+01, -0.31416E+01, ... - set arrow from -0.31416E+01, 0.31416E+01, ... - : - ##### End Set Brillouin-Zone Boundary ##### - - splot \ - 'correlation.dat' u 1:2:3 w l tit '1' (2) - pause -1 - -#. When we want to write the figure to a file, - this line is uncommented. - For pasting this figure on the paper etc., - we write the setting of font, line-color, and so on. - For more details, please see the manual of gnuplot. -#. Plotting the file in :ref:`correlation`. - -.. _correlation: - -Correlation function at wide range of *k* ------------------------------------------ - -This file is generated by ``corplot``, and -read from gnuplot through :ref:`gnuplot`. -The file name is ``correlation.dat``. - -:: - - -0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 - -0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - -0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 - -0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.00000E+00 -0.62832E+01 0.18435E+00 0.00000E+00 - 0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 - 0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 - - -0.62832E+01 -0.47124E+01 0.36159E-01 0.00000E+00 - -0.47124E+01 -0.47124E+01 0.20921E-01 0.00000E+00 - -0.31416E+01 -0.47124E+01 0.11372E-01 0.00000E+00 - : - -The 1st and the 2nd column contains the :math:`k` vector (Cartesian). -3rd and the 4th column contains the correlation function and its standard error, respectively. diff --git a/doc/fourier/en/fourier_overview_en.rst b/doc/fourier/en/fourier_overview_en.rst deleted file mode 100644 index 63c2bc91..00000000 --- a/doc/fourier/en/fourier_overview_en.rst +++ /dev/null @@ -1,63 +0,0 @@ -Overview -======== - -This document is the manual for the utility -to perform the Fourier transformation of the correlation function -in the site representation generated by mVMC or :math:`{\mathcal H}\Phi`. - -Prerequisite ------------- - -The prerequisite of this utility is the same as that of mVMC or :math:`{\mathcal H}\Phi`. - -.. _supported: - -Supported quantities --------------------- - -This utility supports the Fourier transformation of the following quantities: - -One-body correlations - -.. math:: - :nowrap: - - \begin{align} - \langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle - \\ - \langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle - \end{align} - -Density-density correlation - -.. math:: - - \begin{align} - \langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle - \equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat \rho}_{i} {\hat \rho}_{j}\rangle - \end{align} - -Spin-Spin correlations - -.. math:: - :nowrap: - - \begin{align} - \langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat S}_{i}^{z} {\hat S}_{j}^{z} \rangle - \\ - \langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat S}_{i}^{+} {\hat S}_{j}^{-} \rangle - \\ - \langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat {\bf S}}_{i} \cdot {\hat {\bf S}}_{j} \rangle - \end{align} - diff --git a/doc/fourier/en/fourier_tutorial_en.rst b/doc/fourier/en/fourier_tutorial_en.rst deleted file mode 100644 index c061fd42..00000000 --- a/doc/fourier/en/fourier_tutorial_en.rst +++ /dev/null @@ -1,116 +0,0 @@ -.. _tutorial: - -Tutorial -======== - -This tutorial is done by using the input file -in ``sample/Standard/Spin/HeisenbergSquare/``. - -Run HPhi/vmc.out ----------------- - -- For :math:`{\mathcal H}\Phi` - - Calculate the ground state and the correlation function at that state. - - .. code-block:: bash - - $ ../../../../src/HPhi -s StdFace.def - -- For mVMC - - Optimize the trial wavefunction. - - .. code-block:: bash - - $ ../../../../src/vmc.out -s StdFace.def - - Add the following line in ``StdFace.def`` to compute the correlation function. - - :: - - NVMCCalMode = 1 - - Compute the correlation function. - - .. code-block:: bash - - $ ../../../../src/vmc.out -s StdFace.def output/zqp_opt.dat - -Then the one- and two-body correlation function are written to files -in the ``output/`` directory. - -Related files - -- StdFace.def (See the manuals for mVMC/:math:`{\mathcal H}\Phi`) -- zqp_opt.dat (See the manual for mVMC) -- greenone.def (:ref:`greenindex`) -- greentwo.def (:ref:`greenindex`) - -Fourier transformation of correlation functions ------------------------------------------------ - -Perform the Fourier transformation of the correlation function -by using the utility ``fourier``. - -.. code-block:: bash - - $ ../../../../tool/fourier namelist.def geometry.dat - -Then the Fourier-transformed correlation functions are -written to a file in ``output/``. - -Related files - -- output/zvo_cisajs_001.dat (:ref:`zvocisajs`) -- output/zvo_cisajs.dat (:ref:`zvocisajs`) -- output/zvo_cisajscktalt_001.dat (:ref:`zvocisajs`) -- output/zvo_cisajscktalt.dat (:ref:`zvocisajs`) -- geometry.dat (:ref:`geometry`) -- output/zvo_corr.dat (:ref:`zvocorr`) - -Display correlation functions ------------------------------ - -Plot the correlation function in the :math:`k` space -by using the utility ``corplot``. - -.. code-block:: bash - - $ ../../../../tool/corplot output/zvo_corr.dat - -Then the following message appears in the terminal. - -:: - - ##### Plot Start ##### - - Please specify target number from below (0 or Ctrl-C to exit): - - Real Part Without ErrorBar - [ 1] Up-Up [ 2] Down-Down [ 3] Density-Density [ 4] SzSz [ 5] S+S- [ 6] S-S+ - Imaginary Part Without ErrorBar - [11] Up-Up [12] Down-Down [13] Density-Density [14] SzSz [15] S+S- [16] S-S+ - Real Part With ErrorBar - [21] Up-Up [22] Down-Down [23] Density-Density [24] SzSz [25] S+S- [26] S-S+ - Imaginary Part With ErrorBar - [31] Up-Up [32] Down-Down [33] Density-Density [34] SzSz [35] S+S- [36] S-S+ - - Target : - -Type a number corresponding to the quantity to be plotted (for example ``4``) -and press ``Enter``, -then gnuplot is launched and the 3D figure is displayed (Fig. :num:`corplotpng`). - -.. _corplotpng: - -.. figure:: ../figs/corplot.png - - The 3D picture when ``Target : 4``. - The solid black lines indicate the Brillouin zone. - -Related files - -- kpoint.dat (:ref:`kpoint`) -- correlation.gp (:ref:`gnuplot`) -- correlation.dat (:ref:`correlation`) diff --git a/doc/fourier/en/fourier_util_en.rst b/doc/fourier/en/fourier_util_en.rst deleted file mode 100644 index 858e5418..00000000 --- a/doc/fourier/en/fourier_util_en.rst +++ /dev/null @@ -1,94 +0,0 @@ -Behavior of each utility -======================== - -Utility ``fourier`` -------------------- - -This utility is used as follows: - -.. code-block:: bash - - $ ${PATH}/fourier ${NAMELIST} ${GEOMETRY} - -where ``${PATH}`` is the path to the directory where -the executable ``fourier`` exists, -${NAMELIST} is the NameList input-file name of :math:`{\mathcal H}\Phi`/mVMC, and -${GEOMETRY} is the path to the :ref:`geometry` file. - -The behavior of this utility is slightly different between the correlation functions from -each mode of :math:`{\mathcal H}\Phi` (Lanczos, TPQ, Full diagonalization, LOBCG) -and mVMC. -In the following cases, we assume that -``CDataFileHead`` in the ModPara input file is ``"zvo"`` (default). - -HPhi-Lanczos -~~~~~~~~~~~~ - -In this case, ``HPhi`` writes correlation functions to the files -``zvo_cisajs.dat`` (one body) and ``zvo_cisajscktalt.dat`` (two body) -in ``output/`` directory. -``fourier`` utility reads this files, performs the Fourier transformation, and -generate single file ``zvo_corr.dat`` in ``output/`` directory. - -HPhi-TPQ -~~~~~~~~ - -``HPhi`` writes correlation functions to files -``zvo_cisajs_run*step*.dat`` (one body), ``zvo_cisajscktalt_run*step*.dat`` (two body) -at each trial and TPQ step to the ``output/`` directory. -``fourier`` utility reads the one- and the two-body correlation function at each trial/TPQ-step, -and performs Fourier transformation, and -write to a file ``zvo_corr_run*step*.dat`` in ``output/`` directory. - -HPhi-Full diagonalization and LOBCG -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -``HPhi`` writes correlation functions to files -``zvo_cisajs_eigen*.dat`` (one body) and ``zvo_cisajscktalt_eigen*.dat`` (two body) -for each wavefunction to the ``output/`` directory. -``fourier`` utility reads the one- and the two-body correlation function at each state -and performs Fourier transformation, and -write to a file ``zvo_corr_eigen*.dat`` in ``output/``. - -mVMC -~~~~ - -``vmc.out`` performs calculations according to the input parameters ``NDataIdxStart`` and ``NDataQtySmp`` -in ``ModPara`` file, and it generates -``zvo_cisajs_???.dat`` (one body) and ``zvo_cisajscktalt_???.dat`` (two body) -in ``output/`` directory. -``fourier`` utility reads all of these files, performs Fourier transformation, -computes the average - -.. math:: - - \begin{align} - \langle A \rangle = \frac{1}{N_{\rm Try}} \sum_{i=1}^{N_{\rm Try}} A_i - \end{align} - -and the standard error - -.. math:: - - \begin{align} - \delta A = \frac{1}{N_{\rm Try} - 1} - \sqrt{\frac{1}{N_{\rm Try}} \sum_{i=1}^{N_{\rm Try}} (A_i - \langle A \rangle)^2} - \end{align} - -of the real- and imaginary-part of each correlation function, and -writes them to a file ``zvo_corr_eigen*.dat`` in ``output/`` directory. - -Utility ``corplot`` -------------------- - -This utility is used as follows: - -.. code-block:: bash - - $ ${PATH}/corplot ${CORR1} ${CORR2} ${CORR3} ... - -where ``${PATH}`` is the path to the directory which contains the executable ``corplot``, -${CORR1}, ${CORR2}, ${CORR3}, ... are :ref:`zvocorr` files -generated by the utility ``fourier``. -Therefore, this 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The text files are in $(BUILDDIR)/text." - -man: - $(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man - @echo - @echo "Build finished. The manual pages are in $(BUILDDIR)/man." - -texinfo: - $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo - @echo - @echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo." - @echo "Run \`make' in that directory to run these through makeinfo" \ - "(use \`make info' here to do that automatically)." - -info: - $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo - @echo "Running Texinfo files through makeinfo..." - make -C $(BUILDDIR)/texinfo info - @echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo." - -gettext: - $(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale - @echo - @echo "Build finished. The message catalogs are in $(BUILDDIR)/locale." - -changes: - $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes - @echo - @echo "The overview file is in $(BUILDDIR)/changes." - -linkcheck: - $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck - @echo - @echo "Link check complete; look for any errors in the above output " \ - "or in $(BUILDDIR)/linkcheck/output.txt." - -doctest: - $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest - @echo "Testing of doctests in the sources finished, look at the " \ - "results in $(BUILDDIR)/doctest/output.txt." - -xml: - $(SPHINXBUILD) -b xml $(ALLSPHINXOPTS) $(BUILDDIR)/xml - @echo - @echo "Build finished. The XML files are in $(BUILDDIR)/xml." - -pseudoxml: - $(SPHINXBUILD) -b pseudoxml $(ALLSPHINXOPTS) $(BUILDDIR)/pseudoxml - @echo - @echo "Build finished. The pseudo-XML files are in $(BUILDDIR)/pseudoxml." diff --git a/doc/fourier/ja/conf.py b/doc/fourier/ja/conf.py deleted file mode 100644 index aa6da3d6..00000000 --- a/doc/fourier/ja/conf.py +++ /dev/null @@ -1,262 +0,0 @@ -# -*- coding: utf-8 -*- -# -# Fourier documentation build configuration file, created by -# sphinx-quickstart on Sat Jan 7 22:10:04 2017. -# -# This file is execfile()d with the current directory set to its -# containing dir. -# -# Note that not all possible configuration values are present in this -# autogenerated file. -# -# All configuration values have a default; values that are commented out -# serve to show the default. - -import sys -import os - -# If extensions (or modules to document with autodoc) are in another directory, -# add these directories to sys.path here. If the directory is relative to the -# documentation root, use os.path.abspath to make it absolute, like shown here. -#sys.path.insert(0, os.path.abspath('.')) - -# -- General configuration ------------------------------------------------ - -# If your documentation needs a minimal Sphinx version, state it here. -#needs_sphinx = '1.0' - -# Add any Sphinx extension module names here, as strings. They can be -# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom -# ones. -extensions = [ - 'sphinx.ext.mathjax', - 'sphinx_numfig' -] - -# Add any paths that contain templates here, relative to this directory. -templates_path = ['_templates'] - -# The suffix of source filenames. -source_suffix = '.rst' - -# The encoding of source files. -#source_encoding = 'utf-8-sig' - -# The master toctree document. -master_doc = 'index' - -# General information about the project. -project = u'fourier' -copyright = u'2017, kawamura' - -# The version info for the project you're documenting, acts as replacement for -# |version| and |release|, also used in various other places throughout the -# built documents. -# -# The short X.Y version. -version = '0.1' -# The full version, including alpha/beta/rc tags. -release = '0.1.1' - -# The language for content autogenerated by Sphinx. Refer to documentation -# for a list of supported languages. -language = 'ja' - -# There are two options for replacing |today|: either, you set today to some -# non-false value, then it is used: -#today = '' -# Else, today_fmt is used as the format for a strftime call. -#today_fmt = '%B %d, %Y' - -# List of patterns, relative to source directory, that match files and -# directories to ignore when looking for source files. -exclude_patterns = ['_build'] - -# The reST default role (used for this markup: `text`) to use for all -# documents. -#default_role = None - -# If true, '()' will be appended to :func: etc. cross-reference text. -#add_function_parentheses = True - -# If true, the current module name will be prepended to all description -# unit titles (such as .. function::). -#add_module_names = True - -# If true, sectionauthor and moduleauthor directives will be shown in the -# output. They are ignored by default. -#show_authors = False - -# The name of the Pygments (syntax highlighting) style to use. -pygments_style = 'sphinx' - -# A list of ignored prefixes for module index sorting. -#modindex_common_prefix = [] - -# If true, keep warnings as "system message" paragraphs in the built documents. -#keep_warnings = False - - -# -- Options for HTML output ---------------------------------------------- - -# The theme to use for HTML and HTML Help pages. See the documentation for -# a list of builtin themes. -html_theme = 'default' - -# Theme options are theme-specific and customize the look and feel of a theme -# further. For a list of options available for each theme, see the -# documentation. -#html_theme_options = {} - -# Add any paths that contain custom themes here, relative to this directory. -#html_theme_path = [] - -# The name for this set of Sphinx documents. If None, it defaults to -# " v documentation". -#html_title = None - -# A shorter title for the navigation bar. Default is the same as html_title. -#html_short_title = None - -# The name of an image file (relative to this directory) to place at the top -# of the sidebar. -#html_logo = None - -# The name of an image file (within the static path) to use as favicon of the -# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 -# pixels large. -#html_favicon = None - -# Add any paths that contain custom static files (such as style sheets) here, -# relative to this directory. They are copied after the builtin static files, -# so a file named "default.css" will overwrite the builtin "default.css". -html_static_path = ['_static'] - -# Add any extra paths that contain custom files (such as robots.txt or -# .htaccess) here, relative to this directory. These files are copied -# directly to the root of the documentation. -#html_extra_path = [] - -# If not '', a 'Last updated on:' timestamp is inserted at every page bottom, -# using the given strftime format. -#html_last_updated_fmt = '%b %d, %Y' - -# If true, SmartyPants will be used to convert quotes and dashes to -# typographically correct entities. -#html_use_smartypants = True - -# Custom sidebar templates, maps document names to template names. -#html_sidebars = {} - -# Additional templates that should be rendered to pages, maps page names to -# template names. -#html_additional_pages = {} - -# If false, no module index is generated. -#html_domain_indices = True - -# If false, no index is generated. -#html_use_index = True - -# If true, the index is split into individual pages for each letter. -#html_split_index = False - -# If true, links to the reST sources are added to the pages. -#html_show_sourcelink = True - -# If true, "Created using Sphinx" is shown in the HTML footer. Default is True. -#html_show_sphinx = True - -# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. -#html_show_copyright = True - -# If true, an OpenSearch description file will be output, and all pages will -# contain a tag referring to it. The value of this option must be the -# base URL from which the finished HTML is served. -#html_use_opensearch = '' - -# This is the file name suffix for HTML files (e.g. ".xhtml"). -#html_file_suffix = None - -# Output file base name for HTML help builder. -htmlhelp_basename = 'testdoc' - - -# -- Options for LaTeX output --------------------------------------------- - -latex_elements = { -# The paper size ('letterpaper' or 'a4paper'). -#'papersize': 'letterpaper', - -# The font size ('10pt', '11pt' or '12pt'). -#'pointsize': '10pt', - -# Additional stuff for the LaTeX preamble. -'preamble': '\usepackage{pxjahyper}', - 'classoptions': ',dvipdfmx,openany' -} - -# Grouping the document tree into LaTeX files. List of tuples -# (source start file, target name, title, -# author, documentclass [howto, manual, or own class]). -latex_documents = [ - ('index', 'fourier.tex', u'Fourier Documentation', - u'kawamura', 'manual'), -] - -# The name of an image file (relative to this directory) to place at the top of -# the title page. -#latex_logo = None - -# For "manual" documents, if this is true, then toplevel headings are parts, -# not chapters. -#latex_use_parts = False - -# If true, show page references after internal links. -#latex_show_pagerefs = False - -# If true, show URL addresses after external links. -#latex_show_urls = False - -# Documents to append as an appendix to all manuals. -#latex_appendices = [] - -# If false, no module index is generated. -#latex_domain_indices = True - - -# -- Options for manual page output --------------------------------------- - -# One entry per manual page. List of tuples -# (source start file, name, description, authors, manual section). -man_pages = [ - ('index', 'fourier', u'fourier Documentation', - [u'kawamura'], 1) -] - -# If true, show URL addresses after external links. -#man_show_urls = False - - -# -- Options for Texinfo output ------------------------------------------- - -# Grouping the document tree into Texinfo files. List of tuples -# (source start file, target name, title, author, -# dir menu entry, description, category) -texinfo_documents = [ - ('index', 'fourier', u'Fourier Documentation', - u'kawamura', 'fourier', 'One line description of project.', - 'Miscellaneous'), -] - -# Documents to append as an appendix to all manuals. -#texinfo_appendices = [] - -# If false, no module index is generated. -#texinfo_domain_indices = True - -# How to display URL addresses: 'footnote', 'no', or 'inline'. -#texinfo_show_urls = 'footnote' - -# If true, do not generate a @detailmenu in the "Top" node's menu. -#texinfo_no_detailmenu = False diff --git a/doc/fourier/ja/fourier_tutorial_ja.rst b/doc/fourier/ja/fourier_tutorial_ja.rst deleted file mode 100644 index a9bee6f4..00000000 --- a/doc/fourier/ja/fourier_tutorial_ja.rst +++ /dev/null @@ -1,115 +0,0 @@ -.. _tutorial: - -チュートリアル -============== - -このチュートリアルは ``sample/Standard/Spin/HeisenbergSquare/`` -にあるインプットファイルを用いて行う. - -HPhi/vmc.out の実行 -------------------- - -- :math:`{\mathcal H}\Phi` の場合 - - 基底状態および相関関数の計算を行う. - - .. code-block:: bash - - $ ../../../../src/HPhi -s StdFace.def - -- mVMC の場合 - - 変分波動関数の最適化を行う. - - .. code-block:: bash - - $ ../../../../src/vmc.out -s StdFace.def - - 相関関数を計算するために, ``StdFace.def`` に以下の行を付け加える. - - :: - - NVMCCalMode = 1 - - 相関関数を計算する. - - .. code-block:: bash - - $ ../../../../src/vmc.out -s StdFace.def output/zqp_opt.dat - -これにより, カレントディレクトリの ``output/`` 以下に -1体および2体の相関関数が出力される. - -関連するファイル - -- StdFace.def (mVMC/:math:`{\mathcal H}\Phi` のマニュアル参照) -- zqp_opt.dat (mVMCのマニュアル参照) -- greenone.def (:ref:`greenindex`) -- greentwo.def (:ref:`greenindex`) - -相関関数のフーリエ変換 ----------------------- - -ユーティリティプログラム ``fourier`` を使って, -相関関数をフーリエ変関する. - -.. code-block:: bash - - $ ../../../../tool/fourier namelist.def geometry.dat - -これにより, カレントディレクトリの ``output/`` 以下に -フーリエ変換された相関関数が出力される. - -関連するファイル - -- output/zvo_cisajs_001.dat (:ref:`zvocisajs`) -- output/zvo_cisajs.dat (:ref:`zvocisajs`) -- output/zvo_cisajscktalt_001.dat (:ref:`zvocisajs`) -- output/zvo_cisajscktalt.dat (:ref:`zvocisajs`) -- geometry.dat (:ref:`geometry`) -- output/zvo_corr.dat (:ref:`zvocorr`) - -相関関数のプロット ------------------- - -ユーティリティプログラム ``corplot`` を使って, -相関関数を :math:`k` 空間でプロットする. - -.. code-block:: bash - - $ ../../../../tool/corplot output/zvo_corr.dat - -この時, ターミナルには次のように標準入力を促すメッセージが現れる. - -:: - - ##### Plot Start ##### - - Please specify target number from below (0 or Ctrl-C to exit): - - Real Part Without ErrorBar - [ 1] Up-Up [ 2] Down-Down [ 3] Density-Density [ 4] SzSz [ 5] S+S- [ 6] S-S+ - Imaginary Part Without ErrorBar - [11] Up-Up [12] Down-Down [13] Density-Density [14] SzSz [15] S+S- [16] S-S+ - Real Part With ErrorBar - [21] Up-Up [22] Down-Down [23] Density-Density [24] SzSz [25] S+S- [26] S-S+ - Imaginary Part With ErrorBar - [31] Up-Up [32] Down-Down [33] Density-Density [34] SzSz [35] S+S- [36] S-S+ - - Target : - -プロットしたい量に対応する数字(例えば4)を入力し, -``Enter`` キーを押すと gnuplot が起動して3Dグラフが表示される(図 :num:`corplotpng` ). - -.. _corplotpng: - -.. figure:: ../figs/corplot.png - - Target : 4 としてプロットした図. - 黒線は第一ブリルアンゾーンを表す. - -関連するファイル - -- kpoint.dat (:ref:`kpoint`) -- correlation.gp (:ref:`gnuplot`) -- correlation.dat (:ref:`correlation`) diff --git a/doc/fourier/ja/index.rst b/doc/fourier/ja/index.rst deleted file mode 100644 index e3a51d3c..00000000 --- a/doc/fourier/ja/index.rst +++ /dev/null @@ -1,24 +0,0 @@ -.. test documentation master file, created by - sphinx-quickstart on Sat Jan 7 22:10:04 2017. - You can adapt this file completely to your liking, but it should at least - contain the root `toctree` directive. - -Welcome to HPhi/mVMC Fourie-Transformation utility's documentation! -=================================================================== - -.. toctree:: - :maxdepth: 3 - - fourier_overview_ja.rst - fourier_tutorial_ja.rst - fourier_format_ja.rst - fourier_util_ja.rst - fourier_contact_ja.rst - -.. Indices and tables -.. ================== - -.. * :ref:`genindex` -.. * :ref:`modindex` -.. * :ref:`search` - diff --git a/doc/fourier/ja/fourier_contact_ja.rst b/doc/jp/fourier/contact.rst similarity index 100% rename from doc/fourier/ja/fourier_contact_ja.rst rename to doc/jp/fourier/contact.rst diff --git a/doc/fourier/ja/fourier_format_ja.rst b/doc/jp/fourier/format.rst similarity index 100% rename from doc/fourier/ja/fourier_format_ja.rst rename to doc/jp/fourier/format.rst diff --git a/doc/jp/fourier/fourier_format_ja.rst b/doc/jp/fourier/fourier_format_ja.rst deleted file mode 100644 index f78ad8c3..00000000 --- a/doc/jp/fourier/fourier_format_ja.rst +++ /dev/null @@ -1,250 +0,0 @@ -.. _fileformat: - -ファイルフォーマット -==================== - -.. _geometry: - -ジオメトリー ------------- - -:ref:`tutorial` でのファイル名は ``geometry.dat`` . -mVMC/:math:`{\mathcal H}\Phi` のスタンンダードモードを用いた場合には -上記のファイル名で自動的に生成されるので, とくに気にする必要はない. - -:: - - 1.000000 0.000000 0.000000 (1) - 0.000000 1.000000 0.000000 (1) - 0.000000 0.000000 1.000000 (1) - 0.000000 0.000000 0.000000 (2) - 4 0 0 (3) - 0 4 0 (3) - 0 0 1 (3) - 0.000000 0.000000 0.000000 (4) - 1.000000 0.000000 0.000000 (4) - 2.000000 0.000000 0.000000 (4) - 3.000000 0.000000 0.000000 (4) - 0.000000 1.000000 0.000000 (4) - 1.000000 1.000000 0.000000 (4) - 2.000000 1.000000 0.000000 (4) - 3.000000 1.000000 0.000000 (4) - 0.000000 2.000000 0.000000 (4) - 1.000000 2.000000 0.000000 (4) - 2.000000 2.000000 0.000000 (4) - 3.000000 2.000000 0.000000 (4) - 0.000000 3.000000 0.000000 (4) - 1.000000 3.000000 0.000000 (4) - 2.000000 3.000000 0.000000 (4) - 3.000000 3.000000 0.000000 (4) - -#. 単位格子ベクトル. 任意の単位. -#. 1体項がシミュレーションセルの境界を跨いだときに付く位相(単位degree) -#. シミュレーションセルの形状を指定する三本の整数ベクトル. - スタンダードモードの入力パラメーター ``a0W``, ``a0L``, ``a0H``, ``a1W``... - に対応する. -#. 各サイトの座標. 単位格子ベクトルに対するフラクショナル座標として入力する. - - -サイト表示の1体および2体相関関数 --------------------------------- - -.. _greenindex: - -計算する相関関数のインデックスの指定 -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -mVMC/:math:`{\mathcal H}\Phi` で計算する相関関数を指定する. -スタンダードモードを使った場合には自動的に生成される. -総合的な説明はmVMC/:math:`{\mathcal H}\Phi` のマニュアルを参照. -:ref:`tutorial` でのファイル名は ``greenone.def`` (1体)および ``greentwo.def`` (2体)である. - -:ref:`supported` にある相関関数を計算するためには, -以下のようにインデックスを指定する必要がある. - -- :math:`\langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle` - - :math:`\langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle` - に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅するようにする. - -- :math:`\langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle` - - :math:`\langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle` - に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅するようにする. - -- :math:`\langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle` および - :math:`\langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle` - - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i \sigma} {\hat c}_{j \sigma'}^{\dagger} {\hat c}_{j \sigma'}\rangle` - に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅し, - :math:`\sigma` および :math:`\sigma'` が :math:`\uparrow`, :math:`\downarrow` を網羅するようにする. - -- :math:`\langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle` および - :math:`\langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle` - - :math:`{\mathcal H}\Phi` の場合は - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i -\sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{j \sigma}\rangle` - に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅し, - :math:`\sigma` が :math:`\uparrow`, :math:`\downarrow` を網羅するようにする. - mVMC の場合は - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{j \sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{i -\sigma}\rangle` - に対して, :math:`i` および :math:`j` がそれぞれ全てのサイトを網羅し, - :math:`\sigma` が :math:`\uparrow`, :math:`\downarrow` を網羅するようにする. - いずれの場合も演算子の順番に注意にすること. - -スタンダードモードのデフォルト(``outputmode="corr"``)では, -自動的に上記のインデックスが指定されるため, 特に気にする必要はない. - -.. _zvocisajs: - -サイト表示の1体および2体相関関数の計算結果 -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -:ref:`greenindex` で指定したインデックスを持つ相関関数が -mVMC/:math:`{\mathcal H}\Phi` によって計算され, -ファイルに出力される. -総合的な説明はmVMC/:math:`{\mathcal H}\Phi` のマニュアルを参照. -:ref:`tutorial` でのファイル名は -``output/zvo_cisajs_001.dat`` および ``output/zvo_cisajscktalt_001.dat`` (mVMC), -``output/zvo_cisajs.dat`` および ``output/zvo_cisajscktalt.dat`` (:math:`{\mathcal H}\Phi`). - -``fourier`` ユーティリティはこのファイルを読み込んで計算を行う. -この時, (スタンダードモードを使わず自分でインデックスを指定するなどにより) -:ref:`greenindex` で挙げたインデックスの相関関数のなかで欠けているものがある場合, -それを 0 として扱う. - -.. _zvocorr: - -プリミティブゾーン内の相関関数 ------------------------------- - -Fourier変換された相関関数(波数表示)が入っている. -ユーティリイティ ``fourier`` によって生成される. -:ref:`tutorial` でのファイル名は ``output/zvo_corr.dat`` である. - -:: - - #HPhi 16 (1) - # kx[1] ky[2] kz[3](Cart.) UpUp[4,5] (Re. Im.) DownDown[6,7] (2) - # Density[8,9] SzSz[10,11] S+S-[12,13] S-S+[14,15] (2) - #k-offset 0.0000000 0.0000000 0.0000000 (3) - 0.00000E+00 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) - 0.15708E+01 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) - : : - -#. ``HPhi`` の出力から作成された場合には ``"#HPhi"``, - ``vmc.out`` の出力から作成された場合には ``"#mVMC"`` と書かれる. - それに続く整数は, プリミティブ ブリルアンゾーン内の :math:`k` 点の数である. -#. 各カラムに出力されている量の説明. -#. シミュレーションセルの境界を跨ぐ一体項に位相が付く場合の, - 一体相関関数の :math:`k` 点の変位. - すなわち, この後の行の4〜7列目の一体相関関数は, - 1〜3列目の :math:`k` 点からこのオフセットの分だけずれた点のものである. -#. :math:`k` 点(デカルト座標)と相関関数. - それぞれの相関関数の実部と虚部が書かれている. - -.. _kpoint: - -corplot用 *k* 点ファイル ------------------------- - -``fourier`` ユーティリティで生成され, -``corplot`` ユーティリティでプロットを行う時に読み込まれる. -ファイル名は ``kpoint.dat`` である. - -:: - - 81 9 (1) - 0.62832E+01 0.00000E+00 0.00000E+00 (2) - 0.00000E+00 0.62832E+01 0.00000E+00 (2) - 0.00000E+00 0.00000E+00 0.62832E+01 (2) - -0.62832E+01 -0.62832E+01 0.00000E+00 1 (3) - -0.47124E+01 -0.62832E+01 0.00000E+00 2 (3) - -0.31416E+01 -0.62832E+01 0.00000E+00 3 - -0.15708E+01 -0.62832E+01 0.00000E+00 4 - 0.00000E+00 -0.62832E+01 0.00000E+00 1 - 0.15708E+01 -0.62832E+01 0.00000E+00 2 - 0.31416E+01 -0.62832E+01 0.00000E+00 3 - 0.47124E+01 -0.62832E+01 0.00000E+00 4 - -#. ``corplot`` でプロットされる :math:`k` 点の総数および - gnuplot のsplotで表示する時の :math:`k` 点の区切り. -#. 逆格子ベクトル(デカルト座標) -#. :math:`k` ベクトル(デカルト座標)と, - その :math:`k` 点と等価なプリミティブゾーン内の :math:`k` 点のインデックス. - このインデックスは :ref:`zvocorr` での :math:`k` 点の番号に対応している. - -.. _gnuplot: - -gnuplot スクリプト ------------------- - -``corplot`` にて作成され, -内部で起動した gnuplot によって読み込まれる. -``corplot`` とは別に 直接gnuplotを起動して, ``load`` でよみこむことも可能である. -ファイル名は ``correlation.gp`` である. - -.. code-block:: gnuplot - - #set terminal pdf color enhanced \ (1) - #dashed dl 1.0 size 20.0cm, 20.0cm (1) - #set output 'correlation.pdf' (1) - #set view 60.0, 30.0 (1) - - set view equal xy - set ticslevel 0 - set hidden3d - set xlabel 'kx' - set ylabel 'ky' - set zrange [ 0.25000E-10: 0.18435E+00] - - set pm3d - set pm3d interpolate 5, 5 - set view 0.0, 0.0 - - ##### Set Brillouin-Zone Boundary ##### - - set arrow from -0.31416E+01, -0.31416E+01, ... - set arrow from -0.31416E+01, 0.31416E+01, ... - : - ##### End Set Brillouin-Zone Boundary ##### - - splot \ - 'correlation.dat' u 1:2:3 w l tit '1' (2) - pause -1 - -#. 図をPDFファイルに出力したい時には, - この行の先頭のコメントアウトを外す. - 論文等に貼る図を作るときには, 適宜この後にフォントの設定等を書く. - 詳しくは gnuplot のマニュアル等を参照. -#. :ref:`correlation` のファイルをプロットしている. - -.. _correlation: - -広範囲の *k* 点での相関関数 ---------------------------- - -``corplot`` にて作成され, -内部で起動した gnuplot によって, -:ref:`gnuplot` を経由して読み込まれる. -ファイル名は ``correlation.dat`` - -:: - - -0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 - -0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - -0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 - -0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.00000E+00 -0.62832E+01 0.18435E+00 0.00000E+00 - 0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 - 0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 - - -0.62832E+01 -0.47124E+01 0.36159E-01 0.00000E+00 - -0.47124E+01 -0.47124E+01 0.20921E-01 0.00000E+00 - -0.31416E+01 -0.47124E+01 0.11372E-01 0.00000E+00 - : - -1, 2列目は :math:`k` ベクトル(デカルト座標)を表す. -3列目は相関関数, 4列目はその標準誤差を表す. diff --git a/doc/jp/fourier/fourier_overview_ja.rst b/doc/jp/fourier/fourier_overview_ja.rst deleted file mode 100644 index 6a32c9a8..00000000 --- a/doc/jp/fourier/fourier_overview_ja.rst +++ /dev/null @@ -1,63 +0,0 @@ -概要 -==== - -本資料は, mVMC および :math:`{\mathcal H}\Phi` で計算された -サイト表示の相関関数をFourier変換し, 出力するユーティリティに関するマニュアルである. - -要件 ----- - -本ユーティリティの使用要件はmVMC および :math:`{\mathcal H}\Phi` と同じである. - -.. _supported: - -対応する量 ----------- - -本ユーティリティは以下の相関関数のFourier変換に対応している. - -1体相関 - -.. math:: - :nowrap: - - \begin{align} - \langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle - \\ - \langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle - \end{align} - -密度-密度相関 - -.. math:: - - \begin{align} - \langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle - \equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle ({\hat \rho}_{i} - \langle {\hat \rho}_{i} \rangle) - ({\hat \rho}_{j} - \langle {\hat \rho}_{j} \rangle) \rangle - \end{align} - -スピン-スピン相関 - -.. math:: - :nowrap: - - \begin{align} - \langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat S}_{i}^{z} {\hat S}_{j}^{z} \rangle - \\ - \langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat S}_{i}^{+} {\hat S}_{j}^{-} \rangle - \\ - \langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat {\bf S}}_{i} \cdot {\hat {\bf S}}_{j} \rangle - \end{align} - diff --git a/doc/jp/fourier/fourier_util_ja.rst b/doc/jp/fourier/fourier_util_ja.rst deleted file mode 100644 index fe995e6f..00000000 --- a/doc/jp/fourier/fourier_util_ja.rst +++ /dev/null @@ -1,94 +0,0 @@ -各ユーティリティの動作について -============================== - -``fourier`` ユーティリティ --------------------------- - -このユーティリティーは, 次のようにして使う. - -.. code-block:: bash - - $ ${PATH}/fourier ${NAMELIST} ${GEOMETRY} - -ここで, ``${PATH}`` は ``fourier`` ユーティリティのバイナリのあるディレクトリのパス, -${NAMELIST}は :math:`{\mathcal H}\Phi`/mVMC の NameList インプットファイル名, -${GEOMETRY}は :ref:`geometry` ファイルへのパスである. - -:math:`{\mathcal H}\Phi` の各モード -(Lanczos, TPQ, 全対角化, LOBCG)および mVMC のどの計算で得られた -相関関数のFourier変換を行うかによって, 動作が若干異なる. -以下では ModPara インプットファイルの ``CDataFileHead`` が -``"zvo"`` (デフォルト値)であるとする. - -HPhi-Lanczos -~~~~~~~~~~~~ - -この場合に ``HPhi`` が ``output/`` ディレクトリに出力するサイト表示の相関関数は, -``zvo_cisajs.dat`` (1体), ``zvo_cisajscktalt.dat`` (2体)である. -``fourier`` ユーティリティーは, これらを読み込みFourier変換を行った後, -単一のファイル ``zvo_corr.dat`` を ``output/`` ディレクトリに出力する. - -HPhi-TPQ -~~~~~~~~ - -この場合に ``HPhi`` は, 各試行/TPQステップ毎に -``zvo_cisajs_run*step*.dat`` (1体), ``zvo_cisajscktalt_run*step*.dat`` (2体)というファイルを -``output/`` ディレクトリに出力する. -``fourier`` ユーティリティーは, 各試行/TPQステップ毎に -1体および2体の相関関数を読み込みFourier変換を行った後, -``zvo_corr_run*step*.dat`` という名前のファイルとして ``output/`` ディレクトリに出力する. - -HPhi-全対角化およびLOBCG -~~~~~~~~~~~~~~~~~~~~~~~~ - -この場合に ``HPhi`` は, 各波動関数ごとに -``zvo_cisajs_eigen*.dat`` (1体), ``zvo_cisajscktalt_eigen*.dat`` (2体)というファイルを -``output/`` ディレクトリに出力する. -``fourier`` ユーティリティーは, 各波動関数ごとに -1体および2体の相関関数を読み込みFourier変換を行った後, -``zvo_corr_eigen*.dat`` という名前のファイルとして ``output/`` ディレクトリに出力する. - -mVMC -~~~~ - -この場合に ``vmc.out`` は, ``ModPara`` インプットファイルで指定された -``NDataIdxStart`` および ``NDataQtySmp`` というパラメーターに応じて -試行を行いインデックスをつけられた -``zvo_cisajs_???.dat`` (1体), ``zvo_cisajscktalt_???.dat`` (2体)というファイルを -``output/`` ディレクトリに出力する. -``fourier`` ユーティリティーはそれらのファイルを読み込み, -各試行に対してFourier変換を行った後, -それらの実部, 虚部ごとに平均値 - -.. math:: - - \begin{align} - \langle A \rangle = \frac{1}{N_{\rm Try}} \sum_{i=1}^{N_{\rm Try}} A_i - \end{align} - -および標準誤差 - -.. math:: - - \begin{align} - \delta A = \frac{1}{N_{\rm Try} - 1} - \sqrt{\frac{1}{N_{\rm Try}} \sum_{i=1}^{N_{\rm Try}} (A_i - \langle A \rangle)^2} - \end{align} - -を計算し, 平均値と誤差を含んだ単一のファイル -``zvo_corr_eigen*.dat`` を ``output/`` ディレクトリに出力する. - -``corplot`` ユーティリティ --------------------------- - -このユーティリティーは, 次のようにして使う. - -.. code-block:: bash - - $ ${PATH}/corplot ${CORR1} ${CORR2} ${CORR3} ... - -ここで, ``${PATH}`` は ``corplot`` ユーティリティのバイナリのあるディレクトリのパス, -${CORR1}, ${CORR2}, ${CORR3}, ...は ``fourier`` ルーチンによって生成された -:ref:`zvocorr` ファイルへのパスである. -すなわち, このユーティリティーでは, (TPQ計算による温度依存性を調べる等の用途で) -複数の相関関数ファイルを読み込み, それらを同時にプロットすることができる. diff --git a/doc/jp/fourier/index.rst b/doc/jp/fourier/index.rst index 32e7e7ca..9fe0eade 100644 --- a/doc/jp/fourier/index.rst +++ b/doc/jp/fourier/index.rst @@ -11,11 +11,11 @@ .. toctree:: :maxdepth: 3 - fourier_overview_ja.rst - fourier_tutorial_ja.rst - fourier_format_ja.rst - fourier_util_ja.rst - fourier_contact_ja.rst + overview + tutorial + format + util + contact .. Indices and tables .. ================== diff --git a/doc/fourier/ja/fourier_overview_ja.rst b/doc/jp/fourier/overview.rst similarity index 100% rename from doc/fourier/ja/fourier_overview_ja.rst rename to doc/jp/fourier/overview.rst diff --git a/doc/jp/fourier/fourier_tutorial_ja.rst b/doc/jp/fourier/tutorial.rst similarity index 100% rename from doc/jp/fourier/fourier_tutorial_ja.rst rename to doc/jp/fourier/tutorial.rst diff --git a/doc/fourier/ja/fourier_util_ja.rst b/doc/jp/fourier/util.rst similarity index 100% rename from doc/fourier/ja/fourier_util_ja.rst rename to doc/jp/fourier/util.rst diff --git a/doc/jp/index.rst b/doc/jp/index.rst index 27031302..24993f8e 100644 --- a/doc/jp/index.rst +++ b/doc/jp/index.rst @@ -18,6 +18,7 @@ algorithm.rst appendix.rst fourier/index + wannier/index acknowledge.rst .. Indices and tables diff --git a/doc/jp/fourier/fourier_contact_ja.rst b/doc/jp/wannier/contact.rst similarity index 100% rename from doc/jp/fourier/fourier_contact_ja.rst rename to doc/jp/wannier/contact.rst diff --git a/doc/jp/wannier/format.rst b/doc/jp/wannier/format.rst new file mode 100644 index 00000000..7b51bb6c --- /dev/null +++ b/doc/jp/wannier/format.rst @@ -0,0 +1,11 @@ +ファイルフォーマット +==================== + +ジオメトリー +------------ + +ホッピング, Coulomb積分, 交換積分 +--------------------------------- + +Wannier90の形式に従う. +付属のユーティリティーrespack2wan90.pyを使う. diff --git a/doc/fourier/en/index.rst b/doc/jp/wannier/index.rst similarity index 57% rename from doc/fourier/en/index.rst rename to doc/jp/wannier/index.rst index c3fe30a5..b4f3f3fe 100644 --- a/doc/fourier/en/index.rst +++ b/doc/jp/wannier/index.rst @@ -3,17 +3,18 @@ You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive. -Welcome to HPhi/mVMC Fourie-Transformation utility's documentation! -=================================================================== - +.. _wannier: + +Wannier関数を用いたダウンフォールディング +========================================= .. toctree:: :maxdepth: 3 - fourier_overview_en.rst - fourier_tutorial_en.rst - fourier_format_en.rst - fourier_util_en.rst - fourier_contact_en.rst + overview + tutorial + parameter + format + contact .. Indices and tables .. ================== diff --git a/doc/jp/wannier/overview.rst b/doc/jp/wannier/overview.rst new file mode 100644 index 00000000..5207c3e0 --- /dev/null +++ b/doc/jp/wannier/overview.rst @@ -0,0 +1,20 @@ +概要 +==== + +本資料では, +`RESPACK `_ と +mVMC および :math:`{\mathcal H}\Phi` を用いて, +ダウンフォールディングをした格子モデルを計算する機能について説明する. + +要件 +---- + +`QuantumESPRESSO `_ +もしくは +`xTAPP `_ +を用いてKohn-Sham軌道を用いたのちに, +RESPACKでWannier関数, 誘電関数, 有効相互作用を計算し, +それらを用いて構成した格子モデルを +mVMC もしくは :math:`{\mathcal H}\Phi` +で計算する. +したがってそれらのプログラムが使用可能である必要がある. diff --git a/doc/jp/wannier/parameter.rst b/doc/jp/wannier/parameter.rst new file mode 100644 index 00000000..4c2182de --- /dev/null +++ b/doc/jp/wannier/parameter.rst @@ -0,0 +1,11 @@ +スタンダードモードの入力パラメーター +==================================== + +以下に入力ファイルの例を示す. + +:download:`respack.in <../../../samples/Wannier/Sr2VO4/stan.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/stan.in + +Wannier関数を用いたダウンフォールディングに特有のパラメーターは次の通りである. + diff --git a/doc/jp/wannier/tutorial.rst b/doc/jp/wannier/tutorial.rst new file mode 100644 index 00000000..d4fb49c6 --- /dev/null +++ b/doc/jp/wannier/tutorial.rst @@ -0,0 +1,48 @@ +.. _tutorialwannier: + +チュートリアル +============== + +このチュートリアルでは Sr\ :sub:`2`\ VO\ :sub:`4` +を2次元3軌道Hubbardモデルにダウンフォールドして, +それをHPhi/mVMCで計算する. +DFT計算はQuantumESPRESSOで行う. + +電荷密度のSCF計算 +----------------- + +:download:`scf.in <../../../samples/Wannier/Sr2VO4/scf.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/scf.in + +(Optional) バンド計算と描画 +--------------------------- + +:download:`band.in <../../../samples/Wannier/Sr2VO4/band.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/band.in + +:download:`bands.in <../../../samples/Wannier/Sr2VO4/bands.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/bands.in + +Kohn-Sham軌道の計算 +------------------- + +:download:`nscf.in <../../../samples/Wannier/Sr2VO4/nscf.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/nscf.in + +Wannier関数, 誘電関数, 有効相互作用の計算 +----------------------------------------- + +:download:`respack.in <../../../samples/Wannier/Sr2VO4/respack.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/respack.in + +HPhi/mVMCによるモデル計算 +------------------------- + +:download:`respack.in <../../../samples/Wannier/Sr2VO4/stan.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/stan.in diff --git a/doc/userguide.html b/doc/userguide.html index ca15d9af..78191959 100644 --- a/doc/userguide.html +++ b/doc/userguide.html @@ -10,17 +10,15 @@

mVMC manuals

 diff --git a/sample/Standard/Hubbard/square/UHF/coulombintra.def b/sample/Standard/Hubbard/square/UHF/coulombintra.def deleted file mode 100644 index 47d82e7a..00000000 --- a/sample/Standard/Hubbard/square/UHF/coulombintra.def +++ /dev/null @@ -1,13 +0,0 @@ -============================================= -NCoulombIntra 8 -============================================= -================== CoulombIntra ================ -============================================= - 0 4.000000000000000 - 1 4.000000000000000 - 2 4.000000000000000 - 3 4.000000000000000 - 4 4.000000000000000 - 5 4.000000000000000 - 6 4.000000000000000 - 7 4.000000000000000 diff --git a/sample/Standard/Hubbard/square/UHF/locspn.def b/sample/Standard/Hubbard/square/UHF/locspn.def deleted file mode 100644 index a33a7560..00000000 --- a/sample/Standard/Hubbard/square/UHF/locspn.def +++ /dev/null @@ -1,13 +0,0 @@ -================================ -NlocalSpin 0 -================================ -========i_0LocSpn_1IteElc ====== -================================ - 0 0 - 1 0 - 2 0 - 3 0 - 4 0 - 5 0 - 6 0 - 7 0 diff --git a/sample/Standard/Hubbard/square/UHF/modpara.def b/sample/Standard/Hubbard/square/UHF/modpara.def deleted file mode 100644 index da4f17a9..00000000 --- a/sample/Standard/Hubbard/square/UHF/modpara.def +++ /dev/null @@ -1,12 +0,0 @@ --------------------- -Model_Parameters 0 --------------------- -VMC_Cal_Parameters --------------------- -CDataFileHead zvo -CParaFileHead zqp --------------------- -Nsite 8 -Ncond 8 -2Sz 0 -RndSeed 123456789 diff --git a/sample/Standard/Hubbard/square/UHF/namelist.def b/sample/Standard/Hubbard/square/UHF/namelist.def deleted file mode 100644 index af48420c..00000000 --- a/sample/Standard/Hubbard/square/UHF/namelist.def +++ /dev/null @@ -1,6 +0,0 @@ - ModPara modpara.def - LocSpin locspn.def - Trans trans.def - CoulombIntra coulombintra.def - Orbital orbitalidx.def - Initial initial.def diff --git a/sample/Standard/Hubbard/square/UHF/orbitalidx.def b/sample/Standard/Hubbard/square/UHF/orbitalidx.def deleted file mode 100644 index 8a7c4190..00000000 --- a/sample/Standard/Hubbard/square/UHF/orbitalidx.def +++ /dev/null @@ -1,101 +0,0 @@ -============================================= -NOrbitalIdx 32 -ComplexType 0 -============================================= -============================================= - 0 0 0 - 0 1 1 - 0 2 2 - 0 3 3 - 0 4 4 - 0 5 5 - 0 6 6 - 0 7 7 - 1 0 8 - 1 1 9 - 1 2 10 - 1 3 11 - 1 4 12 - 1 5 13 - 1 6 14 - 1 7 15 - 2 0 2 - 2 1 3 - 2 2 0 - 2 3 1 - 2 4 6 - 2 5 7 - 2 6 4 - 2 7 5 - 3 0 10 - 3 1 11 - 3 2 8 - 3 3 9 - 3 4 14 - 3 5 15 - 3 6 12 - 3 7 13 - 4 0 16 - 4 1 17 - 4 2 18 - 4 3 19 - 4 4 20 - 4 5 21 - 4 6 22 - 4 7 23 - 5 0 24 - 5 1 25 - 5 2 26 - 5 3 27 - 5 4 28 - 5 5 29 - 5 6 30 - 5 7 31 - 6 0 18 - 6 1 19 - 6 2 16 - 6 3 17 - 6 4 22 - 6 5 23 - 6 6 20 - 6 7 21 - 7 0 26 - 7 1 27 - 7 2 24 - 7 3 25 - 7 4 30 - 7 5 31 - 7 6 28 - 7 7 29 - 0 1 - 1 1 - 2 1 - 3 1 - 4 1 - 5 1 - 6 1 - 7 1 - 8 1 - 9 1 - 10 1 - 11 1 - 12 1 - 13 1 - 14 1 - 15 1 - 16 1 - 17 1 - 18 1 - 19 1 - 20 1 - 21 1 - 22 1 - 23 1 - 24 1 - 25 1 - 26 1 - 27 1 - 28 1 - 29 1 - 30 1 - 31 1 diff --git a/sample/Standard/Hubbard/square/UHF/trans.def b/sample/Standard/Hubbard/square/UHF/trans.def deleted file mode 100644 index be5f79a9..00000000 --- a/sample/Standard/Hubbard/square/UHF/trans.def +++ /dev/null @@ -1,53 +0,0 @@ -======================== -NTransfer 48 -======================== -========i_j_s_tijs====== -======================== - 1 0 0 0 1.000000000000000 0.000000000000000 - 0 0 1 0 1.000000000000000 -0.000000000000000 - 1 1 0 1 1.000000000000000 0.000000000000000 - 0 1 1 1 1.000000000000000 -0.000000000000000 - 4 0 0 0 2.000000000000000 0.000000000000000 - 0 0 4 0 2.000000000000000 0.000000000000000 - 4 1 0 1 2.000000000000000 0.000000000000000 - 0 1 4 1 2.000000000000000 0.000000000000000 - 2 0 1 0 1.000000000000000 0.000000000000000 - 1 0 2 0 1.000000000000000 -0.000000000000000 - 2 1 1 1 1.000000000000000 0.000000000000000 - 1 1 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b/sample/Standard/Hubbard/triangular/UHF/locspn.def deleted file mode 100644 index a33a7560..00000000 --- a/sample/Standard/Hubbard/triangular/UHF/locspn.def +++ /dev/null @@ -1,13 +0,0 @@ -================================ -NlocalSpin 0 -================================ -========i_0LocSpn_1IteElc ====== -================================ - 0 0 - 1 0 - 2 0 - 3 0 - 4 0 - 5 0 - 6 0 - 7 0 diff --git a/sample/Standard/Hubbard/triangular/UHF/modpara.def b/sample/Standard/Hubbard/triangular/UHF/modpara.def deleted file mode 100644 index da4f17a9..00000000 --- a/sample/Standard/Hubbard/triangular/UHF/modpara.def +++ /dev/null @@ -1,12 +0,0 @@ --------------------- -Model_Parameters 0 --------------------- -VMC_Cal_Parameters --------------------- -CDataFileHead zvo -CParaFileHead zqp --------------------- -Nsite 8 -Ncond 8 -2Sz 0 -RndSeed 123456789 diff --git a/sample/Standard/Hubbard/triangular/UHF/namelist.def b/sample/Standard/Hubbard/triangular/UHF/namelist.def deleted file mode 100644 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-1.755154532506499271e-03 2.110521956775321506e+00 1.153746456712548163e+00 1.042000000000000037e+00 1.653200000000000003e+01 --1.059617033806546704e+00 1.880735548280553686e-03 2.234123737999189618e+00 9.897808930334904831e-01 1.054000000000000048e+00 1.710000000000000142e+01 --1.109020122839317946e+00 2.211105868474536051e-02 2.206230566972369633e+00 7.916541467856067493e-01 1.475999999999999979e+00 1.835200000000000031e+01 --1.067249881217631424e+00 -2.711039201018973152e-02 2.190100233840712729e+00 9.190714480712544043e-01 4.700000000000000289e-01 1.325999999999999979e+01 --1.160556787008479640e+00 1.762769987227810753e-02 2.279420573570232200e+00 6.911849345679371703e-01 9.160000000000000364e-01 1.712000000000000099e+01 --1.125719250174365804e+00 -1.004128112499796076e-02 2.206496923484447592e+00 7.407623267059330052e-01 7.680000000000000160e-01 1.563199999999999967e+01 --1.154079926569777648e+00 2.347840970120942256e-02 2.470624255522784196e+00 8.526600521015902379e-01 1.205999999999999961e+00 1.843599999999999994e+01 --1.184773392951333770e+00 1.657728256595211724e-02 2.343132906069467669e+00 6.682889576023233191e-01 1.165999999999999925e+00 1.869200000000000017e+01 --1.220550825022413743e+00 -3.298799123798475119e-02 2.419202802009312592e+00 6.203504096539194101e-01 5.560000000000000497e-01 1.678399999999999892e+01 --1.217342849985314057e+00 8.170353682128761452e-03 2.373105056164332982e+00 6.011516118269624176e-01 9.320000000000000506e-01 1.774399999999999977e+01 --1.304243615800864342e+00 7.149170114231536387e-03 2.604733799610227774e+00 5.311112925065260004e-01 1.264000000000000012e+00 1.961599999999999966e+01 --1.307734785778439601e+00 -3.378794218017576456e-02 2.700322771619787066e+00 5.758202703457779847e-01 1.798000000000000043e+00 2.105199999999999960e+01 --1.300494542477001136e+00 1.033363035835862739e-02 2.742461369556960182e+00 6.212171548124786336e-01 1.733999999999999986e+00 2.186800000000000210e+01 --1.311892284105546258e+00 1.530431710353256404e-02 2.584313996376211620e+00 5.009686331864156017e-01 1.183999999999999941e+00 1.664799999999999969e+01 --1.404909877259773898e+00 1.306615949655610563e-03 2.723155301704296427e+00 3.796672371884519670e-01 1.556000000000000050e+00 2.028800000000000026e+01 --1.381913383439247189e+00 -4.748747375240346819e-03 2.890555110276412432e+00 5.135759661750325389e-01 1.644000000000000128e+00 2.196000000000000085e+01 --1.377269856203677811e+00 -1.459229997333191635e-02 2.923398947693177874e+00 5.406491472973041779e-01 5.819999999999999618e-01 1.379600000000000115e+01 --1.430153759667111002e+00 1.082573293254586629e-02 2.888628656128232386e+00 4.120549495053713041e-01 1.836000000000000076e+00 2.228800000000000026e+01 --1.402079978453687703e+00 -3.441449125367958273e-02 2.887029676922209465e+00 4.659555441019509470e-01 2.140000000000000124e+00 2.203200000000000003e+01 --1.471991906253779181e+00 -5.756212511801263830e-03 2.930034925928727052e+00 3.522034184000020773e-01 1.334000000000000075e+00 2.042800000000000082e+01 --1.452305860487387745e+00 -1.469287249250816191e-02 2.938616166063889867e+00 3.928146717956315648e-01 6.460000000000000187e-01 1.814000000000000057e+01 --1.452005507149209285e+00 -3.874399347422800149e-02 3.614816977785802354e+00 7.108906769486161847e-01 1.308000000000000052e+00 1.921600000000000108e+01 --1.512326172243515510e+00 1.009782613044191320e-02 3.081521395609053915e+00 3.471506526266778803e-01 1.602000000000000091e+00 2.143599999999999994e+01 --1.523589232516278313e+00 -5.727010392940705408e-03 3.182537306681461065e+00 3.709427051395103869e-01 1.594000000000000083e+00 2.219600000000000151e+01 --1.497095855627967653e+00 2.539029586482862560e-02 3.188594188024481024e+00 4.214294254952814511e-01 1.491999999999999993e+00 2.055999999999999872e+01 --1.554965177523719211e+00 3.103947799592679958e-03 3.289601536418368610e+00 3.604944325362422486e-01 1.941999999999999948e+00 2.322800000000000153e+01 --1.595847336031926744e+00 -1.730566801357984533e-02 3.325569125912903878e+00 3.053593438839117824e-01 2.049999999999999822e+00 2.440399999999999991e+01 --1.625057888920612426e+00 -6.043381502486355056e-03 3.362260932639079769e+00 2.731387093185071446e-01 2.101999999999999869e+00 2.497200000000000131e+01 --1.582066971117733756e+00 1.126461422830597400e-02 3.642568352635147999e+00 4.550969503998554266e-01 2.362000000000000099e+00 2.868400000000000105e+01 --1.621012514396895865e+00 -4.433583748632874411e-02 3.380726259928480193e+00 2.836976806913112936e-01 1.973999999999999977e+00 2.336400000000000077e+01 --1.665763883756477659e+00 -1.200917569675121442e-02 3.477277542877021510e+00 2.529817770781420116e-01 1.961999999999999966e+00 2.336400000000000077e+01 --1.618193473555416873e+00 2.985564184702460544e-02 3.476408458069264906e+00 3.262531504553021766e-01 1.750000000000000000e+00 2.202799999999999869e+01 --1.680507719942296863e+00 5.919087440114252294e-03 3.535180547780707894e+00 2.517408103036256062e-01 1.969999999999999973e+00 2.334799999999999898e+01 --1.628995878318061141e+00 -4.606416233093399426e-02 3.398478919974990298e+00 2.776236132600620188e-01 1.247999999999999998e+00 1.908800000000000097e+01 --1.704397872131292013e+00 -7.661198486182052222e-04 3.650527657740089360e+00 2.566473312465510359e-01 2.148000000000000131e+00 2.434400000000000119e+01 --1.714118396489123564e+00 3.867747756327541420e-02 3.568966906044171772e+00 2.128234880406886798e-01 2.672000000000000153e+00 2.682400000000000162e+01 --1.687556222625798741e+00 6.132017378938521557e-02 3.588559694952823342e+00 2.551157642445360807e-01 1.884000000000000119e+00 2.281599999999999895e+01 --1.706759765427524611e+00 -3.472377061417489946e-02 3.656945741378539783e+00 2.538179435865995925e-01 1.733999999999999986e+00 2.167600000000000193e+01 --1.754400243747546551e+00 2.492768097274334141e-02 3.728265739839855986e+00 2.105604381658000013e-01 2.350000000000000089e+00 2.458800000000000097e+01 --1.779261486603684883e+00 -4.500861980939067919e-03 3.716584247809814112e+00 1.739675382361895450e-01 3.002000000000000224e+00 2.806000000000000227e+01 --1.793198678629864373e+00 1.753142060077540060e-02 3.842018034259338854e+00 1.944777053511375364e-01 2.806000000000000050e+00 2.807600000000000051e+01 --1.768336283875605375e+00 3.782470057617111359e-02 3.893467383112792835e+00 2.433997030521001803e-01 2.240000000000000213e+00 2.511200000000000188e+01 --1.814684498051243544e+00 -2.152117676940917823e-02 3.888924558392773623e+00 1.804402724992316132e-01 2.593999999999999861e+00 2.539600000000000080e+01 --1.792188745893892543e+00 1.564219389683667305e-02 3.838769260357824731e+00 1.948826837979658611e-01 2.104000000000000092e+00 2.309600000000000009e+01 --1.784823566589541555e+00 -2.756066544813058974e-02 3.840525212097519958e+00 2.047290506966626122e-01 1.921999999999999931e+00 2.233999999999999986e+01 --1.794972801038366761e+00 -1.403891487499879520e-02 3.821889772435763000e+00 1.859946067721428842e-01 2.347999999999999865e+00 2.532799999999999940e+01 --1.819354372989399060e+00 2.262784166126109373e-02 4.026422517006861490e+00 2.158590037909120241e-01 2.213999999999999968e+00 2.353999999999999915e+01 --1.831424131886612905e+00 -1.114888291894278530e-02 3.911848897841589068e+00 1.661540474734368722e-01 2.296000000000000263e+00 2.506400000000000006e+01 --1.848996323885038207e+00 1.292002873609778175e-02 4.014873057841224835e+00 1.741838651172904484e-01 2.808000000000000274e+00 2.811200000000000188e+01 --1.844642492675663492e+00 -4.276860155492249668e-03 3.899378493189240569e+00 1.459455193851904586e-01 2.604000000000000092e+00 2.456000000000000227e+01 --1.880479120260597492e+00 8.772884507230587284e-03 4.127926710851743231e+00 1.672572775002021672e-01 2.903999999999999915e+00 2.918400000000000105e+01 --1.891205137840967776e+00 5.034162594800207363e-02 4.180271646736675173e+00 1.662835844373760086e-01 2.782000000000000028e+00 2.822800000000000153e+01 --1.893376983753203291e+00 3.996819012462803772e-02 4.138958859808761659e+00 1.530187989486208877e-01 3.338000000000000078e+00 3.451599999999999824e+01 --1.892285830801656132e+00 -2.135258090352954233e-02 4.032351698209492241e+00 1.256905951655967191e-01 2.930000000000000160e+00 2.853999999999999915e+01 --1.880404503120835402e+00 -1.351818238643219539e-02 4.067258696893826908e+00 1.500901849910125097e-01 2.044000000000000039e+00 2.602400000000000091e+01 --1.894420291012738122e+00 -7.707951066718953491e-03 4.019210809639611526e+00 1.198672478072352054e-01 2.842000000000000082e+00 2.700400000000000134e+01 --1.910402667913482233e+00 1.867253764083793427e-02 4.111208418530890363e+00 1.261472864950295980e-01 3.399999999999999911e+00 3.263199999999999790e+01 --1.925643519248171343e+00 1.652831530489964462e-04 4.114299533323209523e+00 1.095429342702262249e-01 2.754000000000000004e+00 2.737199999999999989e+01 --1.937716975468330327e+00 -1.783364496431179974e-02 4.160538864332576026e+00 1.077928009647922819e-01 2.859999999999999876e+00 2.711200000000000188e+01 --1.906064092314699199e+00 3.165824148975762697e-02 4.221284726561886913e+00 1.609412471052264204e-01 3.129999999999999893e+00 2.976399999999999935e+01 --1.969500346420724579e+00 -6.947466894257281304e-03 4.286040125103363074e+00 1.049125261580231561e-01 3.708000000000000185e+00 3.411999999999999744e+01 --1.893619299938102296e+00 -4.846529450760501435e-03 4.071769760118912451e+00 1.355057440450787853e-01 1.868000000000000105e+00 2.400799999999999912e+01 --1.961462771877574340e+00 -5.386281798849371777e-03 4.290831190574014187e+00 1.152480297078429111e-01 2.890000000000000124e+00 2.821199999999999974e+01 --1.949610511006282243e+00 -6.389913625072691193e-03 4.209975723719794338e+00 1.075666761926530879e-01 3.104000000000000092e+00 2.690399999999999991e+01 --1.950114223462915852e+00 -2.630159000109863129e-02 4.520334035239052639e+00 1.879917793533786019e-01 2.870000000000000107e+00 2.913200000000000145e+01 --1.947272499364054221e+00 2.194277449900313912e-02 4.248677766672784628e+00 1.200435220290272109e-01 3.502000000000000224e+00 3.201200000000000045e+01 --1.977165806854639829e+00 2.517845021861108215e-02 4.375280351342177632e+00 1.186865597188988264e-01 3.347999999999999865e+00 3.068800000000000239e+01 --1.966055949218621368e+00 3.969151084539382195e-03 4.310779596888598242e+00 1.152154134087517573e-01 2.491999999999999993e+00 2.396000000000000085e+01 --1.988687621032797503e+00 3.038829253598399494e-03 4.321479506035145413e+00 9.268825449804103667e-02 2.370000000000000107e+00 2.435600000000000165e+01 --2.001806222709327621e+00 -1.093700810929714579e-02 4.433268836903983434e+00 1.062189822871236894e-01 4.022000000000000242e+00 3.332399999999999807e+01 --2.010378097795650021e+00 1.163413577281349927e-02 4.460403774100643481e+00 1.035069003910628338e-01 3.978000000000000203e+00 3.442799999999999727e+01 --1.999803992048432510e+00 -1.342573195906116186e-02 4.481967403250141757e+00 1.205599836758593085e-01 3.077999999999999847e+00 2.882000000000000028e+01 --2.013030414531101542e+00 6.893212287164352046e-05 4.440590787592268995e+00 9.582216061007002572e-02 3.062000000000000277e+00 2.853200000000000003e+01 --2.030517423859258042e+00 9.839779888642064334e-03 4.451449572956267531e+00 7.958644033128424444e-02 3.066000000000000281e+00 2.798000000000000043e+01 --2.001991461324770238e+00 -2.038736203877440992e-02 4.506425854543222087e+00 1.240164719349253070e-01 2.028000000000000025e+00 2.457600000000000051e+01 --2.033943026486975558e+00 1.492305308409848374e-02 4.502218811862786829e+00 8.812526785682528452e-02 3.459999999999999964e+00 3.099200000000000088e+01 --2.039202081000584421e+00 -9.515789791828811045e-03 4.498630757368037969e+00 8.176131369394051829e-02 3.625999999999999890e+00 3.213199999999999790e+01 --2.025657027503033447e+00 -1.839456944283368242e-02 4.503585709587241581e+00 9.728430429687758008e-02 2.934000000000000163e+00 2.805199999999999960e+01 --2.027024982259575836e+00 1.809299204646458784e-02 4.468042947018290079e+00 8.716468186118171702e-02 3.609999999999999876e+00 3.265200000000000102e+01 --2.019456820829387489e+00 -1.596202778419010884e-02 4.480266338550095817e+00 9.838170855499400735e-02 2.963999999999999968e+00 2.692000000000000171e+01 --2.060479535089369652e+00 -2.946777405000888545e-03 4.590899744524755910e+00 8.133069992903191325e-02 3.552000000000000046e+00 3.176000000000000156e+01 --2.047913685069898460e+00 1.952765570090821091e-03 4.540203528912875264e+00 8.255717044246856096e-02 3.780000000000000249e+00 3.052800000000000225e+01 --2.073088541821608288e+00 -2.172677547604120324e-02 4.641710589714727497e+00 7.969043012857961183e-02 3.290000000000000036e+00 3.133200000000000074e+01 --2.065839057427787395e+00 -8.136243383586960407e-03 4.620140897533680402e+00 8.253523848935169493e-02 2.991999999999999993e+00 2.777599999999999980e+01 --2.060431300490073170e+00 7.870796534990304877e-03 4.620211883791786711e+00 8.824480714995644459e-02 3.661999999999999922e+00 3.172400000000000020e+01 --2.044990703236904128e+00 1.656444749673181491e-02 4.508942306927029797e+00 7.796961873130463239e-02 2.903999999999999915e+00 2.715200000000000102e+01 --2.066838558962275751e+00 1.588792959264346757e-02 4.618083931632789962e+00 8.086567079681124259e-02 3.548000000000000043e+00 3.024000000000000199e+01 --2.071905595906111230e+00 -9.755000468729251376e-03 4.559146557164234004e+00 6.197610490575416325e-02 3.374000000000000110e+00 2.943599999999999994e+01 --2.069239100465701142e+00 4.337786006970942645e-03 4.654773818009321218e+00 8.710502877600805050e-02 2.653999999999999915e+00 2.384400000000000119e+01 --2.065056145551663835e+00 1.096353804503712517e-02 4.552630711147721776e+00 6.748547062808205044e-02 3.308000000000000274e+00 3.020800000000000196e+01 --2.076558472585962267e+00 -3.014664282784739954e-02 4.648064259901119932e+00 7.723190407900196175e-02 3.040000000000000036e+00 2.628800000000000026e+01 --2.073558117278467616e+00 -1.289235466766454341e-02 4.581663259777078778e+00 6.546791582895079842e-02 2.843999999999999861e+00 2.880000000000000071e+01 --2.084184199888707401e+00 -4.882862753035949535e-03 4.643186535047228780e+00 6.889927295321250644e-02 3.201999999999999957e+00 2.782000000000000028e+01 --2.047787226840443342e+00 -2.106914780904162871e-02 4.584837770760428199e+00 9.299052064745789992e-02 3.169999999999999929e+00 3.051600000000000179e+01 --2.066030760106477793e+00 2.881636946370018729e-03 4.588500097932412203e+00 7.496579218610685547e-02 3.574000000000000288e+00 2.913200000000000145e+01 --2.101956074832999288e+00 5.813604199937847522e-03 4.706970390086400613e+00 6.533017221259254659e-02 3.354000000000000092e+00 3.010800000000000054e+01 --2.063790860077453715e+00 2.056971561645639171e-02 4.685417986809596869e+00 9.973372686923331898e-02 3.101999999999999869e+00 2.742800000000000082e+01 --2.083766224866464789e+00 -8.674045481612274386e-03 4.686202138739569811e+00 7.919631305990997017e-02 3.000000000000000000e+00 2.884799999999999898e+01 --2.071542739464209415e+00 -1.009950491989675646e-02 4.650345831894071580e+00 8.359373917865484116e-02 3.282000000000000028e+00 2.640399999999999991e+01 --2.094098707467347609e+00 -9.006325120453224573e-03 4.702658641094498826e+00 7.232161020278210506e-02 2.875999999999999890e+00 2.781599999999999895e+01 --2.119730271838091262e+00 4.786373815779969634e-03 4.762342257812413493e+00 5.987038432769098417e-02 3.350000000000000089e+00 2.829200000000000159e+01 --2.095826528590822413e+00 4.536883985987650268e-03 4.711004392427511789e+00 7.249860821123584043e-02 3.097999999999999865e+00 2.842800000000000082e+01 --2.091023154938781659e+00 -2.525245122064818069e-03 4.726807742842772164e+00 8.105640465726644817e-02 2.617999999999999883e+00 2.595599999999999952e+01 --2.110169006337327513e+00 -1.188134672090695836e-02 4.717508461141326492e+00 5.934373657318253725e-02 3.669999999999999929e+00 3.378800000000000381e+01 --2.108350107649620497e+00 -8.850385903062890636e-03 4.695094864647605171e+00 5.617516748575897279e-02 2.863999999999999879e+00 2.829599999999999937e+01 --2.117013000207537132e+00 -8.025948201025022780e-03 4.767691269427788647e+00 6.375679898677917568e-02 3.800000000000000266e+00 3.428800000000000381e+01 --2.110511986275810159e+00 -5.596839268197909998e-04 4.779730064285380386e+00 7.306896094561056432e-02 3.855999999999999872e+00 3.507200000000000273e+01 --2.112226747472385480e+00 3.807083963449946727e-03 4.731466709387655456e+00 6.049953004262337980e-02 4.062000000000000277e+00 3.350000000000000000e+01 --2.122735785103154083e+00 1.788078182329766452e-02 4.739857847396901747e+00 5.167364294875381042e-02 3.923999999999999932e+00 3.567200000000000415e+01 --2.109668751448182888e+00 -7.391269123528241463e-04 4.742814845333301221e+00 6.563253217059140943e-02 3.137999999999999901e+00 2.624399999999999977e+01 --2.110636863584861356e+00 1.382922781716112992e-02 4.862286939843729172e+00 9.133381702891364695e-02 3.681999999999999940e+00 3.392399999999999949e+01 --2.127024961049239771e+00 -6.001522364876775081e-03 4.752540768214404743e+00 5.043771331640303085e-02 3.796000000000000263e+00 3.169600000000000151e+01 --2.130476762339088559e+00 -5.278726154588838336e-03 4.882025634077510112e+00 7.556943885258970983e-02 3.451999999999999957e+00 3.110399999999999920e+01 --2.108335697572671918e+00 1.456022967133420790e-02 4.737467679425920508e+00 6.562548309979042427e-02 2.987999999999999989e+00 3.102400000000000091e+01 --2.129677873966199453e+00 -2.296735239447457357e-03 4.902932060836246997e+00 8.100206183688811457e-02 3.395999999999999908e+00 3.221600000000000108e+01 --2.136804699774962568e+00 -2.094018481168730475e-02 4.869754922031269473e+00 6.623350084348454681e-02 3.613999999999999879e+00 3.169999999999999929e+01 --2.138819392566514210e+00 6.178488820640387451e-03 4.795369936159091573e+00 4.824552622218120784e-02 3.938000000000000167e+00 3.261999999999999744e+01 --2.131358862881783889e+00 3.212962350767396228e-03 4.758651642970222362e+00 4.753319517710450498e-02 3.538000000000000256e+00 2.884400000000000119e+01 --2.139670854884587747e+00 2.067060511211928596e-04 4.801159676818405053e+00 4.870224009120467656e-02 4.227999999999999758e+00 3.984799999999999898e+01 --2.131547937285340755e+00 3.949616642690848001e-03 4.797993568688049493e+00 5.600258174916063897e-02 4.020000000000000462e+00 3.371200000000000330e+01 --2.134336032128920202e+00 -2.966367238886951155e-03 4.801948915807060736e+00 5.411847831652349256e-02 3.544000000000000039e+00 3.227199999999999847e+01 --2.130851194267065374e+00 4.134745215133248455e-03 4.785536106529862721e+00 5.394863833971476341e-02 2.709999999999999964e+00 2.433200000000000074e+01 --2.150479807746399796e+00 1.702129075555036328e-02 4.974001011253934124e+00 7.535908282389440493e-02 3.899999999999999911e+00 3.656000000000000227e+01 --2.129408407490395838e+00 -1.946254536959719436e-02 4.743274531958784124e+00 4.580687997341617579e-02 4.025999999999999801e+00 3.478000000000000114e+01 --2.146757178337554972e+00 2.704034234627655971e-03 4.829601576526042273e+00 4.795682388463356344e-02 4.344000000000000306e+00 3.718399999999999750e+01 --2.116508771543754275e+00 3.163956958951450685e-03 4.708024781170442097e+00 5.098298058935561705e-02 3.974000000000000199e+00 3.446800000000000352e+01 --2.155382618971130260e+00 1.878604423472650387e-02 4.839579443717999752e+00 4.150149197100642257e-02 4.008000000000000007e+00 3.476800000000000068e+01 --2.127256771148122727e+00 8.573679793764654711e-05 4.775259781945364601e+00 5.525439924656878193e-02 3.526000000000000245e+00 3.166000000000000014e+01 --2.131638808642919880e+00 1.434049246711081166e-02 4.851830301961605585e+00 6.762663387104189683e-02 3.096000000000000085e+00 2.840800000000000125e+01 --2.119424955972883051e+00 -1.727613653943306168e-02 4.756801431078041986e+00 5.874742435809571922e-02 3.026000000000000245e+00 2.696400000000000219e+01 --2.145979192884098108e+00 3.702297669610079417e-03 4.895206203242120857e+00 6.295798577944004826e-02 3.601999999999999869e+00 3.383599999999999852e+01 --2.171027778697403043e+00 -5.067289706781408568e-03 4.943183313252045963e+00 4.874247479696595248e-02 3.410000000000000142e+00 3.100400000000000134e+01 --2.154248225884530132e+00 1.604194937968321175e-02 4.880041235501058949e+00 5.138010826040666917e-02 3.177999999999999936e+00 3.073199999999999932e+01 --2.158624655699006745e+00 -3.632642160203045870e-03 4.869257936220978245e+00 4.497241108763790768e-02 3.262000000000000011e+00 2.955600000000000094e+01 --2.147354078247586173e+00 -1.319924296899767369e-02 4.826982093356340542e+00 4.669256465296345304e-02 2.843999999999999861e+00 2.714400000000000190e+01 --2.144038935929863943e+00 2.215427337473618776e-03 4.807552569577365986e+00 4.582089585592185460e-02 3.700000000000000178e+00 3.348000000000000398e+01 --2.171121555316350094e+00 2.237943353225172252e-03 4.922291447685556598e+00 4.423359702394463050e-02 4.443999999999999950e+00 3.749600000000000222e+01 --2.160490708042090535e+00 -6.066242833622908235e-04 4.939588827150792838e+00 5.824418635599910854e-02 4.014000000000000234e+00 3.329200000000000159e+01 --2.156503373052220507e+00 -9.753814354817509982e-03 4.879091050814511554e+00 4.908816041117813195e-02 3.975999999999999979e+00 3.428000000000000114e+01 --2.161974503268853098e+00 1.564774251966339486e-02 4.887189609059219286e+00 4.541758892331834718e-02 4.905999999999999694e+00 4.255599999999999739e+01 --2.167121328433862182e+00 -1.356774520501664383e-03 4.909569560792250265e+00 4.538545724630239919e-02 3.395999999999999908e+00 3.093599999999999994e+01 --2.169620092347735785e+00 1.507205396287196377e-03 4.900510291448481048e+00 4.105407537612853347e-02 4.054000000000000270e+00 3.406000000000000227e+01 --2.150339788746195246e+00 1.486883600683673243e-02 4.860470568393549406e+00 5.099788585771587029e-02 4.179999999999999716e+00 3.610399999999999920e+01 --2.172669466521558235e+00 1.146875563026673525e-02 5.013123563788006720e+00 6.190284315912670393e-02 3.302000000000000046e+00 3.063599999999999923e+01 --2.166246854469350502e+00 3.038109486397838448e-03 4.907709759028187513e+00 4.582836796276069241e-02 3.280000000000000249e+00 2.875199999999999889e+01 --2.157110963967358686e+00 1.430276815965967306e-02 4.921127499340501643e+00 5.745614525140806811e-02 3.867999999999999883e+00 3.718399999999999750e+01 --2.179472368561409024e+00 -1.836779071633862226e-02 4.944958615154134485e+00 4.080025594233627206e-02 3.520000000000000018e+00 3.150400000000000134e+01 --2.167024479241231205e+00 1.135818632848557309e-02 4.890387143761086186e+00 4.130946019072000847e-02 4.248000000000000220e+00 4.072800000000000153e+01 --2.181296165952523847e+00 -1.788352274769098096e-02 5.022931584703854924e+00 5.545668841088868123e-02 3.530000000000000249e+00 3.235600000000000165e+01 --2.181188677466903147e+00 1.606864567825642617e-02 5.112044757715975329e+00 7.432942168010621409e-02 2.939999999999999947e+00 2.787999999999999901e+01 --2.150976037088502046e+00 2.802440030479356678e-02 4.887181880530834022e+00 5.576243084336316574e-02 3.052000000000000046e+00 3.015200000000000102e+01 --2.180789885705132214e+00 3.178731514261690322e-05 4.986761363851572426e+00 4.855432801400379195e-02 2.601999999999999869e+00 2.557199999999999918e+01 --2.161492079015528311e+00 -1.651141392365702149e-02 4.963749454382691439e+00 6.224948580555748900e-02 3.665999999999999925e+00 3.388400000000000034e+01 --2.180369029635759848e+00 -1.962924252379074676e-03 4.999665217599808642e+00 5.167090559905988117e-02 3.216000000000000192e+00 3.124000000000000199e+01 --2.189852650708258963e+00 -2.150729512004433130e-02 5.017597378650292761e+00 4.602087248955211846e-02 2.573999999999999844e+00 2.506000000000000227e+01 --2.181139204367039675e+00 4.469263873474589761e-03 4.965256172550101432e+00 4.368495199163210246e-02 3.089999999999999858e+00 3.202000000000000313e+01 --2.178224303439633136e+00 -2.284929701622095966e-02 4.952964295927889005e+00 4.355810457654821916e-02 3.930000000000000160e+00 3.270000000000000284e+01 --2.193124448618182676e+00 -1.746700670556892640e-02 5.035298746930852332e+00 4.668510956795250688e-02 4.517999999999999794e+00 3.756400000000000006e+01 --2.171730816983909129e+00 -6.127187105990848995e-03 4.993849256856434771e+00 5.879789625051213414e-02 2.754000000000000004e+00 2.585200000000000031e+01 --2.174285652384515544e+00 1.783779642393629877e-02 4.927110465002967565e+00 4.200885379850911872e-02 3.950000000000000178e+00 3.505199999999999960e+01 --2.175091746423581274e+00 -2.843609484868375899e-03 4.927837680068472004e+00 4.159528738194942510e-02 3.406000000000000139e+00 3.001200000000000045e+01 --2.186915394073043473e+00 8.068441452392738703e-03 4.976413641412752220e+00 4.048248532756636847e-02 3.930000000000000160e+00 3.269200000000000017e+01 --2.169357342573217107e+00 -8.790701610925365575e-03 5.006478758526673900e+00 6.377258034319109592e-02 2.987999999999999989e+00 2.792800000000000082e+01 --2.194062068948487987e+00 9.819283323018921338e-04 4.992788646934954500e+00 3.715843157723655588e-02 4.290000000000000036e+00 3.778000000000000114e+01 --2.169143214472641468e+00 -1.310902220099066824e-02 4.958580438793686262e+00 5.373965721970243997e-02 3.241999999999999993e+00 2.859600000000000009e+01 --2.186286082284945476e+00 1.677531375906243447e-02 5.440482499660598492e+00 1.380117116828277202e-01 3.399999999999999911e+00 3.294400000000000261e+01 --2.187968600784637285e+00 -4.665332386327099984e-03 5.020770694316943228e+00 4.877491921781779843e-02 3.887999999999999901e+00 3.448799999999999955e+01 --2.178709954643326174e+00 1.096670375534668576e-02 4.994080330103114918e+00 5.201922751988752314e-02 2.998000000000000220e+00 2.981200000000000117e+01 --2.196208728681336986e+00 -5.413594728317747129e-03 5.026189471075965365e+00 4.203837524138046705e-02 3.216000000000000192e+00 3.196000000000000085e+01 --2.178588703866606302e+00 -4.788822248454991694e-03 4.946136945790851946e+00 4.209988156361843537e-02 3.681999999999999940e+00 3.189199999999999946e+01 --2.200291847410922763e+00 -5.652745140867559623e-03 5.049019377408024312e+00 4.288845308010231366e-02 2.193999999999999950e+00 2.352400000000000091e+01 --2.203268593057585267e+00 -1.825659870490317291e-02 5.043458784909155668e+00 3.873348863546115933e-02 3.168000000000000149e+00 3.007199999999999918e+01 --2.190593702341093962e+00 -1.555976568944341006e-02 5.050808789773196139e+00 5.237742882622316992e-02 2.705999999999999961e+00 2.966000000000000014e+01 --2.181952607709483516e+00 1.538020757933336591e-02 5.110654026419140905e+00 7.329997780847957722e-02 3.105999999999999872e+00 3.082799999999999940e+01 --2.210633975121170991e+00 3.827871769347699314e-03 5.091242998668386477e+00 4.180452302353587085e-02 3.038000000000000256e+00 3.117999999999999972e+01 --2.174615630285904544e+00 2.938108202261552598e-04 4.959940506999474863e+00 4.884529177568627117e-02 3.764000000000000234e+00 3.713600000000000279e+01 --2.171739124476536720e+00 2.354370540662854491e-02 4.957600259688893729e+00 5.075889559250275351e-02 3.459999999999999964e+00 3.055199999999999960e+01 --2.203954886058569596e+00 5.438699641284128194e-03 5.023028003525039864e+00 3.407553769146650507e-02 3.720000000000000195e+00 3.428800000000000381e+01 --2.184934698965127264e+00 -9.359429415134885508e-03 4.992773788027048631e+00 4.578175072323333039e-02 2.641999999999999904e+00 2.711599999999999966e+01 --2.201541922696782727e+00 -9.402985980618951481e-03 5.043904301916857236e+00 4.061276955351323520e-02 3.414000000000000146e+00 3.194800000000000040e+01 --2.187256167102137994e+00 -3.932327697104090491e-04 5.003818035557487498e+00 4.592890830481512893e-02 3.173999999999999932e+00 3.190800000000000125e+01 --2.203580639003929864e+00 -1.105291164336705788e-02 5.038994422404212692e+00 3.765552422398461829e-02 4.155999999999999694e+00 3.627199999999999847e+01 --2.192425792847472632e+00 -5.142472678318300329e-03 4.988029108196976757e+00 3.770045167745909864e-02 2.721999999999999975e+00 2.617999999999999972e+01 --2.201588724434145217e+00 8.425476558889552145e-03 5.054590547674587597e+00 4.278437331871041277e-02 3.020000000000000018e+00 2.884799999999999898e+01 --2.171716168407761494e+00 -3.154823947983308348e-03 4.964357531057228101e+00 5.257771953202275417e-02 3.000000000000000000e+00 2.789600000000000080e+01 --2.183888182843015890e+00 6.867325962960559894e-03 4.965537010324697853e+00 4.110023266841342920e-02 3.248000000000000220e+00 3.027200000000000202e+01 --2.212308799664191028e+00 1.310506462210972965e-02 5.047770321223012502e+00 3.124623024794405055e-02 4.397999999999999687e+00 3.920400000000000063e+01 --2.209576209384613410e+00 8.237826365113692928e-03 5.060452144803694097e+00 3.646166114161426830e-02 3.012000000000000011e+00 2.942399999999999949e+01 --2.208454562449968073e+00 -1.470086514989024824e-02 5.055055166274952327e+00 3.631368072214154891e-02 3.839999999999999858e+00 3.355199999999999960e+01 --2.199252613789099531e+00 -5.796251677448281160e-03 5.013347090483147639e+00 3.649805071505881487e-02 3.447999999999999954e+00 3.030400000000000205e+01 --2.184985691234464067e+00 1.055054809075159881e-03 5.047140444970501072e+00 5.717745162054464064e-02 3.717999999999999972e+00 3.478800000000000381e+01 --2.181845442378421041e+00 8.650188347418824239e-03 4.974508448810271766e+00 4.491683985626731407e-02 3.875999999999999890e+00 3.144000000000000128e+01 --2.203455191231872501e+00 -2.444946527545181075e-03 5.125737720763224203e+00 5.571411787274695160e-02 3.264000000000000234e+00 2.791199999999999903e+01 --2.185133986644121507e+00 2.011676171075851144e-02 5.254858140446262205e+00 1.002577328443386290e-01 3.600000000000000089e+00 3.148799999999999955e+01 --2.182544414903989871e+00 1.781048447867000437e-02 5.012027790109658376e+00 5.196315345947006420e-02 2.951999999999999957e+00 2.898400000000000176e+01 --2.197893374475428985e+00 -5.936163114661815142e-03 5.046971508699773068e+00 4.473972709518058560e-02 3.144000000000000128e+00 2.952800000000000225e+01 --2.215549950962302450e+00 6.055759883498872120e-03 5.149710070292655928e+00 4.908325071749340685e-02 2.954000000000000181e+00 2.769200000000000017e+01 --2.236977918425648415e+00 -1.633393002660268184e-03 5.165086830580374766e+00 3.217548014423482483e-02 3.758000000000000007e+00 3.614800000000000324e+01 --2.191087753663243376e+00 3.967787398273183927e-03 5.011227635976077899e+00 4.380726569839291790e-02 3.685999999999999943e+00 3.285999999999999943e+01 --2.226810753775579688e+00 -8.955769972740838109e-03 5.140655928356526516e+00 3.664687573331332909e-02 3.740000000000000213e+00 3.671200000000000330e+01 --2.206208172115220911e+00 3.292844576950910724e-03 5.091666440887355982e+00 4.607799058293206296e-02 2.794000000000000039e+00 2.426800000000000068e+01 --2.202613200893518197e+00 4.037693150504857893e-03 5.080439149338389804e+00 4.717773642730101191e-02 3.350000000000000089e+00 3.221999999999999886e+01 --2.216796148353395335e+00 -8.036539456542370844e-04 5.216870032560947834e+00 6.159369299749521687e-02 4.081999999999999851e+00 4.161999999999999744e+01 --2.225065552563091131e+00 1.028923667809945874e-02 5.193731754893704533e+00 4.897716638402643125e-02 2.810000000000000053e+00 2.785999999999999943e+01 --2.204478116376100694e+00 -5.296834647948066126e-03 5.079505258593898454e+00 4.520699704685700315e-02 2.669999999999999929e+00 2.762000000000000099e+01 --2.228058001425653689e+00 -3.043097470061103139e-03 5.167515816667890505e+00 4.094168281854201202e-02 3.414000000000000146e+00 2.902800000000000225e+01 --2.202052082440013159e+00 -8.718311519570713999e-03 5.028845235236306443e+00 3.703323347848118396e-02 3.911999999999999922e+00 3.459199999999999875e+01 --2.225461869608000853e+00 -1.711817057121191267e-03 5.142612969179683802e+00 3.834757900497858668e-02 3.326000000000000068e+00 2.865200000000000102e+01 --2.232362501432669344e+00 -9.803098292816508560e-03 5.188276849141288061e+00 4.104278826202159558e-02 2.560000000000000053e+00 2.728800000000000026e+01 --2.224175738394489343e+00 -1.777912409034002050e-02 5.176727828113833141e+00 4.624617691471757941e-02 3.721999999999999975e+00 3.298000000000000398e+01 --2.239838112609866982e+00 4.899794379617045115e-03 5.151213488694864395e+00 2.676263055279864619e-02 3.431999999999999940e+00 3.339999999999999858e+01 --2.228108907241255654e+00 9.236566391412535069e-04 5.150818273615381138e+00 3.753599916445019002e-02 2.451999999999999957e+00 2.551999999999999957e+01 --2.238071706785516479e+00 -6.623757955134053528e-03 5.190645781906483514e+00 3.624389945973423288e-02 2.144000000000000128e+00 2.152799999999999869e+01 --2.209358908759378348e+00 1.665394150959450615e-03 5.078815465076407243e+00 4.046900704395436227e-02 4.408000000000000362e+00 4.083200000000000074e+01 --2.222588227540177375e+00 1.467195316500178410e-03 5.154703508332009854e+00 4.348233944721872218e-02 4.176000000000000156e+00 3.841600000000000392e+01 --2.202526048479086285e+00 -9.628702139913203686e-03 5.108856199710556822e+00 5.306862111472151339e-02 3.966000000000000192e+00 3.542000000000000171e+01 --2.205765574006401497e+00 -8.491742138897386688e-03 5.091850155327603211e+00 4.649605658322166629e-02 3.454000000000000181e+00 3.059600000000000009e+01 --2.209022732808599621e+00 -1.914822408061760822e-02 5.092371097142472713e+00 4.333020358717389747e-02 4.102000000000000313e+00 3.686800000000000210e+01 --2.234182963538938527e+00 -1.449325959877916827e-02 5.194369129298092247e+00 4.049622716655972704e-02 2.327999999999999847e+00 2.440800000000000125e+01 --2.195343925076223890e+00 8.644605369256149613e-03 5.095665361411177763e+00 5.724481487451322376e-02 3.754000000000000004e+00 3.083600000000000207e+01 --2.223049028506590474e+00 -8.340437823043642812e-03 5.112261565985813050e+00 3.441937109543691253e-02 3.542000000000000259e+00 3.159600000000000009e+01 --2.227591611697896212e+00 -6.692348924698060184e-03 5.155593897352042099e+00 3.895274231920028973e-02 3.335999999999999854e+00 3.597599999999999909e+01 --2.206077525684415619e+00 3.528380305118043042e-03 5.074585094854485057e+00 4.269109880063511747e-02 3.894000000000000128e+00 3.312400000000000233e+01 --2.237635596639482305e+00 -1.226690586334732748e-02 5.263414163300324411e+00 5.111362253119989402e-02 3.225999999999999979e+00 2.806800000000000139e+01 --2.218044366047908778e+00 -3.664669934901923845e-03 5.122208162893394423e+00 4.114977526055878937e-02 3.653999999999999915e+00 3.324399999999999977e+01 --2.224069491448207980e+00 5.323787601561665462e-04 5.105634539905006264e+00 3.217407030823018349e-02 3.677999999999999936e+00 3.511599999999999966e+01 --2.237329385837086626e+00 9.387762759229511741e-03 5.199333119469833342e+00 3.863953833281907890e-02 2.926000000000000156e+00 3.149200000000000088e+01 --2.225457923451293674e+00 -6.221827428099515993e-03 5.217754544920628845e+00 5.350035519494132641e-02 1.743999999999999995e+00 2.224800000000000111e+01 --2.241174622665801586e+00 -3.560523202435811503e-04 5.164830250985461113e+00 2.826399030857387404e-02 3.677999999999999936e+00 3.506799999999999784e+01 --2.231739749596869160e+00 -2.397986591906648053e-04 5.147614451099966182e+00 3.352003257551750687e-02 3.415999999999999925e+00 2.971199999999999974e+01 --2.249790317931342543e+00 -1.121099908809889073e-03 5.231180673335985354e+00 3.351149050160154991e-02 3.010000000000000231e+00 2.965200000000000102e+01 --2.204986680867331739e+00 1.030563388541728791e-02 5.043001029233268540e+00 3.716691698588205778e-02 3.609999999999999876e+00 3.241199999999999903e+01 --2.233729273433648910e+00 1.079498842587200622e-02 5.229996981971176240e+00 4.811741672414996535e-02 3.008000000000000007e+00 3.051200000000000045e+01 --2.239455787318752389e+00 -5.141267879863315599e-03 5.198930446682124895e+00 3.662613735829670786e-02 3.070000000000000284e+00 2.898799999999999955e+01 --2.225342683331165361e+00 -6.155442094899019750e-03 5.171139312873684446e+00 4.419707775798449589e-02 3.431999999999999940e+00 3.421600000000000108e+01 --2.226689258812543315e+00 -1.251010849573722398e-04 5.141121391033463439e+00 3.690418190625106148e-02 3.326000000000000068e+00 2.884400000000000119e+01 --2.238662230765676053e+00 -1.411926358816120372e-02 5.231138311124832185e+00 4.367969026155259921e-02 2.387999999999999901e+00 2.433600000000000207e+01 --2.254079814152160299e+00 2.692437959344101336e-03 5.244900101236665613e+00 3.227826248100184453e-02 3.173999999999999932e+00 3.136400000000000077e+01 --2.251847156560097485e+00 1.024353430187601582e-02 5.285590857176376112e+00 4.229046079278354214e-02 3.008000000000000007e+00 2.999200000000000088e+01 --2.258025632959084206e+00 -4.051685925970420314e-03 5.321462437492455955e+00 4.368410820893074004e-02 2.942000000000000171e+00 2.942000000000000171e+01 --2.256067522439914264e+00 1.653151523592601493e-02 5.254034422841788121e+00 3.209285361258331498e-02 3.300000000000000266e+00 3.736800000000000210e+01 --2.225504025110582429e+00 2.474434480590234457e-03 5.198499333384178911e+00 4.958982956544321502e-02 2.459999999999999964e+00 2.428000000000000114e+01 --2.239225392152269123e+00 4.781201495282031214e-03 5.233070542309142148e+00 4.365036332267033248e-02 2.046000000000000263e+00 2.070800000000000196e+01 --2.252177767695032973e+00 -4.595295574809254990e-03 5.279578929101062634e+00 4.085091603558826945e-02 2.970000000000000195e+00 2.964400000000000190e+01 --2.243633252089619390e+00 -9.078442710937521462e-03 5.262759992653984753e+00 4.541444610977708046e-02 2.708000000000000185e+00 2.589600000000000080e+01 --2.255162079283426380e+00 -6.956730209175122481e-04 5.294868228173407410e+00 4.111693769768572093e-02 2.164000000000000146e+00 2.476000000000000156e+01 --2.251523292257991748e+00 -8.574925559605214983e-04 5.246202905721502496e+00 3.488479556262581716e-02 3.018000000000000238e+00 3.310000000000000142e+01 --2.255771585683198133e+00 9.854359036694416638e-03 5.303730351490904660e+00 4.223661927270294658e-02 3.810000000000000053e+00 4.250000000000000000e+01 --2.250238568138168915e+00 -1.503861243823573527e-03 5.212674650785471542e+00 2.944443273735201233e-02 3.216000000000000192e+00 2.923199999999999932e+01 --2.259534803827739413e+00 9.495466709547718473e-03 5.244081107572300837e+00 2.708957380720601951e-02 3.890000000000000124e+00 4.383599999999999852e+01 --2.229159793761405606e+00 -1.605457172732230450e-03 5.196145784458609640e+00 4.567866898152589394e-02 3.612000000000000099e+00 3.431199999999999761e+01 --2.252181096255271520e+00 1.140234374700873493e-02 5.267650241777785958e+00 3.842926318031306826e-02 4.709999999999999964e+00 4.604400000000000404e+01 --2.268872044370979779e+00 -4.259951149701301371e-03 5.375276274504024343e+00 4.418196931374733516e-02 2.290000000000000036e+00 2.569999999999999929e+01 --2.246897341808159254e+00 -3.694177027460336833e-03 5.212246088167302283e+00 3.241648217915452102e-02 4.144000000000000128e+00 3.818399999999999750e+01 --2.259171652152379917e+00 1.890884470940524436e-04 5.285111281170344455e+00 3.551326615375358792e-02 2.934000000000000163e+00 2.604400000000000048e+01 --2.248890053152990731e+00 -1.086672543539527434e-02 5.231865313054103517e+00 3.440280044397591580e-02 4.012000000000000455e+00 3.385600000000000165e+01 --2.268802853353852900e+00 1.236389310418966984e-02 5.318595470718715745e+00 3.315325446889685196e-02 2.942000000000000171e+00 2.885200000000000031e+01 --2.247695617366191723e+00 -3.278930635446231220e-04 5.209249091906489326e+00 3.109836786055368216e-02 3.596000000000000085e+00 3.783200000000000074e+01 --2.248053536191639168e+00 1.197710765366013369e-02 5.281025067350527458e+00 4.488368387720952091e-02 3.518000000000000238e+00 3.845199999999999818e+01 --2.270980913362691034e+00 -7.765773953442773637e-04 5.330814160302347560e+00 3.363313260822570205e-02 1.733999999999999986e+00 1.947599999999999909e+01 --2.240178828689090018e+00 1.636030793212938511e-02 5.267346652859187017e+00 4.943860048547058655e-02 3.212000000000000188e+00 3.167999999999999972e+01 --2.257775925664046390e+00 -1.608961655028405763e-03 5.285483001652691470e+00 3.686530588585062301e-02 2.728000000000000203e+00 2.383999999999999986e+01 --2.276745402449676270e+00 -1.998127909850011194e-02 5.360525524085638871e+00 3.389892001478378436e-02 3.879999999999999893e+00 3.919200000000000017e+01 --2.245398518242927466e+00 9.682385129417277192e-03 5.183310452705800486e+00 2.800714247116127542e-02 3.689999999999999947e+00 3.142000000000000171e+01 --2.283700461703947138e+00 -4.227450428419824574e-03 5.361429383288434103e+00 2.801119978069368729e-02 2.512000000000000011e+00 2.762400000000000233e+01 --2.269900770748532803e+00 6.298045411497184796e-03 5.390830985871185810e+00 4.624149667903799249e-02 1.729999999999999982e+00 2.023600000000000065e+01 --2.276741864940255322e+00 1.579710734608106779e-03 5.341951109001393583e+00 3.055623398326967610e-02 2.681999999999999940e+00 2.720400000000000063e+01 --2.281999454182998655e+00 -1.159738027133328355e-03 5.449033912484737563e+00 4.637679961056938305e-02 3.236000000000000210e+00 3.380799999999999983e+01 --2.260684756826158548e+00 -9.172852967663215618e-03 5.305509677040026517e+00 3.806763013372799209e-02 2.713999999999999968e+00 2.525199999999999889e+01 --2.263380434864336266e+00 4.057303660736065205e-04 5.291713285923546728e+00 3.295439686379915412e-02 2.887999999999999901e+00 3.156800000000000139e+01 --2.269936387899856189e+00 9.008469367429739263e-03 5.311552729796363614e+00 3.079808615659413579e-02 2.124000000000000110e+00 2.024800000000000111e+01 --2.252836581649728664e+00 4.683661712009403247e-03 5.268870335700853502e+00 3.813181379535754423e-02 3.644000000000000128e+00 4.023199999999999932e+01 --2.264719375069798257e+00 5.382193955907810766e-03 5.323384140494092698e+00 3.789078647753173212e-02 3.362000000000000099e+00 3.206000000000000227e+01 --2.258211766808072340e+00 -3.625631155735645119e-03 5.250103396232071340e+00 2.952089632656276427e-02 3.427999999999999936e+00 3.300000000000000000e+01 --2.269783713835662464e+00 -4.690447695534441172e-03 5.409247781679706435e+00 4.993487312367984182e-02 2.109999999999999876e+00 2.334799999999999898e+01 --2.259572922282263363e+00 -5.994011771116432470e-03 5.299564014540409929e+00 3.795434387362509737e-02 2.518000000000000238e+00 2.294000000000000128e+01 --2.231703926458333154e+00 2.372223072875929810e-03 5.201120047299457205e+00 4.429272057603785701e-02 3.120000000000000107e+00 3.130400000000000205e+01 --2.279197026220748157e+00 -6.941098718792526948e-03 5.379482316616909898e+00 3.553471210327337898e-02 2.822000000000000064e+00 3.103600000000000136e+01 --2.282604074731590771e+00 3.351699022377281970e-03 5.427776021161584197e+00 4.173662336427894082e-02 2.133999999999999897e+00 2.841199999999999903e+01 --2.280539653115503995e+00 4.864811295087250777e-03 5.360457615453340097e+00 3.067248390852973100e-02 3.020000000000000018e+00 3.165600000000000236e+01 --2.268343070704652131e+00 -1.698321510122180467e-02 5.351113903634894697e+00 3.980926642359136625e-02 3.708000000000000185e+00 3.639200000000000301e+01 --2.260751799137330487e+00 2.398738812532592618e-04 5.299169747462999069e+00 3.681684976478730165e-02 4.070000000000000284e+00 3.941199999999999903e+01 --2.256573852181152695e+00 -6.417752466816029067e-03 5.311009078154846463e+00 4.295939945655771752e-02 4.288000000000000256e+00 4.375200000000000244e+01 --2.274155436956210252e+00 1.097506229516324178e-03 5.376964063324429333e+00 3.967246052160080388e-02 2.221999999999999975e+00 2.703600000000000136e+01 --2.288574988978094193e+00 -2.950318706003918906e-03 5.407241467804484003e+00 3.238884657506212184e-02 3.097999999999999865e+00 3.210000000000000142e+01 --2.245726138601944477e+00 -4.689315697470837485e-03 5.228364534199344327e+00 3.668446706518856126e-02 3.914000000000000146e+00 4.334000000000000341e+01 --2.287264147101187639e+00 1.905327053837435961e-02 5.422854164233409158e+00 3.634623091691310121e-02 1.981999999999999984e+00 2.822800000000000153e+01 --2.279599586964517144e+00 5.779575430568301836e-03 5.336339593342621868e+00 2.687586175254265061e-02 3.363999999999999879e+00 3.735999999999999943e+01 --2.264086375260200512e+00 5.674146753571840049e-03 5.312818551539970180e+00 3.640814669770025408e-02 4.474000000000000199e+00 4.523600000000000421e+01 --2.274182120702409549e+00 3.677897582372576663e-03 5.309411437907159304e+00 2.657927366479614917e-02 2.950000000000000178e+00 2.766000000000000014e+01 --2.295339517452853695e+00 5.862583960712556587e-03 5.464651350655297612e+00 3.719422963939134075e-02 2.986000000000000210e+00 3.436399999999999721e+01 --2.284625284782605181e+00 1.654394327032040340e-02 5.410198120723188175e+00 3.637013848588849935e-02 2.046000000000000263e+00 3.203600000000000136e+01 --2.310958053989884853e+00 -5.877775686571895704e-03 5.526398746292735531e+00 3.478390123847700105e-02 1.378000000000000114e+00 2.288400000000000034e+01 --2.261993789010113609e+00 -4.815256306081676894e-03 5.264570117101238900e+00 2.890243228324873917e-02 3.204000000000000181e+00 3.328800000000000381e+01 --2.299172980020093071e+00 -2.948330655382157706e-03 5.479472977360402730e+00 3.655739204731872638e-02 2.343999999999999861e+00 2.324800000000000111e+01 --2.292927950926053171e+00 1.725606080922326147e-02 5.407679397976157709e+00 2.838640797026772619e-02 3.212000000000000188e+00 3.688799999999999812e+01 --2.277721015576740005e+00 -9.383481644355717161e-03 5.379251186515811689e+00 3.680875171678309882e-02 3.004000000000000004e+00 3.205599999999999739e+01 --2.310877946946001238e+00 3.553024974900561867e-03 5.494181752029240862e+00 2.883546410836778165e-02 2.640000000000000124e+00 2.877599999999999980e+01 --2.287218389158239606e+00 6.074123082848609766e-03 5.355737262380672270e+00 2.375210244347961824e-02 4.320000000000000284e+00 4.358400000000000318e+01 --2.275270715428013180e+00 3.720397868827869312e-03 5.417171460878257960e+00 4.641256053232880457e-02 4.738000000000000433e+00 4.596399999999999864e+01 --2.271303817031195660e+00 7.221535436710829889e-04 5.344020241243171654e+00 3.589920841407263224e-02 3.466000000000000192e+00 3.239600000000000080e+01 --2.295140938762319838e+00 -9.215163607730286841e-04 5.409732610430006972e+00 2.696790295356589484e-02 2.975999999999999979e+00 3.556000000000000227e+01 --2.306910706776081454e+00 1.381273305507521761e-03 5.476289054639366327e+00 2.902121118670215189e-02 1.834000000000000075e+00 2.550000000000000000e+01 --2.295819735033922449e+00 4.848278116745288052e-03 5.456497415264442097e+00 3.521980945531523466e-02 2.192000000000000171e+00 2.657600000000000051e+01 --2.286499858491537029e+00 4.685282422077040668e-03 5.367692764282360862e+00 2.669115714804872960e-02 2.720000000000000195e+00 2.924800000000000111e+01 --2.287644914468893287e+00 -4.467109178770755501e-03 5.413807658714221205e+00 3.447648916262158192e-02 1.985999999999999988e+00 2.581200000000000117e+01 --2.280261879092064348e+00 -1.132358916842757506e-03 5.375734562771279812e+00 3.387501802553234687e-02 3.014000000000000234e+00 3.337199999999999989e+01 --2.270049477451138831e+00 -4.011366489417354450e-03 5.378988454120562146e+00 4.382068191587568107e-02 1.644000000000000128e+00 2.073600000000000065e+01 --2.307559397777119159e+00 -4.306833203219350564e-03 5.486595400010966905e+00 3.036860853164169427e-02 1.606000000000000094e+00 1.754800000000000182e+01 --2.265791486428274215e+00 1.338632112526724023e-03 5.352990542349018277e+00 4.269223672281948628e-02 2.641999999999999904e+00 2.696400000000000219e+01 --2.286914950849712191e+00 9.417585368614856539e-03 5.441790491593889278e+00 4.044636094291860495e-02 1.304000000000000048e+00 1.817600000000000193e+01 --2.327192542378873519e+00 -1.486466948397975260e-03 5.558997807151870418e+00 2.643472978631676920e-02 2.370000000000000107e+00 2.730799999999999983e+01 --2.284388373769856706e+00 -2.376879947005811154e-03 5.411620409072860127e+00 3.701737530179272095e-02 1.481999999999999984e+00 1.853200000000000003e+01 --2.317783992843151619e+00 -5.610944821805610196e-03 5.484523313015646551e+00 2.090500530557993022e-02 2.112000000000000099e+00 2.036800000000000210e+01 --2.281496194964338642e+00 -1.142716460880785143e-03 5.390383761377730565e+00 3.557095437526761744e-02 3.320000000000000284e+00 3.418399999999999750e+01 --2.304383737239892760e+00 -3.490478107929145205e-03 5.478482165622739153e+00 3.168629103118538598e-02 9.260000000000000453e-01 1.717200000000000060e+01 --2.304308431297271920e+00 2.882290893061290960e-04 5.550920392280791482e+00 4.540304522625390055e-02 5.580000000000000515e-01 1.399600000000000044e+01 --2.301807448343334173e+00 1.612585541633161645e-02 5.455842243101283628e+00 2.957947592947468562e-02 2.034000000000000252e+00 2.442000000000000171e+01 --2.309247900082923355e+00 6.212969016169677186e-03 5.489345801934415015e+00 2.936653293444493884e-02 2.681999999999999940e+00 3.007600000000000051e+01 --2.282512608118663966e+00 9.174697443147594028e-03 5.392086618636589890e+00 3.492633753073820513e-02 3.820000000000000284e+00 3.603200000000000358e+01 --2.302578073008834991e+00 -1.106055849164498325e-02 5.473419116004177631e+00 3.228570320455132620e-02 2.886000000000000121e+00 3.337199999999999989e+01 --2.300677420629393843e+00 -2.328931322869442350e-03 5.432499216646889728e+00 2.632965289303385720e-02 1.620000000000000107e+00 1.907199999999999918e+01 --2.278589774072178109e+00 4.369125745131018264e-03 5.380646406517455738e+00 3.632833975259130294e-02 2.796000000000000263e+00 3.140800000000000125e+01 --2.323001687716391483e+00 -1.144634391502279656e-02 5.522876245798714834e+00 2.337458751363698239e-02 2.315999999999999837e+00 2.308800000000000097e+01 --2.296959475118516281e+00 -7.622788125248224252e-03 5.437736338790847945e+00 3.061659382607830396e-02 1.588000000000000078e+00 2.059199999999999875e+01 --2.300009768099211982e+00 -2.227510304215109954e-03 5.466856089096286730e+00 3.342046713571800165e-02 1.834000000000000075e+00 2.176399999999999935e+01 --2.329456300509198385e+00 7.869631281041915630e-03 5.537863385472499900e+00 2.051227447928562209e-02 2.116000000000000103e+00 2.453600000000000136e+01 --2.339741578144009626e+00 4.284716108345597296e-03 5.596262696705922579e+00 2.225192715666192769e-02 2.466000000000000192e+00 2.770800000000000196e+01 --2.313509919754464850e+00 -2.758230277256511122e-03 5.494598830028643910e+00 2.657670590272963665e-02 1.451999999999999957e+00 1.517600000000000016e+01 --2.312293078149690650e+00 -1.013975661871660897e-02 5.476795508423743186e+00 2.427297355623481839e-02 2.588000000000000078e+00 2.944800000000000040e+01 --2.281499242538778116e+00 -1.802553079817147607e-03 5.377350530118873984e+00 3.306316450544486557e-02 1.717999999999999972e+00 1.798799999999999955e+01 --2.304503908687016711e+00 -1.510701018732584422e-03 5.512265077089821830e+00 3.794570461144975565e-02 1.816000000000000059e+00 2.926399999999999935e+01 --2.298633151628735494e+00 -7.978424575735568181e-03 5.444654622478456218e+00 3.042243902727954225e-02 2.383999999999999897e+00 2.124800000000000111e+01 --2.325305106278007905e+00 8.188170792148283857e-04 5.578622190376347767e+00 3.173199312735705546e-02 1.750000000000000000e+00 1.843599999999999994e+01 --2.287353108247291100e+00 6.490040949882030542e-03 5.430118897580299198e+00 3.784482161544673595e-02 2.374000000000000110e+00 2.734799999999999898e+01 --2.277727570087226372e+00 -1.281549178952986687e-02 5.364821964453886594e+00 3.397612789394520438e-02 1.997999999999999998e+00 2.154800000000000182e+01 --2.298136158689267017e+00 6.587920749614461363e-03 5.430737424192762397e+00 2.824495349530034560e-02 4.972000000000000419e+00 4.415200000000000102e+01 --2.338350632179468036e+00 1.629122123321520912e-02 5.602408498981871432e+00 2.445353507264919068e-02 2.116000000000000103e+00 2.794399999999999906e+01 --2.315747094553170626e+00 -7.035040977350364919e-03 5.537482247392427226e+00 3.256658589236993695e-02 2.044000000000000039e+00 2.719200000000000017e+01 --2.302699074460260231e+00 1.121166548857406564e-04 5.486358643311019634e+00 3.468896687753240254e-02 1.979999999999999982e+00 2.116799999999999926e+01 --2.307791842489954615e+00 4.052502879687570870e-04 5.432941926083381112e+00 2.009766821726849742e-02 4.004000000000000448e+00 4.014399999999999835e+01 --2.325260126974870722e+00 -5.425910972709018301e-03 5.546215676882290779e+00 2.576191618051609442e-02 1.862000000000000099e+00 2.138800000000000168e+01 --2.314914355973590965e+00 -1.407795102382517448e-02 5.524030699674630895e+00 3.071368439633601760e-02 2.153999999999999915e+00 2.422800000000000153e+01 --2.308225631451554793e+00 1.850739710730481616e-02 5.493448318201274994e+00 3.087205003970907094e-02 2.339999999999999858e+00 2.139199999999999946e+01 --2.285190578392066740e+00 1.023524076924352266e-02 5.381043473858227344e+00 3.037547746443877358e-02 3.918000000000000149e+00 3.810800000000000409e+01 --2.314736808656881362e+00 1.894829641160291744e-03 5.452402007284399055e+00 1.761561005243487271e-02 3.879999999999999893e+00 4.095199999999999818e+01 --2.341720217914095681e+00 -3.263128588585264417e-03 5.565585734191558664e+00 1.493524943247195348e-02 3.494000000000000217e+00 3.169200000000000017e+01 --2.286305011407650856e+00 7.943739160790486836e-03 5.406775680923338712e+00 3.431848584837471350e-02 1.967999999999999972e+00 2.124000000000000199e+01 --2.286201827670160114e+00 -6.150537226077871893e-03 5.463383738786981247e+00 4.525713484090689714e-02 7.179999999999999716e-01 1.674800000000000111e+01 --2.326511979959596577e+00 5.058629628561798347e-03 5.554992383624755448e+00 2.628202328102284546e-02 1.648000000000000131e+00 1.701600000000000179e+01 --2.292411578095236546e+00 2.724568155152667318e-03 5.446026529237533609e+00 3.631724624155394099e-02 2.298000000000000043e+00 2.701200000000000045e+01 --2.301700529840897680e+00 -5.303877935224915983e-03 5.586352034700774460e+00 5.444455016212267767e-02 4.560000000000000164e-01 2.400799999999999912e+01 --2.324208975814212597e+00 1.709926203064608382e-03 5.526847885941357674e+00 2.311972700632374672e-02 1.530000000000000027e+00 2.533999999999999986e+01 --2.308018107413654096e+00 -8.490021873762703189e-03 5.476480200074381521e+00 2.802924321259369148e-02 1.959999999999999964e+00 2.292000000000000171e+01 --2.327564103017883745e+00 1.887720843473926838e-02 5.562226788743783956e+00 2.650174652748595039e-02 1.842000000000000082e+00 2.233999999999999986e+01 --2.320465402180533765e+00 -7.754951216166821801e-03 5.539980528223225065e+00 2.882969689140312680e-02 2.446000000000000174e+00 2.643599999999999994e+01 --2.323693248237924003e+00 1.204326188742662999e-02 5.519626587339084622e+00 2.215582625739246844e-02 3.220000000000000195e+00 3.828800000000000381e+01 --2.333285828072439561e+00 1.588083641113617172e-03 5.556201214432104685e+00 2.056689124121799384e-02 2.294000000000000039e+00 2.961200000000000188e+01 --2.330880812362612353e+00 -3.176428864125670562e-03 5.571189642044672929e+00 2.542851194459694320e-02 1.802000000000000046e+00 2.217200000000000060e+01 --2.348322924072967055e+00 -3.844254325989188408e-03 5.628641814612917571e+00 2.066796915346887087e-02 2.758000000000000007e+00 4.223600000000000421e+01 --2.314836332724325985e+00 7.247677030686317315e-03 5.472747050360146304e+00 2.129692188371372710e-02 4.993999999999999773e+00 4.570799999999999841e+01 --2.331751817282111450e+00 6.565298375914504179e-03 5.581139665175906650e+00 2.647390695521278231e-02 2.085999999999999854e+00 2.887600000000000122e+01 --2.351868084870373021e+00 1.080995913705729873e-02 5.700792074541850774e+00 3.058011582534424927e-02 7.279999999999999805e-01 1.787199999999999989e+01 --2.312672763179051572e+00 4.064456907873105831e-03 5.565080652108426840e+00 4.049277101196006173e-02 1.808000000000000052e+00 2.303200000000000003e+01 --2.342240202455879938e+00 1.373374959324434900e-03 5.675986921324605916e+00 3.461334572596089232e-02 1.646000000000000130e+00 2.135600000000000165e+01 --2.327046763149403397e+00 3.354989210832207223e-03 5.581853895340891825e+00 3.077893569820204511e-02 1.989999999999999991e+00 2.367600000000000193e+01 --2.364171351933467946e+00 2.856479845292757974e-03 5.712041735482339178e+00 2.195452070556872665e-02 1.669999999999999929e+00 3.090000000000000213e+01 --2.290783809198869925e+00 -9.394197568942880619e-04 5.443427017273895885e+00 3.729903887827637488e-02 1.906000000000000139e+00 2.294800000000000040e+01 --2.321152213877837323e+00 -1.169719851301515706e-02 5.561752433452415545e+00 3.221775296735521210e-02 1.906000000000000139e+00 2.299600000000000222e+01 --2.350888596316976997e+00 4.794318808218346085e-03 5.688994839375830281e+00 2.935700063708605867e-02 -1.799999999999999933e-01 1.450399999999999956e+01 --2.302438837469278354e+00 2.680206538100846428e-02 5.547581933993472880e+00 4.604646286644972775e-02 2.145999999999999908e+00 2.619600000000000151e+01 --2.315471487401404627e+00 2.698545604985844518e-03 5.540317891040267284e+00 3.336569417794057330e-02 3.971999999999999975e+00 4.137599999999999767e+01 --2.339699382893897450e+00 -8.540976180386941966e-03 5.594718361772175186e+00 2.197611535740785771e-02 1.806000000000000050e+00 2.802800000000000225e+01 --2.304247823508657422e+00 -3.218474342724326272e-04 5.503928242286889372e+00 3.660754564360984425e-02 1.054000000000000048e+00 1.819600000000000151e+01 --2.344384071377190182e+00 -1.401300416700850980e-03 5.653780929943599709e+00 2.868163680602290114e-02 2.061999999999999833e+00 3.201200000000000045e+01 --2.320972505893196480e+00 9.005456757909067328e-03 5.525391598926787218e+00 2.566009020601094787e-02 3.930000000000000160e+00 4.166799999999999926e+01 --2.333529930886949266e+00 -8.700454246987567378e-03 5.626137110013712750e+00 3.315492089918182367e-02 1.973999999999999977e+00 2.395599999999999952e+01 --2.329163537687484187e+00 -1.193069719670897602e-02 5.609956600392457915e+00 3.401145743485873424e-02 4.359999999999999987e-01 9.583999999999999631e+00 --2.347600724924892912e+00 6.666634403055221418e-04 5.669901109047545518e+00 2.879041479861797759e-02 2.939999999999999836e-01 1.035599999999999987e+01 --2.349356432517049953e+00 -1.435979925027358606e-02 5.642603278511668208e+00 2.219327836846050200e-02 8.240000000000000657e-01 1.851999999999999957e+01 --2.313098590664940613e+00 5.745104968248561199e-03 5.592832811819161698e+00 4.528690969517236431e-02 1.400000000000000133e+00 2.206400000000000006e+01 --2.338493849468264330e+00 7.300647997355053098e-03 5.570791405699838883e+00 1.866582028735580892e-02 3.518000000000000238e+00 3.119600000000000151e+01 --2.298670081466239079e+00 6.980160687877033122e-03 5.491369172558970391e+00 3.923877175496136294e-02 1.636000000000000121e+00 1.583200000000000074e+01 --2.310107123625416925e+00 -5.210351928896264813e-03 5.506023527520190974e+00 3.173270204371416575e-02 8.040000000000000480e-01 2.142399999999999949e+01 --2.332240297111978666e+00 1.106784823170626911e-03 5.618667734804423830e+00 3.296704690364440221e-02 6.900000000000000577e-01 1.073200000000000109e+01 --2.331678952873777355e+00 1.497307462046207306e-03 5.636067183447965867e+00 3.666424327431011543e-02 5.000000000000000000e-01 1.056000000000000050e+01 --2.329457299246093349e+00 2.723758774745651699e-04 5.598410093747747673e+00 3.170416201136790763e-02 2.808000000000000274e+00 4.127199999999999847e+01 --2.355297263008757191e+00 7.406756351263946332e-03 5.727207975623031189e+00 3.237769974693729957e-02 7.399999999999999911e-01 1.404800000000000004e+01 --2.294795933910989127e+00 -4.579082056886477894e-04 5.455119668829426338e+00 3.589583488466330935e-02 1.969999999999999973e+00 1.694800000000000040e+01 --2.330433579943108846e+00 6.887481672440782729e-03 5.575845850109744539e+00 2.665829251667740582e-02 1.592000000000000082e+00 1.558399999999999963e+01 --2.371816014903194603e+00 1.594339000399667668e-04 5.783843811600408280e+00 2.814544648042834746e-02 3.080000000000000071e+00 4.487199999999999989e+01 --2.343699645876526905e+00 4.580807622247982415e-03 5.608122302414332516e+00 2.095967770528381693e-02 2.270000000000000018e+00 2.242800000000000082e+01 --2.356381655187294033e+00 -1.439846220487445193e-03 5.683294284031139121e+00 2.354841974942362831e-02 8.320000000000000728e-01 1.522400000000000020e+01 --2.359801657479541070e+00 8.912531629146408160e-04 5.678258663432790065e+00 1.968019144231284573e-02 1.334000000000000075e+00 1.530000000000000071e+01 --2.345501807315514053e+00 2.832307238718301365e-04 5.623088011244188777e+00 2.212337000516066340e-02 1.526000000000000023e+00 1.342800000000000082e+01 --2.324856466704976476e+00 -9.935393366225049247e-03 5.542469865959279041e+00 2.538569669318711461e-02 2.370000000000000107e+00 2.857199999999999918e+01 --2.340493344256870056e+00 -1.992994028209911506e-03 5.611060483377792174e+00 2.430474490639737695e-02 2.483999999999999986e+00 2.232799999999999940e+01 --2.323935113868535129e+00 4.591680924273920314e-03 5.607330332700819930e+00 3.825267604850222242e-02 -8.399999999999999689e-01 1.257600000000000051e+01 --2.358409685645401765e+00 5.203954264357925526e-03 5.684642604112464248e+00 2.201747697817554514e-02 2.221999999999999975e+00 3.451599999999999824e+01 --2.326171603105092078e+00 -1.531480496893701743e-03 5.583419587676806906e+00 3.184912824422756611e-02 7.740000000000000213e-01 1.901200000000000045e+01 --2.343907989188075636e+00 6.452629048041697880e-03 5.624726136102117913e+00 2.378883514827099740e-02 2.970000000000000195e+00 3.390800000000000125e+01 --2.338596753399119876e+00 -5.695288595986752744e-03 5.610006859665617185e+00 2.575815920488398400e-02 1.104000000000000092e+00 2.806400000000000006e+01 --2.338443846448488905e+00 4.715354847233702192e-03 5.667080919079851675e+00 3.633514169031455687e-02 4.780000000000000360e-01 1.542800000000000082e+01 --2.346784973772324978e+00 -9.256822879719137434e-03 5.637696983395469097e+00 2.361080287158571697e-02 2.080000000000000182e-01 1.541600000000000037e+01 --2.342177483897297741e+00 4.672287545283437121e-03 5.666125983705163627e+00 3.285995236859084317e-02 1.544000000000000039e+00 1.321600000000000108e+01 --2.354220775885808692e+00 -9.643169522967620644e-03 5.680495309137294946e+00 2.487280563435167319e-02 -2.280000000000000082e-01 8.448000000000000398e+00 --2.358707596169494991e+00 -2.120645288951095251e-03 5.666158391991515941e+00 1.844937526926988466e-02 9.779999999999999805e-01 2.217200000000000060e+01 --2.343259519526285750e+00 -6.028012074564054927e-04 5.609566459533443350e+00 2.161775352475808071e-02 3.316000000000000281e+00 2.680799999999999983e+01 --2.328534263182197694e+00 -6.879844929829188015e-03 5.584921083879017978e+00 3.000753496956527766e-02 4.740000000000000324e-01 1.792399999999999949e+01 --2.317755158054511266e+00 -1.795307122870000958e-03 5.569318652767077715e+00 3.673121008304801316e-02 4.939999999999999947e-01 1.615599999999999881e+01 --2.361549963151992504e+00 4.165472539997764202e-04 5.684709978711310896e+00 1.932809756868584389e-02 6.940000000000000613e-01 1.919600000000000151e+01 --2.347670754375685398e+00 3.078695767332838111e-03 5.686506709762492839e+00 3.173683414439648631e-02 -1.020000000000000073e-01 1.278800000000000026e+01 --2.344750834899162584e+00 -9.494022579864175304e-03 5.711900926319130711e+00 3.888124763417061258e-02 5.979999999999999760e-01 1.041200000000000081e+01 --2.340328218549899475e+00 3.720829010098543246e-04 5.623173019152826413e+00 2.666291610315934743e-02 7.599999999999999811e-02 5.232000000000000206e+00 --2.348709261834930118e+00 -4.305357178319360253e-03 5.687406057664412096e+00 3.098260443474592021e-02 5.020000000000000018e-01 1.699599999999999866e+01 --2.346231331889802707e+00 -4.241472121847549015e-03 5.666067740290895216e+00 2.928547516139571802e-02 8.579999999999999849e-01 1.449200000000000088e+01 --2.351201146949750687e+00 -1.102958261524922788e-02 5.699405483779694137e+00 3.091133577756435130e-02 -5.140000000000000124e-01 2.382799999999999940e+01 --2.437317427980747464e+00 8.646446875211244096e-03 6.167505365577248710e+00 3.817113922698715800e-02 -2.220000000000000195e+00 2.411200000000000188e+01 --2.322095679552504066e+00 -5.887143012531308520e-03 5.583510814272131029e+00 3.547296956631983134e-02 8.780000000000000027e-01 1.329199999999999982e+01 --2.350503201841142698e+00 4.019286326384424214e-03 5.658371852880722308e+00 2.415568685594147655e-02 2.439999999999999947e+00 2.193599999999999994e+01 --2.333684333061339267e+00 -3.901574513731086743e-04 5.574264026229748481e+00 2.353636597952881923e-02 2.512000000000000011e+00 2.396799999999999997e+01 --2.363547304261314874e+00 -4.752672755676912858e-03 5.684073460561365643e+00 1.747984821785495899e-02 1.370000000000000107e+00 1.119599999999999973e+01 --2.347593963902114389e+00 -1.208156260642738462e-05 5.702217868755753649e+00 3.466042575110347967e-02 3.220000000000000084e-01 1.850000000000000000e+01 --2.355606892459620294e+00 -1.007210313529208721e-02 5.686759592469402769e+00 2.479126801526278234e-02 -7.500000000000000000e-01 1.070000000000000107e+01 --2.366586264778976378e+00 -5.736609181106858829e-03 5.748667222785865505e+00 2.639572464112208139e-02 1.112000000000000099e+00 1.882400000000000162e+01 --2.374227433877428517e+00 3.741880116476976447e-03 5.779328910091795279e+00 2.524943229976142622e-02 8.980000000000000204e-01 2.973199999999999932e+01 --2.387236537391367097e+00 5.535076007229819493e-04 5.857915372354957739e+00 2.790296197186713234e-02 -1.740000000000000158e-01 1.567600000000000016e+01 --2.376227296320664095e+00 6.057987349657219765e-03 5.736926341937372165e+00 1.600265991278780262e-02 3.119999999999999996e-01 9.807999999999999829e+00 --2.363819242667829723e+00 5.360939548109763635e-03 5.713735878023924464e+00 2.255089272684502807e-02 1.743999999999999995e+00 2.573600000000000065e+01 --2.349914198134667398e+00 -9.131568703057561451e-03 5.673276942293540515e+00 2.733077887837554246e-02 6.660000000000000364e-01 1.837199999999999989e+01 --2.336893520276474678e+00 4.492917279041689846e-03 5.602071064928494160e+00 2.580768668256141346e-02 4.819999999999999840e-01 1.451600000000000001e+01 --2.341105859671548828e+00 3.190696104576409842e-03 5.688269006038139786e+00 3.785242046236772517e-02 -2.880000000000000338e-01 1.620800000000000196e+01 --2.357548052302018693e+00 4.031894589564080124e-03 5.663695851575138107e+00 1.900192760486137111e-02 2.072000000000000064e+00 2.096799999999999997e+01 --2.355623437615942617e+00 1.597929736020840819e-02 5.711548530762649456e+00 2.915831095328649467e-02 1.685999999999999943e+00 2.367600000000000193e+01 --2.334174798438728438e+00 -1.449734445169948739e-02 5.689061766898728223e+00 4.405562742950797778e-02 1.960000000000000075e-01 2.425600000000000023e+01 --2.354113620074492985e+00 -4.653138688337053394e-03 5.716633624966450000e+00 3.152659418232901106e-02 1.594000000000000083e+00 1.791600000000000037e+01 --2.337722964916856938e+00 -1.056408646407752498e-02 5.625170302641024023e+00 2.925499362413380364e-02 1.574000000000000066e+00 1.485999999999999943e+01 --2.363398646762446376e+00 5.127580929235216189e-03 5.709104198726619117e+00 2.208701698630885502e-02 3.880000000000000115e-01 5.080000000000000071e+00 --2.366507652059962385e+00 3.770206033153786045e-03 5.705256442404444073e+00 1.872282530614791107e-02 2.252000000000000224e+00 2.041600000000000037e+01 --2.337604380320996711e+00 -1.286795188149662545e-04 5.606244346198769435e+00 2.595897187073101242e-02 1.850000000000000089e+00 2.440399999999999991e+01 --2.368435886416865088e+00 9.488949502403741867e-03 5.738242412760505395e+00 2.290361241596707356e-02 3.400000000000000244e-01 1.914400000000000190e+01 --2.325506444847729171e+00 -8.733948563535220500e-04 5.620017321221437712e+00 3.920774655026380839e-02 -2.099999999999999922e-01 1.143599999999999994e+01 --2.335683926458668402e+00 -2.148745514439916963e-03 5.652622462307801854e+00 3.614547138827767930e-02 1.532000000000000028e+00 1.588799999999999990e+01 --2.332746348283930349e+00 4.233023958815661236e-03 5.640382062817338671e+00 3.649973683364966109e-02 -3.240000000000000102e-01 1.595199999999999996e+01 --2.347928585663234369e+00 -5.301544303478902646e-03 5.638520944756275632e+00 2.279545319537781140e-02 7.860000000000000320e-01 1.499600000000000044e+01 --2.357683580017666092e+00 7.982951967636636031e-03 5.773386613843670467e+00 3.859126641185171847e-02 -1.066000000000000059e+00 1.390000000000000036e+01 --2.377344316676983649e+00 7.646755675553520114e-03 5.770486535741308209e+00 2.097422917831723646e-02 1.193999999999999950e+00 2.229200000000000159e+01 --2.357683308454229021e+00 1.079940590598352755e-02 5.769194357313047306e+00 3.780771882939784612e-02 -9.979999999999999982e-01 1.359600000000000009e+01 --2.375296659846297231e+00 1.217065660491654412e-02 5.740888992155268156e+00 1.744098408424240090e-02 8.020000000000000462e-01 1.204400000000000048e+01 --2.361129591362768121e+00 -4.694855521232776615e-04 5.701718593561214021e+00 2.274197219314712942e-02 8.000000000000000167e-02 1.208000000000000007e+01 --2.367940249888257576e+00 7.045239313767701073e-03 5.770229711628788394e+00 2.905856100336064868e-02 1.092000000000000082e+00 1.704800000000000182e+01 --2.328843709785754168e+00 -7.324807876040737367e-03 5.630604969276757465e+00 3.815328588698536916e-02 2.459999999999999964e-01 1.094800000000000040e+01 --2.348427980749315580e+00 -2.203066175829279574e-03 5.660883686557023786e+00 2.642824082536109412e-02 3.860000000000000098e-01 1.164400000000000013e+01 --2.349321083339428462e+00 1.038704055184239443e-03 5.703560093689802990e+00 3.338229076330811312e-02 -6.920000000000000595e-01 1.085599999999999987e+01 --2.354360693106704705e+00 -9.109550463750537216e-03 5.753740005941695657e+00 3.796983243740409408e-02 1.616000000000000103e+00 2.567200000000000060e+01 --2.335767016311060651e+00 3.521238293251240884e-03 5.654792478996735205e+00 3.646506381411222797e-02 -1.120000000000000023e-01 1.159999999999999964e+01 --2.380991453865648477e+00 1.140009542330396725e-02 5.870978457379040449e+00 3.553538989811484694e-02 2.217999999999999972e+00 3.937199999999999989e+01 --2.356028567653558614e+00 3.925281681862908233e-03 5.711291276610830359e+00 2.889152298444658609e-02 1.933999999999999941e+00 2.000400000000000134e+01 --2.318402732433386237e+00 -4.821831187975995393e-03 5.589395353174030134e+00 3.987570999356050000e-02 2.459999999999999964e+00 2.516799999999999926e+01 --2.354439543663270573e+00 -1.707001480617957091e-04 5.697546754844720951e+00 2.780991840304980825e-02 7.239999999999999769e-01 1.664799999999999969e+01 --2.359303413724859855e+00 1.211798788756893392e-03 5.706997339465472940e+00 2.527350418520918698e-02 1.920000000000000040e-01 1.091999999999999993e+01 --2.378483809886512201e+00 -8.184737137740791951e-03 5.745115665783694148e+00 1.550706558558077007e-02 2.061999999999999833e+00 2.233999999999999986e+01 --2.379310339416319753e+00 -1.787670585418881658e-03 5.761960746796040311e+00 1.781155294263618571e-02 6.440000000000000169e-01 2.817600000000000193e+01 --2.353332379742617331e+00 -5.305333670682589944e-03 5.709044379948158721e+00 3.083761328322925238e-02 -4.720000000000000306e-01 1.532000000000000028e+01 --2.331985987558251594e+00 -3.265109970512901361e-03 5.613354952133572162e+00 3.221003730834305634e-02 2.097999999999999865e+00 1.953999999999999915e+01 --2.390616008571030182e+00 -1.362276638296616021e-03 5.773794177402058914e+00 1.027877354737293837e-02 -8.320000000000000728e-01 4.751999999999999780e+00 --2.367471287932341184e+00 -7.023953061585571376e-04 5.713537194481855153e+00 1.937857823851244637e-02 1.148000000000000131e+00 9.104000000000000981e+00 --2.351952695411871908e+00 -1.324808784367107958e-02 5.716155881180102760e+00 3.325034789916383321e-02 2.720000000000000195e-01 2.204800000000000182e+01 --2.379958735495375954e+00 1.148473095833042138e-03 5.758040250981288466e+00 1.656590276599045203e-02 1.799999999999999933e-01 8.096000000000000085e+00 --2.354750527364259938e+00 1.894594881148759684e-04 5.702058523905781939e+00 2.835214040741801389e-02 -4.660000000000000253e-01 1.241999999999999993e+01 --2.372382712892046719e+00 9.902692595423640345e-03 5.769850084282711400e+00 2.511438276991944524e-02 2.677999999999999936e+00 2.899600000000000222e+01 --2.361767453657763305e+00 4.351920761269608448e-04 5.718227797655050182e+00 2.514935111907306772e-02 3.260000000000000120e-01 1.220400000000000063e+01 --2.357316335895228931e+00 -1.696930111764761648e-03 5.691654342984244330e+00 2.424089155551328173e-02 2.680000000000000160e-01 1.232799999999999940e+01 --2.370056739781926769e+00 2.437914838637292650e-03 5.781667446370573948e+00 2.928168008516127130e-02 7.860000000000000320e-01 1.466000000000000014e+01 --2.395391975169860022e+00 5.148325737536915692e-03 5.881205647051704233e+00 2.496058898666919310e-02 4.275999999999999801e+00 5.273600000000000421e+01 --2.382514650238896525e+00 8.763720499187293081e-03 5.789675701090005511e+00 1.991845489272580511e-02 2.709999999999999964e+00 3.474799999999999756e+01 --2.385295597710583859e+00 9.212208726102706982e-03 5.821167354970274488e+00 2.307209353460996579e-02 3.411999999999999922e+00 2.924800000000000111e+01 --2.362643453786330117e+00 8.574229261477510702e-03 5.701869056232446553e+00 2.141846746171158916e-02 1.084000000000000075e+00 9.471999999999999531e+00 --2.381078985000173898e+00 -7.510750869842787274e-03 5.791558914944921810e+00 2.149186180373555827e-02 2.459999999999999964e-01 1.017200000000000060e+01 --2.346025302384834976e+00 -1.705818554447650339e-03 5.649723214939031735e+00 2.650507184787456033e-02 4.939999999999999947e-01 1.005199999999999960e+01 --2.369347094606490955e+00 -4.412730985239418820e-03 5.722776896971745408e+00 1.940068801248403391e-02 1.819999999999999951e-01 1.329199999999999982e+01 --2.329204502283888978e+00 -3.590252009337276118e-03 5.621488245351972779e+00 3.617466530330804009e-02 -1.219999999999999973e-01 1.113199999999999967e+01 --2.372452986042908663e+00 -4.204970526987628597e-03 5.741944480252798577e+00 2.013974013265331861e-02 1.138000000000000123e+00 1.723600000000000065e+01 --2.376143611405792999e+00 2.264779388963888192e-03 5.759020080652399898e+00 2.000438427452572512e-02 3.019999999999999907e-01 5.171999999999999709e+00 --2.315755212714034172e+00 -6.263507994410002014e-03 5.556052809250211055e+00 3.602809553540640974e-02 1.546000000000000041e+00 1.714000000000000057e+01 --2.364833703380197161e+00 4.509074348782857698e-03 5.729328408823542773e+00 2.446651449746079302e-02 3.250000000000000000e+00 3.216400000000000148e+01 --2.347896890071560883e+00 4.824763652041528551e-04 5.669672073189349071e+00 2.848945765370904104e-02 5.899999999999999689e-01 9.492000000000000881e+00 --2.358037822349499546e+00 -2.349946957289363557e-03 5.688145063563275095e+00 2.298163240431400772e-02 2.700000000000000178e-01 5.315999999999999837e+00 --2.353147214787413510e+00 9.091412951372231099e-03 5.655984999014097347e+00 2.138765752685256247e-02 1.213999999999999968e+00 1.085200000000000031e+01 --2.379143958595774766e+00 -1.229663806872298990e-03 5.810717148424648038e+00 2.656852566536538687e-02 1.020000000000000073e-01 1.642000000000000171e+01 --2.353646274926330051e+00 -3.742990428779665278e-03 5.683004278481672777e+00 2.586992919162070179e-02 1.199999999999999956e-01 1.583200000000000074e+01 --2.340153875916896720e+00 7.234785565169868891e-03 5.691814106349053048e+00 3.932033449407314196e-02 3.762000000000000011e+00 3.241199999999999903e+01 --2.378279954401985918e+00 -1.098438912132583198e-03 5.739117804185032590e+00 1.465619358210038317e-02 5.340000000000000302e-01 7.100000000000000533e+00 --2.351281992943327293e+00 1.566834461383309401e-03 5.684504560455009958e+00 2.821185048582326022e-02 -3.739999999999999991e-01 1.646000000000000085e+01 --2.366088919767649124e+00 9.744989810235388456e-04 5.714798076410319005e+00 2.079502624183603154e-02 -1.660000000000000087e-01 1.022799999999999976e+01 --2.350023764755909017e+00 -6.959176396438311075e-03 5.687714639172932962e+00 2.986871458146143216e-02 6.039999999999999813e-01 1.215200000000000102e+01 --2.374261339949507388e+00 -1.917550938246487735e-03 5.743473593538978683e+00 1.886521882266687863e-02 3.920000000000000151e-01 1.297600000000000087e+01 --2.379690282785307698e+00 1.460571380208315964e-02 5.781885813315112088e+00 2.089142451834596556e-02 -2.220000000000000029e-01 7.548000000000000043e+00 --2.337493336773225572e+00 -9.104112265303476704e-05 5.718410595008517561e+00 4.658515520434614032e-02 1.054000000000000048e+00 1.710000000000000142e+01 --2.351393233932662419e+00 -2.482769028533849450e-03 5.637223760296542707e+00 1.956118370684365587e-02 1.435999999999999943e+00 2.041600000000000037e+01 --2.358328701289403195e+00 -5.274737109929287723e-03 5.692599728816308158e+00 2.351793478871319620e-02 2.580000000000000071e-01 9.644000000000000128e+00 --2.395931359048956821e+00 5.812598950172618954e-03 5.830936182986361516e+00 1.573841200928860831e-02 2.068000000000000060e+00 1.764000000000000057e+01 --2.370082108723438274e+00 -4.385624276451271022e-03 5.734824774396063418e+00 2.091340858235982147e-02 1.459999999999999909e-01 1.104400000000000048e+01 --2.360910954754313007e+00 6.211237280111508302e-03 5.705087763147224322e+00 2.351472993803608788e-02 -4.740000000000000324e-01 8.788000000000000256e+00 --2.379345201855035619e+00 1.670090397725945697e-02 5.786106438143414188e+00 2.189745609951876740e-02 9.800000000000000377e-02 1.336400000000000077e+01 --2.381970555871714801e+00 -5.277372940092109853e-03 5.745146410935562109e+00 1.256270649559408821e-02 4.420000000000000040e-01 7.259999999999999787e+00 --2.363801183009297091e+00 -3.278801891754533088e-03 5.691459473930263968e+00 1.858962832209649571e-02 2.454000000000000181e+00 1.601200000000000045e+01 --2.373980838678893868e+00 1.686034944869092356e-03 5.758869243659355597e+00 2.183821887608021484e-02 -1.213999999999999968e+00 1.092399999999999949e+01 --2.381158118909360244e+00 -2.944231112727732375e-03 5.791559541836676317e+00 2.144988292641321348e-02 4.179999999999999827e-01 1.767600000000000193e+01 --2.378111292230746798e+00 -1.386576347926103767e-03 5.775938100533424269e+00 2.131035961798701320e-02 -1.332000000000000073e+00 1.322400000000000020e+01 --2.355357882968764471e+00 3.971215030840721631e-03 5.668338057882179370e+00 2.173490402795958884e-02 6.039999999999999813e-01 9.304000000000000270e+00 --2.348838145457806892e+00 4.046269695414227846e-03 5.688802858141734475e+00 3.112385610080498771e-02 9.959999999999999964e-01 1.143200000000000038e+01 --2.355386600800974506e+00 7.855675087686548458e-03 5.699254817789491945e+00 2.725717215650228994e-02 4.140000000000000346e-01 9.348000000000000753e+00 --2.362086933309741177e+00 3.222833220487955185e-03 5.744828944961588135e+00 2.963411130251603423e-02 -1.600000000000000033e-01 1.032799999999999940e+01 --2.352922648427473895e+00 1.931162087739963455e-03 5.667473721074932413e+00 2.370149415240772189e-02 7.960000000000000409e-01 1.443200000000000038e+01 --2.350488122982381078e+00 -8.227307710472078848e-04 5.673099688472420077e+00 2.684320462435216964e-02 1.090000000000000080e+00 1.178800000000000026e+01 --2.395599420976941563e+00 1.241674771153826115e-02 5.892935083359629012e+00 2.675838027859269580e-02 2.812000000000000277e+00 2.634400000000000119e+01 --2.344407718737350876e+00 1.654513677829235700e-03 5.640388281521365954e+00 2.622376464721240183e-02 3.002000000000000224e+00 2.190000000000000213e+01 --2.335068962636203782e+00 -7.801120998103024638e-03 5.668829180751147945e+00 3.963144328590484378e-02 1.940000000000000058e-01 1.405199999999999960e+01 --2.362104497151654936e+00 4.201724052134313790e-03 5.739479752123421541e+00 2.865606885786945932e-02 -7.680000000000000160e-01 7.520000000000000462e+00 --2.340779239932299305e+00 5.395975464448422333e-03 5.663472050273438363e+00 3.360576723481330241e-02 1.439999999999999947e+00 1.006400000000000006e+01 --2.367200652323929955e+00 -2.301714658312570532e-03 5.735694763705246224e+00 2.356318257355981619e-02 -1.518000000000000016e+00 9.131999999999999673e+00 --2.392161465736483805e+00 5.835457531261514438e-03 5.778341433345967282e+00 9.751405841040436395e-03 1.247999999999999998e+00 1.164000000000000057e+01 --2.371182736941165548e+00 1.007439174017754971e-02 5.748919692319627295e+00 2.242785844240877471e-02 3.343999999999999861e+00 3.161599999999999966e+01 --2.359107576381492155e+00 -6.079994286734493811e-03 5.705733965434773403e+00 2.519711116785026267e-02 -1.044000000000000039e+00 1.148799999999999955e+01 --2.363476724420877417e+00 -3.409752938991148993e-03 5.710312885567547347e+00 2.224391498035542883e-02 1.846000000000000085e+00 1.392399999999999949e+01 --2.339701032239197787e+00 2.826272931585423719e-03 5.637436772482510960e+00 2.981461159967035285e-02 1.832000000000000073e+00 1.714400000000000190e+01 --2.400515013056655267e+00 5.496083199495445035e-03 5.820188624632214314e+00 1.000000794845562133e-02 7.020000000000000684e-01 1.006799999999999962e+01 --2.369490241786258888e+00 -6.174683062076186460e-04 5.740408805129653125e+00 2.242835309915459929e-02 -9.320000000000000506e-01 1.180000000000000071e+01 --2.375012413736176775e+00 5.967434130369933358e-03 5.734753953710948871e+00 1.665779852154565879e-02 -3.099999999999999978e-01 6.588000000000000078e+00 --2.393094140840575701e+00 3.328910791622986809e-03 5.898523632148824802e+00 2.996208019732020042e-02 -1.334000000000000075e+00 2.053200000000000003e+01 --2.341222094321498748e+00 -5.558711003584859440e-04 5.659917317426570449e+00 3.258255970214971736e-02 6.260000000000000009e-01 9.435999999999999943e+00 --2.354103894713035494e+00 -2.972953661732436609e-03 5.682599043170631248e+00 2.540087632086824448e-02 8.860000000000000098e-01 1.554000000000000092e+01 --2.376594602432973602e+00 1.808876873731019887e-03 5.730827733745435637e+00 1.462693280757895557e-02 -1.002000000000000002e+00 4.155999999999999694e+00 --2.382283585589694219e+00 6.869246906256347603e-03 5.741945043010872496e+00 1.172220539784710538e-02 4.080000000000000293e-01 6.703999999999999737e+00 --2.370638348926697336e+00 -4.756288996732390209e-03 5.725658940474087188e+00 1.880160209045024858e-02 4.179999999999999827e-01 7.500000000000000000e+00 --2.398132076839689208e+00 5.032945242882756916e-03 5.795052332098046932e+00 7.640065259131230066e-03 1.600000000000000033e-01 9.295999999999999375e+00 --2.316386623204794937e+00 2.763830624449493956e-03 5.580678277040958868e+00 4.007111439644744227e-02 2.700000000000000178e-01 7.323999999999999844e+00 --2.380725225340210915e+00 -1.166670867702751004e-02 5.766849358146338922e+00 1.739306131665303151e-02 -5.420000000000000373e-01 1.379600000000000115e+01 --2.397830068279529492e+00 -4.518563706557228270e-03 5.857984347069885800e+00 1.884185171920606944e-02 2.256000000000000227e+00 2.919200000000000017e+01 --2.382635524551099948e+00 1.059005542520877370e-02 5.763127207012471054e+00 1.511966627775813629e-02 -7.640000000000000124e-01 4.791999999999999815e+00 --2.387061101408650465e+00 7.948566090114277810e-03 5.818299230214917017e+00 2.106769294259781822e-02 -8.020000000000000462e-01 6.124000000000000554e+00 --2.395377242438605503e+00 1.868783295343389925e-02 5.940717395643348553e+00 3.517018554042600220e-02 2.665999999999999925e+00 2.794000000000000128e+01 --2.399227266053841845e+00 -4.191207869619599166e-03 5.926609626665751307e+00 2.957874798413576145e-02 3.883999999999999897e+00 4.459199999999999875e+01 --2.376959087723035324e+00 2.591174119054911237e-03 5.743283090977655547e+00 1.651844121110217570e-02 4.919999999999999929e-01 4.592000000000000526e+00 --2.310030814065380245e+00 -8.631568186455969641e-04 5.589141975392331929e+00 4.739238873739586716e-02 -3.940000000000000169e-01 8.564000000000000057e+00 --2.337648541978885053e+00 -1.753936272780361660e-03 5.638416131975530377e+00 3.180578291079470821e-02 2.593999999999999861e+00 2.455600000000000094e+01 --2.349683287358413697e+00 9.973290333491242540e-03 5.808434278030484066e+00 5.200293455984705826e-02 8.940000000000000169e-01 1.666799999999999926e+01 --2.342624694147366515e+00 4.635324228896996537e-03 5.641188495923921131e+00 2.792179994065768778e-02 3.340000000000000191e-01 4.411999999999999922e+00 --2.365901718291569811e+00 -7.328537125461669251e-03 5.740908877793976295e+00 2.559230389524364338e-02 6.300000000000000044e-01 1.192399999999999949e+01 --2.340786039127402685e+00 9.373157728183432623e-04 5.640505025227365188e+00 2.942413093955953754e-02 8.760000000000000009e-01 1.504000000000000092e+01 --2.400304840676207530e+00 6.892827673110855057e-03 5.827095437388599031e+00 1.136654883819696385e-02 2.560000000000000053e-01 5.943999999999999950e+00 --2.364106623366295956e+00 -8.255067613504977336e-03 5.717397754833166701e+00 2.293585516017541265e-02 -3.619999999999999885e-01 7.243999999999999773e+00 --2.394151179190141754e+00 7.677695614137246055e-04 5.787059062424525280e+00 9.612315762650910922e-03 -7.799999999999999989e-02 4.120000000000000329e-01 --2.376199940808973565e+00 1.977909354078849925e-03 5.738957487606758612e+00 1.640348031592084310e-02 -1.199999999999999956e-01 8.455999999999999517e+00 --2.381547682230344964e+00 3.471612594615959557e-03 5.749662297780507636e+00 1.372698312677377887e-02 1.292000000000000037e+00 7.072000000000000064e+00 --2.324788922266183278e+00 4.917546334023097446e-03 5.586558698284187052e+00 3.364517493091793987e-02 6.300000000000000044e-01 9.044000000000000483e+00 --2.342511273967775587e+00 2.714922209392464994e-03 5.648028726130442045e+00 2.927581294512857438e-02 -1.680000000000000104e-01 5.911999999999999922e+00 --2.355798480543141782e+00 6.238736558070770953e-03 5.717984728383108894e+00 3.028547946945894104e-02 1.721999999999999975e+00 1.499600000000000044e+01 --2.355657071009516823e+00 4.694668179227714198e-03 5.704001784899061178e+00 2.789876185159329003e-02 4.380000000000000004e-01 5.195999999999999730e+00 --2.392793271049954207e+00 1.017221807070850699e-02 5.848792649299460855e+00 2.148577052954782352e-02 -9.160000000000000364e-01 1.343200000000000038e+01 --2.394939441462738294e+00 1.126732496680156806e-02 5.845576527770038666e+00 1.908272675930043974e-02 -9.360000000000000542e-01 8.960000000000000853e+00 --2.360257436652041019e+00 -3.711092923164963781e-03 5.776875355965347403e+00 3.698154359497213273e-02 -5.460000000000000409e-01 1.523600000000000065e+01 --2.360428215110417671e+00 -1.731514722943649793e-03 5.693263024857942334e+00 2.183071453478554330e-02 1.179999999999999938e+00 1.584800000000000075e+01 --2.335426823375810201e+00 -4.784710293869142415e-04 5.704592443037936000e+00 4.590451955323860550e-02 6.500000000000000222e-01 1.106000000000000050e+01 --2.372140307628872513e+00 -2.108439410900873369e-03 5.739925278695164224e+00 2.005705348275243702e-02 8.459999999999999742e-01 9.788000000000000256e+00 --2.377156359212782011e+00 -4.862197198325149232e-03 5.741243392001593726e+00 1.597965297301465540e-02 -5.919999999999999707e-01 7.400000000000000355e+00 --2.371661324637055035e+00 2.959621848264730112e-04 5.730742365630855595e+00 1.883890700985847710e-02 5.260000000000000231e-01 4.435999999999999943e+00 --2.356904234834082068e+00 -3.078357027140746129e-03 5.710655908324203445e+00 2.801605378700826668e-02 7.479999999999999982e-01 1.179199999999999982e+01 --2.338289993914747011e+00 -2.468553433103625946e-03 5.655924515412142028e+00 3.444024902492854451e-02 2.851999999999999869e+00 1.644800000000000040e+01 --2.368714533271754075e+00 -2.880645719359592547e-03 5.745815698818556250e+00 2.405743564697331374e-02 1.330000000000000071e+00 6.788000000000000256e+00 --2.378225555981545725e+00 -3.581760585486951261e-03 5.747243607801057586e+00 1.613302716505857215e-02 -1.100000000000000006e-01 3.540000000000000036e+00 --2.331335852644089268e+00 -5.551577166738126158e-03 5.661267479626883592e+00 4.158951972839019379e-02 -6.680000000000000382e-01 8.104000000000000981e+00 --2.365639105589828262e+00 -1.233084469361555915e-05 5.784375578536469220e+00 3.361666378358246082e-02 1.100000000000000006e-01 9.700000000000001066e+00 --2.357705583521262582e+00 3.421701191753011122e-03 5.702324733750229413e+00 2.581739109456764741e-02 -6.800000000000000488e-01 6.839999999999999858e+00 --2.369386211672805498e+00 -6.154434158847845761e-03 5.734723033454964813e+00 2.148488292596890253e-02 -3.780000000000000027e-01 1.553200000000000003e+01 --2.372150516855930924e+00 3.660846984988227852e-03 5.730861591847713044e+00 1.843269287768094927e-02 -4.319999999999999951e-01 1.703999999999999915e+01 --2.370270080313102490e+00 -1.606114956092391088e-03 5.761224323341066267e+00 2.545951311799486000e-02 -2.840000000000000302e-01 1.215200000000000102e+01 --2.373052235352294925e+00 1.213162582335358328e-02 5.847797913579683815e+00 3.834986143993886903e-02 -1.056000000000000050e+00 2.012800000000000011e+01 --2.384002079255741258e+00 9.216407130878238180e-03 5.771061093306972367e+00 1.536675564538022599e-02 -1.280000000000000027e-01 1.617600000000000193e+01 --2.369707827290951752e+00 7.996130343383115943e-03 5.713970317324902126e+00 1.749794163380915049e-02 -4.380000000000000004e-01 6.604000000000000092e+00 --2.345209169603199584e+00 6.056264423851534170e-03 5.684531381330812039e+00 3.352934616087070718e-02 5.800000000000000294e-02 1.169200000000000017e+01 --2.388906814563657388e+00 -2.717765180526404614e-03 5.792399465668331970e+00 1.498213903694118471e-02 -1.185999999999999943e+00 1.006000000000000050e+01 --2.340601885982999786e+00 2.266807607229592587e-03 5.663324919127442847e+00 3.374912653994262962e-02 -1.338000000000000078e+00 1.228400000000000070e+01 --2.405092161534652107e+00 2.062903107709583052e-03 5.828521183913736969e+00 7.613493962281627468e-03 -6.199999999999999956e-02 5.879999999999999671e-01 --2.383354903166244210e+00 4.776594629451008135e-03 5.766608113405467861e+00 1.516765142697751312e-02 1.506000000000000005e+00 8.012000000000000455e+00 --2.365534662224474172e+00 -1.278453267095622020e-03 5.728398315678355779e+00 2.370351739742580441e-02 1.495999999999999996e+00 1.887199999999999989e+01 --2.359261612205122205e+00 -8.339633769391428114e-03 5.773510538491589017e+00 3.722142862404411584e-02 -1.965999999999999970e+00 1.011599999999999966e+01 --2.390679011851156055e+00 -4.763410914966813292e-03 5.831714842292081258e+00 2.034859237433285506e-02 1.522000000000000020e+00 1.229199999999999982e+01 --2.373368753132533371e+00 -4.651477439182393793e-03 5.821144014711688186e+00 3.341056867978559053e-02 9.899999999999999911e-01 1.230799999999999983e+01 --2.383906632187035690e+00 2.231225784740076615e-03 5.784192502177710971e+00 1.780156209615470567e-02 1.650000000000000133e+00 1.586000000000000121e+01 --2.332478165463009567e+00 8.285436870949061975e-04 5.657811633004299345e+00 3.995164433598052262e-02 2.616000000000000103e+00 2.006400000000000006e+01 --2.353130005052488372e+00 4.709935645303470544e-03 5.638972947411823533e+00 1.836378881467281773e-02 1.282000000000000028e+00 8.067999999999999616e+00 --2.380261072258433863e+00 6.648369641388648032e-04 5.763339936721544099e+00 1.724355375943121063e-02 1.747999999999999998e+00 7.576000000000000512e+00 --2.381284736519201140e+00 -4.416891888583337165e-03 5.764057366038279007e+00 1.648542413411784729e-02 -1.382000000000000117e+00 9.460000000000000853e+00 --2.379567206827042369e+00 1.796336849056934509e-03 5.771335557339667410e+00 1.924744839690719495e-02 7.800000000000000266e-01 8.983999999999999986e+00 --2.373579042118538318e+00 -1.477866639145356421e-03 5.724449904784337129e+00 1.607521258553686397e-02 6.280000000000000027e-01 4.975999999999999979e+00 --2.373606788515007171e+00 3.702840696727357009e-03 5.757243023151387362e+00 2.186574426125309500e-02 6.940000000000000613e-01 7.347999999999999865e+00 --2.357743283350837604e+00 -1.061837655767376102e-03 5.702898145886001302e+00 2.589359462350422636e-02 -4.560000000000000164e-01 1.178400000000000070e+01 --2.369989187470173064e+00 -1.312377631460410858e-03 5.718799599844607506e+00 1.814996181870989420e-02 -3.880000000000000115e-01 7.152000000000000135e+00 --2.369271231279570511e+00 8.069247836124252341e-05 5.720438238622928218e+00 1.905995856337227082e-02 1.366000000000000103e+00 1.239600000000000080e+01 --2.372962744751072606e+00 5.906179302912814739e-03 5.752025643871768956e+00 2.148243387618058858e-02 9.619999999999999662e-01 9.875999999999999446e+00 --2.360494661583903309e+00 -1.029413446214772236e-03 5.769855086592969862e+00 3.552028972802734330e-02 -1.538000000000000034e+00 1.448399999999999999e+01 --2.381726224757857224e+00 -2.210525708199315240e-03 5.795516396141644933e+00 2.166223257034544450e-02 -9.040000000000000258e-01 5.592000000000000526e+00 --2.392012904303186360e+00 1.165687356521129996e-03 5.759915411709112476e+00 6.673786099005551281e-03 -3.280000000000000138e-01 2.800000000000000266e+00 --2.356099537276232336e+00 2.294818871752471543e-03 5.692867684644913773e+00 2.551634331898667077e-02 8.100000000000000533e-01 1.426800000000000068e+01 --2.371725041995785599e+00 -2.665525959400254306e-03 5.786393532142444229e+00 2.867371492153414012e-02 -1.779999999999999916e-01 1.282000000000000028e+01 --2.363729335718355973e+00 3.246138357409565460e-03 5.721784490682130908e+00 2.407920790145765336e-02 3.780000000000000027e-01 1.105199999999999960e+01 --2.387212211598621625e+00 3.584958840079261865e-03 5.784937166575475409e+00 1.511127863309226146e-02 -2.740000000000000213e-01 3.060000000000000053e+00 --2.349179847414863964e+00 -3.085082249972876441e-03 5.662467188889829472e+00 2.605565519369682989e-02 2.280000000000000082e-01 8.951999999999999957e+00 --2.366894043321051466e+00 -5.294054327440860311e-03 5.723050902615105962e+00 2.155900670707242006e-02 6.039999999999999813e-01 9.008000000000000895e+00 --2.385257454696340762e+00 1.168700813440849565e-03 5.788548800015615114e+00 1.741670134164563510e-02 1.298000000000000043e+00 1.438799999999999990e+01 --2.349192988919776681e+00 -6.208478623649119239e-03 5.690727345828180184e+00 3.114867055503835191e-02 1.116000000000000103e+00 1.040000000000000036e+01 --2.366384541715665701e+00 1.601606294623034729e-03 5.712030586756259076e+00 2.004489854986217165e-02 9.360000000000000542e-01 8.320000000000000284e+00 --2.357561249301436845e+00 -2.673411717171096918e-03 5.709773103173491293e+00 2.728561337825553476e-02 1.590000000000000080e+00 1.075600000000000023e+01 --2.372995472308527809e+00 -8.443047043153463840e-03 5.783708331426522520e+00 2.706060461984338694e-02 -1.594000000000000083e+00 1.352400000000000091e+01 --2.383987875113305677e+00 5.099711499489997801e-03 5.755552913704276463e+00 1.268179907884256150e-02 -2.600000000000000228e-02 2.100000000000000089e+00 --2.365826790936995216e+00 2.542130439232538879e-03 5.721478811224033123e+00 2.221182039894979351e-02 3.599999999999999867e-01 1.070400000000000063e+01 --2.347725084147820329e+00 -1.917209895430562177e-03 5.690695358027362261e+00 3.245228022966165082e-02 -6.079999999999999849e-01 1.198399999999999999e+01 --2.390707567461718419e+00 2.243540336573996135e-03 5.801137562702486150e+00 1.498378488441215635e-02 1.360000000000000098e-01 1.228000000000000114e+01 --2.395163601310406953e+00 5.339078621217587710e-04 5.817157575873723729e+00 1.400570181168082906e-02 1.574000000000000066e+00 1.338799999999999990e+01 --2.357738514946559505e+00 -2.440679930349178624e-03 5.717026696030877098e+00 2.843665713920330920e-02 1.231999999999999984e+00 1.812000000000000099e+01 --2.386895779697750797e+00 -7.503879129925989863e-03 5.817954800540346305e+00 2.115237761530244440e-02 -7.840000000000000302e-01 9.263999999999999346e+00 --2.371856404962950471e+00 -1.004164137317931646e-03 5.759248138427730979e+00 2.373787603596944421e-02 1.368000000000000105e+00 1.455199999999999960e+01 --2.394788160121776865e+00 -3.698016023064320569e-03 5.806977411016652546e+00 1.254148368862501028e-02 -2.704000000000000181e+00 1.436800000000000033e+01 --2.348387560572134269e+00 -7.357092059153488503e-03 5.660776467267585765e+00 2.641662095925543380e-02 -1.788000000000000034e+00 9.791999999999999815e+00 --2.355948349744879877e+00 6.655372613527359832e-05 5.691304401180122596e+00 2.536923663544859639e-02 2.216000000000000192e+00 1.205600000000000094e+01 --2.369342333428804626e+00 -9.168806523417560861e-03 5.754956968549965524e+00 2.510167143426619146e-02 -1.272000000000000020e+00 8.056000000000000938e+00 --2.354839948887824885e+00 -2.838229197308744702e-03 5.758932560569747672e+00 3.852584857358504200e-02 -9.759999999999999787e-01 1.228000000000000114e+01 --2.345352014003200924e+00 2.294846760096356381e-02 5.688962974058449973e+00 3.393277240884316759e-02 7.620000000000000107e-01 1.193200000000000038e+01 --2.371153215425791494e+00 7.849825537201688894e-03 5.745401636675979695e+00 2.184936559175966464e-02 1.245999999999999996e+00 8.284000000000000696e+00 --2.357439933938747956e+00 1.180778437709334612e-02 5.703689970240700902e+00 2.622349431523173305e-02 2.508000000000000007e+00 1.860800000000000054e+01 --2.402313446150412979e+00 -2.270066517622867583e-03 5.889776527799277517e+00 2.055945198876098223e-02 -2.072000000000000064e+00 1.524000000000000021e+01 --2.387997834076041492e+00 -4.412473002575763477e-03 5.771589820537227133e+00 1.209936712499999102e-02 1.159999999999999920e+00 6.991999999999999993e+00 --2.373491983400488614e+00 -1.056560958861646124e-02 5.808731068099683092e+00 3.105044474400700180e-02 -7.379999999999999893e-01 1.747599999999999909e+01 --2.376233933942418108e+00 5.468275395133372074e-03 5.743696750459809763e+00 1.719968181644258853e-02 1.437999999999999945e+00 1.516399999999999970e+01 --2.355848491158237135e+00 -1.076989966855076020e-03 5.684807331531474439e+00 2.428488594456384986e-02 5.640000000000000568e-01 1.527200000000000024e+01 --2.369128981967695058e+00 -3.176933099501873161e-03 5.764890663977344509e+00 2.709666951200500121e-02 1.799999999999999933e-01 2.135999999999999943e+01 --2.396048838902055778e+00 1.299336759293148735e-02 5.850606491536782805e+00 1.899309876845692996e-02 -7.299999999999999822e-01 1.004400000000000048e+01 --2.350099190116712311e+00 -1.624843273011658800e-03 5.700329413558035796e+00 3.211227969663178056e-02 9.959999999999999964e-01 6.280000000000000249e+00 --2.397731412498610215e+00 -5.061466041846717639e-03 5.816528001965891370e+00 1.171211720696439286e-02 -4.599999999999999922e-02 1.059600000000000009e+01 --2.376604990632090963e+00 -1.005305197779845713e-02 5.755194983814628351e+00 1.887925555001118000e-02 9.460000000000000631e-01 7.988000000000000433e+00 --2.356344510948009230e+00 -7.004340452383919129e-04 5.702617294026082639e+00 2.706170761004942846e-02 -6.159999999999999920e-01 3.304000000000000270e+00 --2.380250171286000249e+00 6.534867840045179878e-03 5.742987863533567605e+00 1.363796385695188393e-02 7.399999999999999634e-02 7.996000000000000441e+00 --2.355253833432604083e+00 -1.011463862843511863e-02 5.677297372188365721e+00 2.339237181630767631e-02 1.392000000000000126e+00 8.272000000000000242e+00 --2.359071949202510954e+00 7.460730582853656451e-03 5.660258093636714172e+00 1.704654765266292935e-02 7.200000000000000844e-02 1.368000000000000105e+00 --2.298016782254275636e+00 1.123859113446435201e-02 5.567306517005634170e+00 5.416253929588069060e-02 1.606000000000000094e+00 1.162000000000000099e+01 --2.407388803925008869e+00 4.473292172854977967e-03 5.914617526617803378e+00 2.053920813465268808e-02 -1.167999999999999927e+00 1.216000000000000014e+01 --2.351563024861232254e+00 2.776731856302080731e-04 5.687864640588370158e+00 2.857505738322714886e-02 3.059999999999999942e-01 1.278800000000000026e+01 --2.387124957334662678e+00 6.099261283939398821e-03 5.796573113464615901e+00 1.721441443796850601e-02 1.384000000000000119e+00 8.535999999999999588e+00 --2.383812797142911943e+00 -7.373736989781552384e-03 5.771017466661641393e+00 1.553671387859597089e-02 1.536000000000000032e+00 1.033600000000000030e+01 --2.381935150899762377e+00 -8.597048403555185292e-03 5.755730724821448874e+00 1.443360694328188649e-02 5.280000000000000249e-01 1.333600000000000030e+01 --2.352792719163796065e+00 1.733874927437341600e-03 5.663443654005714478e+00 2.308694129222283245e-02 1.839999999999999969e-01 6.000000000000000000e+00 --2.366100446808739211e+00 -1.453042793646217631e-03 5.704745877998401049e+00 1.898890835147006712e-02 3.699999999999999956e-01 1.098000000000000043e+01 --2.383143195086617094e+00 -6.957677721282750326e-03 5.812382379165572210e+00 2.339383225578585412e-02 -5.799999999999999600e-01 1.795200000000000173e+01 --2.385155709710105487e+00 -6.758367583444705243e-03 5.763082895110648529e+00 1.300347071208085917e-02 2.315999999999999837e+00 1.664000000000000057e+01 --2.379604260288922912e+00 -4.849008485340622863e-03 5.742284902007754432e+00 1.407447298192193545e-02 1.421999999999999931e+00 7.708000000000000185e+00 --2.342439379168715696e+00 -7.868242871530761740e-03 5.660261132195140377e+00 3.153756106060126574e-02 4.640000000000000235e-01 1.270400000000000063e+01 --2.375408136217613819e+00 3.536170301917322678e-03 5.755244120509797945e+00 1.996291900785076429e-02 1.344000000000000083e+00 1.220800000000000018e+01 --2.371625768361721676e+00 -3.534059833709633867e-03 5.729913708919868398e+00 1.871539118392159806e-02 1.116000000000000103e+00 8.807999999999999829e+00 --2.387669782833040433e+00 -6.223173231833067746e-04 5.842153200092587539e+00 2.476509999631421391e-02 -9.779999999999999805e-01 1.924399999999999977e+01 --2.378567276558115839e+00 6.092302660578492041e-03 5.797788338494846094e+00 2.476180382024520746e-02 3.160000000000000031e-01 1.021600000000000108e+01 --2.351241079046044735e+00 -2.028547563636425022e-02 5.793052072013174403e+00 4.764979420370805269e-02 -5.040000000000000036e-01 1.291999999999999993e+01 --2.379184175332853979e+00 -4.103757554447176083e-03 5.774346360229881903e+00 2.010019138610868311e-02 -6.380000000000000115e-01 1.447600000000000087e+01 --2.381447096370375327e+00 -6.463483615266846054e-03 5.773614645781672827e+00 1.802002339735766720e-02 1.004000000000000004e+00 1.440799999999999947e+01 --2.405471320852365480e+00 -6.703675182494035160e-04 5.935135935965743847e+00 2.572325602989404200e-02 2.494000000000000217e+00 2.419600000000000151e+01 --2.399878616577332036e+00 1.094917298313919079e-03 5.809020025261221853e+00 8.611812658696650982e-03 8.080000000000000515e-01 6.823999999999999844e+00 --2.337431994835311500e+00 -2.422531176230924722e-03 5.634924546074774554e+00 3.135632613144640618e-02 1.016000000000000014e+00 1.154400000000000048e+01 --2.361289222131505827e+00 -2.591427570087830989e-04 5.689635623170654632e+00 2.043669799155377331e-02 -9.619999999999999662e-01 4.908000000000000362e+00 --2.394901226209077638e+00 -1.566519099322758509e-03 5.785321406031732394e+00 8.676078243765076095e-03 4.319999999999999951e-01 4.751999999999999780e+00 --2.353668798265946993e+00 5.347631528030164991e-03 5.702124362342416930e+00 2.929356841562712546e-02 -1.175999999999999934e+00 5.320000000000000284e+00 --2.356863553699302116e+00 2.633963473264344830e-03 5.717392615552723711e+00 2.926571835139963468e-02 6.360000000000000098e-01 1.384800000000000075e+01 --2.325560636361883482e+00 -3.656508731605878897e-03 5.614867852377757096e+00 3.819990082306852497e-02 -2.999999999999999889e-02 1.045199999999999996e+01 --2.358065998357889548e+00 -9.501941879466700713e-03 5.816652759257759264e+00 4.602019847681656367e-02 6.600000000000000311e-01 1.050399999999999956e+01 --2.379907399437138693e+00 -3.546994932173957310e-03 5.750388150431678724e+00 1.525268768837525005e-02 -3.699999999999999956e-01 7.508000000000000007e+00 --2.391215256170429182e+00 1.270876667204517627e-02 5.900361381868539645e+00 3.182124098937878093e-02 -1.268000000000000016e+00 1.500000000000000000e+01 --2.391356951506720563e+00 4.191135130974623854e-03 5.772677525953969990e+00 9.449231309194941128e-03 1.180000000000000077e-01 3.084000000000000075e+00 --2.358149170499051372e+00 -6.370036831664695372e-03 5.695855163857738823e+00 2.425214549642990686e-02 3.920000000000000151e-01 1.048799999999999955e+01 --2.370463764256446115e+00 1.060701576894348616e-02 5.720941640426450370e+00 1.806331588048778677e-02 8.419999999999999707e-01 7.323999999999999844e+00 --2.375296587301002571e+00 -5.578680989222874545e-03 5.778190539637087397e+00 2.411560221752227090e-02 8.040000000000000480e-01 1.543999999999999950e+01 --2.371914713801918317e+00 8.719593590539308247e-05 5.746430293539647849e+00 2.140975853687111102e-02 8.960000000000000187e-01 1.021600000000000108e+01 --2.399497547761735738e+00 4.458397785314090027e-03 5.947949471658680487e+00 3.305192571199905976e-02 -1.933999999999999941e+00 2.040399999999999991e+01 --2.359792593910574166e+00 -1.639129390506002121e-03 5.682537059680234925e+00 2.045528803720862362e-02 7.780000000000000249e-01 7.148000000000000576e+00 --2.402251138528584296e+00 1.135819575487929814e-03 5.915077904722348734e+00 2.499881157683056521e-02 1.715999999999999970e+00 2.048799999999999955e+01 --2.373885078801976523e+00 2.769841951361783072e-03 5.779074956530436680e+00 2.550355998581435232e-02 -8.539999999999999813e-01 7.692000000000000171e+00 --2.367671699008085273e+00 -6.833044450800670154e-03 5.726565625097110868e+00 2.150482995997766988e-02 -2.800000000000000266e-01 9.048000000000000043e+00 --2.375880629816579326e+00 -2.591207406999398478e-03 5.745766113592988056e+00 1.788135742659718169e-02 4.380000000000000004e-01 1.311599999999999966e+01 --2.394240061367353789e+00 1.036111844810099977e-02 5.842550364401295049e+00 1.916072394270894666e-02 -2.780000000000000249e-01 7.524000000000000021e+00 --2.346359094829970182e+00 2.047386558433763638e-03 5.658837906366846582e+00 2.786790255336747332e-02 1.973999999999999977e+00 1.397199999999999953e+01 --2.369239752223060602e+00 -2.094839537774794130e-03 5.712817341978473351e+00 1.772700428164014977e-02 -1.360000000000000098e-01 6.871999999999999886e+00 --2.399595465341029410e+00 2.044363680031917492e-03 5.971515807315022961e+00 3.706881595200588186e-02 2.133999999999999897e+00 2.263599999999999923e+01 --2.371129192709158673e+00 -1.642709628638195545e-03 5.725526553172253230e+00 1.836712943412465229e-02 2.139999999999999958e-01 6.556000000000000050e+00 --2.407095911718217351e+00 4.535556434932017100e-03 5.880597003245613408e+00 1.491577300930267171e-02 -1.407999999999999918e+00 1.074399999999999977e+01 --2.373478832553735707e+00 -2.233961272986689697e-03 5.736774608151469224e+00 1.834727884837109024e-02 -3.200000000000000067e-02 7.360000000000000320e+00 --2.394526667124055486e+00 -1.098397410748013815e-02 5.804813110716223967e+00 1.232851754182451645e-02 -2.458000000000000185e+00 1.350800000000000090e+01 --2.351312189764286575e+00 4.823818748046245289e-03 5.712919822408903947e+00 3.331338421605275352e-02 1.876000000000000112e+00 1.528800000000000026e+01 --2.350108586347127826e+00 4.280545173579133021e-03 5.698381626138245615e+00 3.174257018019639720e-02 -3.900000000000000133e-01 6.435999999999999943e+00 --2.351335971060722230e+00 -4.243624357492013083e-03 5.689123529426670878e+00 2.899139854878225731e-02 1.554000000000000048e+00 8.612000000000000099e+00 --2.376378961215054986e+00 -9.742388702587622892e-03 5.758850473913439849e+00 1.972368533217747077e-02 1.231999999999999984e+00 1.541600000000000037e+01 --2.382450829997151853e+00 1.824764585507012912e-02 5.853338450928099235e+00 3.104901925258818363e-02 1.440000000000000169e-01 1.278400000000000070e+01 --2.377708861891827841e+00 -9.709506217113290580e-03 5.755870289822601293e+00 1.805658997043360983e-02 -9.100000000000000311e-01 1.606800000000000139e+01 --2.350765296700843887e+00 9.486788947873176989e-03 5.721809576469142122e+00 3.536538124218377432e-02 -1.378000000000000114e+00 1.362800000000000011e+01 --2.355938292261654077e+00 6.219747900978767584e-03 5.665265257561740597e+00 2.066529089128752578e-02 1.231999999999999984e+00 1.232000000000000028e+01 --2.386087782102388033e+00 1.146764823694229087e-02 5.768616463561008878e+00 1.313830880234875299e-02 5.859999999999999654e-01 2.756000000000000227e+00 --2.362948634232306944e+00 6.262804287698019992e-04 5.703114125252685795e+00 2.141776899342587304e-02 -2.880000000000000338e-01 4.919999999999999929e+00 --2.342769768721042922e+00 1.541931204900395813e-02 5.632851531966856840e+00 2.615423963585227635e-02 1.114000000000000101e+00 8.859999999999999432e+00 --2.382681950280033600e+00 -4.672803643466444737e-03 5.750282847291724231e+00 1.286612529279694377e-02 -4.979999999999999982e-01 3.012000000000000011e+00 --2.344817531848029102e+00 6.638707440181642423e-04 5.655122300701829197e+00 2.854617160157612091e-02 2.380000000000000171e-01 3.588000000000000078e+00 --2.393429261675540598e+00 -2.637117881056514224e-03 5.793636407904870111e+00 1.136626266050110891e-02 -1.638000000000000123e+00 8.428000000000000824e+00 --2.407055018178042793e+00 9.586924167280120451e-03 5.857873025832769365e+00 1.099091272209613661e-02 -3.280000000000000138e-01 6.903999999999999915e+00 --2.373922552058090663e+00 -4.950526293255644826e-04 5.754494551052546925e+00 2.111353779448692236e-02 5.240000000000000213e-01 8.912000000000000810e+00 --2.375590007661510406e+00 -1.079419323866223634e-03 5.756167651914251060e+00 1.997654695945527692e-02 1.288000000000000034e+00 1.094400000000000084e+01 --2.404545757331269407e+00 1.669981301177784691e-02 5.855693482156437923e+00 1.262676056958730690e-02 -7.079999999999999627e-01 5.136000000000000121e+00 --2.360766992609961701e+00 2.891282717646573904e-03 5.721072411580289341e+00 2.652431688489266179e-02 1.140000000000000124e+00 1.220000000000000107e+01 --2.369960379060665367e+00 -1.298112325394504014e-03 5.720367610977080908e+00 1.845390335507974405e-02 2.860000000000000320e-01 6.259999999999999787e+00 --2.368583999700879517e+00 -5.442442027755391327e-04 5.716552735416011721e+00 1.895865616361250630e-02 1.312000000000000055e+00 7.983999999999999986e+00 --2.383884011408669679e+00 -1.282075941319246390e-02 5.814099513403264474e+00 2.299741145735584649e-02 4.700000000000000289e-01 1.514000000000000057e+01 --2.374711005433610911e+00 -3.459875773855594899e-03 5.736584538111491938e+00 1.725328831837730573e-02 8.579999999999999849e-01 8.060000000000000497e+00 --2.364114254418971939e+00 2.908412604717645292e-03 5.722997126100827892e+00 2.396386933368151867e-02 1.582000000000000073e+00 1.237199999999999989e+01 --2.401269424236140093e+00 -3.974056093672789260e-03 5.828507975508447458e+00 1.081585325855637277e-02 1.084000000000000075e+00 1.325600000000000023e+01 --2.379151670711502575e+00 -7.090274352981351322e-03 5.762448621342115551e+00 1.800810677610511709e-02 -1.189999999999999947e+00 1.185200000000000031e+01 --2.364782769483876557e+00 -8.823551625177034063e-03 5.781863963497108294e+00 3.387307651749744269e-02 -6.440000000000000169e-01 8.775999999999999801e+00 --2.378263250025653086e+00 3.052473987306615361e-03 5.810679006239209521e+00 2.731797838428148481e-02 1.200000000000000025e-02 2.213599999999999923e+01 --2.325986487366461297e+00 -1.533047771457947926e-03 5.671112425328799667e+00 4.822211038347058026e-02 -1.332000000000000073e+00 9.695999999999999730e+00 --2.377413231773836788e+00 -2.651615606901885046e-03 5.750201091009818022e+00 1.735391569250507859e-02 -3.940000000000000169e-01 7.652000000000000135e+00 --2.348558675106007687e+00 -2.531843235326707107e-03 5.675174864411485665e+00 2.890411415359172079e-02 5.340000000000000302e-01 8.364000000000000767e+00 --2.368711528372671626e+00 3.926874127617912234e-03 5.796775699880033272e+00 3.313855239013653586e-02 2.680000000000000160e-01 1.105600000000000094e+01 --2.358188483670696112e+00 6.268850465641103223e-03 5.728312512754990315e+00 3.005512634763895727e-02 9.480000000000000648e-01 8.464000000000000412e+00 --2.341526851493220818e+00 5.647908232422636787e-03 5.726656644400537566e+00 4.446833877034339633e-02 -1.720000000000000140e-01 1.682400000000000162e+01 --2.391391526377646404e+00 1.234375424276903986e-03 5.778877551665067891e+00 1.051269316658985480e-02 1.372000000000000108e+00 1.056000000000000050e+01 --2.387942022709913292e+00 -5.609319368876775243e-03 5.817510453298375239e+00 2.019320511876577726e-02 -9.699999999999999734e-01 1.379600000000000115e+01 --2.360040594940492564e+00 3.581410177435799275e-03 5.724596041754070441e+00 2.778647640747805569e-02 7.680000000000000160e-01 1.706400000000000006e+01 --2.367575549050107586e+00 6.400749772314136103e-03 5.745888679385279474e+00 2.503806355707520470e-02 2.048000000000000043e+00 1.289600000000000080e+01 --2.350477604961477951e+00 -3.666802078643378524e-03 5.675089934674659276e+00 2.720551450059060725e-02 6.920000000000000595e-01 1.132000000000000028e+01 --2.381207005981227809e+00 1.221854590995719893e-03 5.756325398000610605e+00 1.519785091455112640e-02 -7.800000000000000266e-01 9.192000000000000171e+00 --2.381487690029552073e+00 -1.586338577909419324e-05 5.751086516661494841e+00 1.403563926101453196e-02 8.699999999999999956e-01 5.171999999999999709e+00 --2.375763386279801992e+00 3.440462221721323193e-03 5.794305324545247160e+00 2.657875862542507031e-02 3.084000000000000075e+00 2.799200000000000088e+01 --2.345943692729917540e+00 -1.858012037054450685e-03 5.646891055711466656e+00 2.606157456681962303e-02 7.520000000000000018e-01 5.152000000000000135e+00 --2.386422479041097944e+00 2.353722465270085412e-03 5.785173931069316211e+00 1.582872793586998991e-02 3.059999999999999942e-01 7.012000000000000455e+00 --2.351634579646795231e+00 -2.546711234900251057e-04 5.670215530150985117e+00 2.532105697978535852e-02 -1.499999999999999944e-01 6.988000000000000433e+00 --2.362124440193032804e+00 6.078662816890399376e-03 5.717667592089286543e+00 2.471885830427023381e-02 -2.500000000000000000e-01 3.596000000000000085e+00 --2.367543970953981614e+00 -2.651387009801096733e-04 5.724518752330178373e+00 2.127537130804409149e-02 9.000000000000000222e-01 1.864799999999999969e+01 --2.354994548347020267e+00 -3.690083390904414992e-03 5.688382187067968054e+00 2.566552163399479086e-02 -6.420000000000000151e-01 1.017999999999999972e+01 --2.388901655550978997e+00 2.537770276553533502e-03 5.775706901016095962e+00 1.206203311840953023e-02 1.179999999999999938e+00 7.096000000000000085e+00 --2.363222034370952240e+00 4.822936801222594237e-03 5.713587812003099842e+00 2.304426550526693721e-02 1.268000000000000016e+00 8.096000000000000085e+00 --2.360768869750226706e+00 -1.301070941237230869e-02 5.784198512307618500e+00 3.775940277127645683e-02 8.260000000000000675e-01 1.468400000000000105e+01 --2.359412234195962466e+00 4.173058956438563220e-03 5.745886257092980287e+00 3.215588916927165225e-02 5.800000000000000294e-02 8.524000000000000909e+00 --2.370886382301474082e+00 1.909328923082833328e-03 5.715738321522840337e+00 1.683388044042611470e-02 2.840000000000000302e-01 5.743999999999999773e+00 --2.409949280570648167e+00 3.238183950524164967e-02 5.957216664947535989e+00 2.516168828535240293e-02 -1.122000000000000108e+00 9.179999999999999716e+00 --2.380429915028219767e+00 4.306317138809194651e-03 5.779700900605175384e+00 1.997681861404010731e-02 5.999999999999999778e-01 1.180799999999999983e+01 --2.358429657625260578e+00 -2.442585320425373239e-04 5.757987668776590517e+00 3.520142564052058248e-02 -1.762000000000000011e+00 1.249200000000000088e+01 --2.389671193567367347e+00 -3.073763963395841916e-04 5.807434918751197550e+00 1.696974607604245094e-02 -3.460000000000000298e-01 1.150000000000000000e+01 --2.408725205754512100e+00 5.449054213645157171e-03 5.933035574885040297e+00 2.257641123223662685e-02 2.584000000000000075e+00 1.741600000000000037e+01 --2.368072087207687915e+00 1.256102659753953552e-03 5.809598249518336921e+00 3.599079504947406277e-02 1.776000000000000023e+00 1.367999999999999972e+01 --2.377553136651169297e+00 -3.653865868377686663e-03 5.729361766092950781e+00 1.354422765905667451e-02 3.280000000000000138e-01 4.336000000000000298e+00 --2.370910300766710055e+00 -3.180408664623741912e-03 5.735990193553265115e+00 2.041259076976298728e-02 2.020000000000000129e-01 1.212400000000000055e+01 --2.367390056201085002e+00 -1.241240201955966281e-03 5.728046478614983172e+00 2.203680797453754295e-02 8.980000000000000204e-01 7.740000000000000213e+00 --2.363474457709714205e+00 1.027171457382913128e-03 5.691275033003059924e+00 1.884355154607503594e-02 1.720000000000000140e-01 9.416000000000000369e+00 --2.391690964013456711e+00 9.228084717833810301e-04 5.786925274434042699e+00 1.166693293517788964e-02 7.780000000000000249e-01 5.844000000000000306e+00 --2.367244179303865437e+00 1.223975523996848926e-02 5.804021646534104129e+00 3.563824007353945389e-02 -8.659999999999999920e-01 1.109200000000000053e+01 --2.381668193146659007e+00 -2.757138249483093596e-03 5.749866225235361838e+00 1.366273525886285700e-02 1.878000000000000114e+00 9.580000000000000071e+00 --2.391457356507673104e+00 -1.642915872592499993e-03 5.771742476520706155e+00 9.208845529081724837e-03 1.100000000000000089e+00 6.783999999999999808e+00 --2.400492300074310581e+00 -3.011057665469569350e-03 5.852178296746983754e+00 1.558169562558692732e-02 -9.400000000000000577e-01 1.737600000000000122e+01 --2.327138250184171309e+00 2.840511731198341883e-03 5.691399909972080451e+00 5.092758697038970994e-02 -6.720000000000000417e-01 1.880000000000000071e+01 --2.363055823419018875e+00 -3.116631359263172946e-03 5.709871279817358314e+00 2.253007143803413201e-02 5.580000000000000515e-01 1.599600000000000044e+01 --2.356419872279404970e+00 -2.468332060743623838e-03 5.658696419793803223e+00 1.908313065942953551e-02 1.559999999999999998e-01 6.576000000000000512e+00 --2.397588986281389722e+00 -2.487412136695101462e-03 5.857243479677240572e+00 1.892543943154253311e-02 4.380000000000000004e-01 1.917200000000000060e+01 --2.364675295771226260e+00 4.406734670577115037e-04 5.750836708466551705e+00 2.846131958234136144e-02 1.700000000000000122e-01 8.644000000000000128e+00 --2.358543499088715301e+00 -1.685402222272708393e-03 5.698950081365654619e+00 2.448689341577690512e-02 -4.040000000000000258e-01 6.320000000000000284e+00 --2.373603577898614869e+00 3.782003656769005861e-03 5.745038015904061268e+00 1.970188746212869768e-02 -5.300000000000000266e-01 1.057200000000000095e+01 --2.385387013740589701e+00 -3.219954784873221235e-03 5.779088564939665496e+00 1.563877947560323584e-02 -4.120000000000000329e-01 5.919999999999999929e+00 --2.390527786693740442e+00 -3.190977681239764042e-03 5.780774907836839560e+00 1.157047581343643126e-02 2.700000000000000178e-01 9.451999999999999957e+00 --2.378828642279382066e+00 4.185733300901991333e-03 5.769116303412947566e+00 1.948054499589340835e-02 8.539999999999999813e-01 1.358000000000000007e+01 --2.371653817313595258e+00 -2.635975198501755434e-03 5.746413383937818864e+00 2.162770532261722167e-02 -1.358000000000000096e+00 1.051600000000000001e+01 --2.398432564069974404e+00 3.395129418636139845e-03 5.875993250525364253e+00 2.146538354987647182e-02 -8.000000000000000167e-03 1.684799999999999898e+01 --2.368991511755279777e+00 -2.931106906202435736e-03 5.741964722358791740e+00 2.313164206536497125e-02 -5.799999999999999600e-01 1.396000000000000085e+01 --2.377861956531025722e+00 -6.920738508319653794e-03 5.754884501364310623e+00 1.777621638802498807e-02 -6.840000000000000524e-01 1.728000000000000114e+01 --2.376797600289968670e+00 7.488184920396148345e-03 5.780701070875809755e+00 2.325335918584823039e-02 4.380000000000000004e-01 7.291999999999999815e+00 --2.395287782241428243e+00 -3.544701963281947192e-03 5.853782323117321162e+00 2.027751803521601545e-02 -7.000000000000000666e-02 1.278800000000000026e+01 --2.364706828924627580e+00 2.418133010175031652e-03 5.749179998595416841e+00 2.813449983459860582e-02 -1.440000000000000169e-01 1.766400000000000148e+01 --2.368773855882159829e+00 8.519305460896069160e-03 5.739497919186463903e+00 2.284505055930962161e-02 -9.919999999999999929e-01 1.141600000000000037e+01 --2.378080728737466121e+00 -6.230554295503543420e-04 5.745114587055663691e+00 1.588703706406541932e-02 -2.760000000000000231e-01 5.552000000000000490e+00 --2.347453765820025851e+00 -4.905479092252987283e-03 5.675733906295247877e+00 2.996446688442884823e-02 1.000000000000000021e-02 1.416399999999999970e+01 --2.343602929490206321e+00 -5.249165140904576282e-03 5.659424788007025420e+00 3.038064501006152926e-02 4.979999999999999982e-01 7.540000000000000036e+00 --2.387529878168910713e+00 5.954359135407785025e-03 5.773516274116409441e+00 1.282557770449924313e-02 9.800000000000000377e-02 2.491999999999999993e+00 --2.349455872519758515e+00 -7.724667668699980970e-03 5.657544939449884680e+00 2.489492636154795602e-02 5.320000000000000284e-01 1.063199999999999967e+01 --2.405450195622767851e+00 1.340969576405405192e-03 5.832669294972800955e+00 8.031745976760627098e-03 -6.119999999999999885e-01 6.344000000000000306e+00 --2.355296198575799860e+00 -4.340218628250463659e-03 5.690278360957692350e+00 2.574173322652322654e-02 1.179999999999999938e+00 9.672000000000000597e+00 --2.396323856043656608e+00 2.348814358741882404e-03 5.818344539476578703e+00 1.322794818909363811e-02 1.191999999999999948e+00 1.407200000000000095e+01 --2.373390921351528071e+00 -6.477418588123515578e-03 5.736962293796959322e+00 1.843598827526378436e-02 9.120000000000000329e-01 8.631999999999999673e+00 --2.382343780770838748e+00 -8.032630833976987100e-04 5.749742452590378861e+00 1.306982520131761034e-02 -1.859999999999999987e-01 5.387999999999999901e+00 --2.385465453996102436e+00 1.698433849664185424e-02 5.808766032043000571e+00 2.063762466387084049e-02 -2.139999999999999958e-01 8.907999999999999474e+00 --2.357118703851941000e+00 2.803394532188690103e-03 5.721522869696140212e+00 2.978577224540094118e-02 1.522000000000000020e+00 1.490000000000000036e+01 --2.353989065538249381e+00 1.438856701223414913e-03 5.651581980403155292e+00 1.990721156637990583e-02 2.800000000000000266e-01 8.432000000000000384e+00 --2.407142457117667167e+00 -2.052762751795429372e-03 5.822375416820237959e+00 4.837122158240306398e-03 4.440000000000000058e-01 5.807999999999999829e+00 --2.387801471136485887e+00 -2.796590160832635678e-03 5.762878304876184465e+00 1.074413653284128287e-02 7.279999999999999805e-01 5.416000000000000369e+00 --2.350070862119922666e+00 -7.277260496493557877e-03 5.660510985770609516e+00 2.489937570472930059e-02 -2.139999999999999958e-01 1.109200000000000053e+01 --2.368577641525609678e+00 -8.841277322091818094e-05 5.724063132679925836e+00 2.030299740583573972e-02 1.616000000000000103e+00 1.243999999999999950e+01 --2.370783365523321251e+00 -5.945351243559588057e-03 5.722647866444838805e+00 1.813434242904876995e-02 -3.480000000000000315e-01 7.232000000000000206e+00 --2.368334114929639522e+00 -2.327208159156254029e-03 5.740544486583738504e+00 2.344824853024355532e-02 -6.000000000000000125e-03 7.411999999999999922e+00 --2.360286078901099316e+00 -6.525410123695157133e-03 5.689873788071071026e+00 2.132364096435892739e-02 8.739999999999999991e-01 9.652000000000001023e+00 --2.346765715971085076e+00 -3.998067372563233850e-03 5.692648678873607260e+00 3.364433974408914674e-02 -4.979999999999999982e-01 9.668000000000001037e+00 --2.356702075392975715e+00 -5.787275797875262966e-03 5.730729261154325016e+00 3.179321132445381975e-02 -8.000000000000000444e-01 8.407999999999999474e+00 --2.369561504414159359e+00 -1.336513196068025858e-03 5.728194766503520441e+00 2.019077040867191253e-02 -3.639999999999999902e-01 3.328000000000000291e+00 --2.387807598312411184e+00 -4.377166815416495653e-03 5.790628716086198224e+00 1.559997577120099399e-02 -2.137999999999999901e+00 1.374800000000000111e+01 --2.389576645476381156e+00 7.708007359161332683e-05 5.781555289634710881e+00 1.251799803786209954e-02 5.100000000000000089e-01 3.331999999999999851e+00 --2.379202501800407266e+00 3.304858030001888054e-03 5.761952737978384143e+00 1.789823680552238630e-02 -6.580000000000000293e-01 8.307999999999999829e+00 --2.384568468399907104e+00 -2.525648215531085296e-03 5.783220544854046352e+00 1.706497625198784632e-02 4.859999999999999876e-01 1.098799999999999955e+01 --2.375744004396605824e+00 -3.979390746193142182e-03 5.730661543663535085e+00 1.531737960047052823e-02 -5.919999999999999707e-01 5.112000000000000099e+00 --2.342053894662287750e+00 -2.534599347517645245e-05 5.658948708781599279e+00 3.167281783984080695e-02 1.539999999999999980e-01 7.692000000000000171e+00 --2.369180801041884887e+00 6.730725515138408395e-03 5.759552996571583705e+00 2.608149181466794947e-02 -1.026000000000000023e+00 1.075600000000000023e+01 --2.370394592535248091e+00 5.356806104058451940e-04 5.708683315081003684e+00 1.600206232568514297e-02 -3.480000000000000315e-01 9.423999999999999488e+00 --2.395930414292766653e+00 1.835539724252554595e-03 5.793903670322595012e+00 9.304255879701416737e-03 -4.000000000000000083e-03 4.959999999999999964e+00 --2.378232207598403480e+00 1.656280828975778422e-03 5.756308521731032357e+00 1.773548759741847350e-02 -3.160000000000000031e-01 1.344800000000000040e+01 --2.377523035886327296e+00 -3.775728525448864437e-03 5.740489162931051048e+00 1.553792916901045214e-02 7.000000000000000666e-01 6.735999999999999766e+00 --2.383893458323682157e+00 -1.206295682092272227e-03 5.752192673481376417e+00 1.218385844004748683e-02 6.099999999999999867e-01 3.300000000000000266e+00 --2.351164703765440400e+00 -2.893307891766663895e-03 5.779601430793231742e+00 4.551389770487292152e-02 -8.320000000000000728e-01 1.195199999999999996e+01 --2.349044636763902627e+00 6.162228937516342833e-03 5.705807395908617963e+00 3.401205715467299495e-02 4.640000000000000235e-01 9.064000000000000057e+00 --2.389053987275747470e+00 8.738718544338493254e-04 5.788269905885249145e+00 1.413710245128273896e-02 9.400000000000000022e-02 8.763999999999999346e+00 --2.382641760156811284e+00 1.000917416842762690e-02 5.788989095650396877e+00 1.967610106989785279e-02 -1.032000000000000028e+00 9.567999999999999616e+00 --2.383722568549140775e+00 6.946145823695796173e-04 5.766011285534005104e+00 1.476145114851847018e-02 -2.780000000000000249e-01 1.174800000000000111e+01 --2.373276047970760416e+00 8.029010468104095036e-03 5.746707283229898877e+00 2.025246337265311850e-02 0.000000000000000000e+00 1.052800000000000047e+01 --2.388604722966814808e+00 3.553171600474175525e-04 5.781483385156878541e+00 1.332948527164495856e-02 -4.599999999999999922e-02 3.028000000000000025e+00 --2.388615882613160046e+00 -5.307989705712626294e-03 5.763538358780186499e+00 1.015989561695935378e-02 -4.859999999999999876e-01 6.980000000000000426e+00 --2.391417133125715022e+00 3.119725951831272062e-03 5.788955865197940476e+00 1.224898143891627739e-02 5.399999999999999939e-02 8.099999999999999645e+00 --2.355717872834750981e+00 6.800182238769404306e-04 5.671385660093431369e+00 2.198028593082382298e-02 -9.180000000000000382e-01 6.940000000000000391e+00 --2.410440076680034238e+00 -6.503185799034535888e-04 5.831438338528481147e+00 3.651444680186076951e-03 -1.900000000000000022e-01 2.084000000000000075e+00 --2.369778759803843116e+00 -1.113548477953224753e-03 5.747836644626636904e+00 2.350159541390808154e-02 -2.139999999999999958e-01 1.590799999999999947e+01 --2.388890531169182374e+00 -3.438673405690513031e-03 5.770800549975065863e+00 1.120886165278429936e-02 -5.300000000000000266e-01 3.548000000000000043e+00 --2.370391329883685394e+00 -5.464503081040025280e-03 5.725774590295071853e+00 1.903059389349829461e-02 9.759999999999999787e-01 7.943999999999999950e+00 --2.367739657543594500e+00 -4.538144623720341900e-03 5.682940247089416808e+00 1.367890075313834240e-02 1.421999999999999931e+00 1.357200000000000095e+01 --2.397012822368597362e+00 3.701138511814220863e-03 5.800529074538068208e+00 9.540595259498853634e-03 9.020000000000000240e-01 9.684000000000001052e+00 --2.371622654133407337e+00 4.802348208806822213e-03 5.745667212920589684e+00 2.151311233420991065e-02 -1.296000000000000041e+00 5.719999999999999751e+00 --2.398465457824948910e+00 2.687528023008627347e-03 5.831064117649563450e+00 1.362950723010703143e-02 -1.288000000000000034e+00 9.136000000000001009e+00 --2.385706019512551457e+00 -1.078708710566798207e-02 5.814417575995386223e+00 2.151730721041993089e-02 1.921999999999999931e+00 1.041999999999999993e+01 --2.378982199047865009e+00 1.768192370847584440e-04 5.731205799921069044e+00 1.265989729778187710e-02 5.859999999999999654e-01 8.556000000000000938e+00 --2.399063341212895661e+00 6.915628330648131324e-03 5.839054672835422011e+00 1.449120457539405417e-02 1.479999999999999982e+00 1.366399999999999970e+01 --2.371056236678545037e+00 5.716304250078298741e-04 5.770069622869110404e+00 2.635421066257317632e-02 8.499999999999999778e-01 1.478000000000000114e+01 --2.357433856982407150e+00 -5.230837497814925900e-03 5.710182853109615486e+00 2.745915925977764072e-02 8.080000000000000515e-01 8.528000000000000469e+00 --2.401410988737032515e+00 -2.774097563362981373e-03 5.828813054162255369e+00 1.075384161852381906e-02 1.586000000000000076e+00 1.076399999999999935e+01 --2.386880026498538143e+00 -2.260870775783900555e-03 5.844922371036681774e+00 2.592685439780357051e-02 -2.320000000000000118e-01 1.732000000000000028e+01 --2.357670188649624965e+00 8.951377135400623818e-04 5.723783124129093736e+00 2.971461723691777579e-02 1.614000000000000101e+00 1.664400000000000190e+01 --2.380436919318274391e+00 -9.221627927578515335e-03 5.729668588869142987e+00 1.110578509873061739e-02 7.199999999999999734e-01 3.983999999999999986e+00 --2.370981225946084514e+00 -5.640466698236790664e-03 5.736753868914681753e+00 2.047557259119456990e-02 1.667999999999999927e+00 1.401600000000000001e+01 --2.362892962453511103e+00 -3.156747484873766683e-03 5.767737025512731819e+00 3.303498073706484517e-02 3.800000000000000044e-01 1.281600000000000072e+01 --2.397825059237330692e+00 -4.422860862169124101e-03 5.787822746848727995e+00 6.643747273571047086e-03 1.155999999999999917e+00 7.248000000000000220e+00 --2.375974493074019200e+00 7.792869648375165201e-03 5.761009007421268535e+00 2.047175922973739140e-02 -1.431999999999999940e+00 1.131199999999999939e+01 --2.370711343444066976e+00 -3.255511514523184470e-03 5.723277220086189665e+00 1.832163344554883777e-02 -1.124000000000000110e+00 5.624000000000000554e+00 --2.384826236194904858e+00 8.066333677880517094e-04 5.865886489028030226e+00 3.138313094482855087e-02 -5.020000000000000018e-01 1.459600000000000009e+01 --2.373710824322400992e+00 -1.357422788381362419e-03 5.747867317678838184e+00 2.011865103456142098e-02 2.260000000000000064e-01 5.932000000000000384e+00 --2.391581881586792857e+00 -4.705976864525823929e-03 5.817026302801339810e+00 1.701058647264410556e-02 3.400000000000000244e-02 6.339999999999999858e+00 --2.375322681448924556e+00 -7.348737654236932142e-03 5.743269553929057025e+00 1.789152363146803357e-02 -4.620000000000000218e-01 9.108000000000000540e+00 --2.360481849140569022e+00 -5.954806239469310689e-03 5.714464380063344784e+00 2.557141551923874587e-02 9.120000000000000329e-01 1.040799999999999947e+01 --2.374087565573755665e+00 1.480275286822884751e-03 5.738337323461244033e+00 1.810389986435363002e-02 1.404000000000000137e+00 1.644800000000000040e+01 --2.375430966621481232e+00 -3.922810874492733968e-03 5.771015763488716921e+00 2.273679293131739693e-02 -6.620000000000000329e-01 8.916000000000000369e+00 --2.386915403234845634e+00 -1.448493989786751694e-02 5.803466781094954285e+00 1.851040141119551091e-02 -1.779999999999999916e-01 1.150000000000000000e+01 --2.372265238277071919e+00 -1.294798750403264049e-03 5.745332179586391419e+00 2.091189820084947068e-02 -5.160000000000000142e-01 1.129599999999999937e+01 --2.405067164193770868e+00 -5.321162574318747882e-03 5.833576125437071269e+00 8.495753379530899749e-03 -2.840000000000000302e-01 6.136000000000000121e+00 --2.362730969797799396e+00 -4.518161647050122280e-04 5.713494673117058831e+00 2.346555596456748743e-02 -1.572000000000000064e+00 8.048000000000000043e+00 --2.352598122805939607e+00 -4.186886504283772632e-03 5.692492765141352606e+00 2.849661913331639346e-02 -9.400000000000000022e-02 6.884000000000000341e+00 --2.355587286772566458e+00 6.439664595737633161e-03 5.716380158491235264e+00 3.017964005738217950e-02 2.000000000000000042e-03 7.243999999999999773e+00 --2.329253393849765263e+00 1.151075636318496000e-02 5.665332794743658695e+00 4.414336745811234253e-02 -1.219999999999999973e-01 1.782799999999999940e+01 --2.379007128047219144e+00 -7.582146440550164603e-03 5.751151090909973895e+00 1.613183187434796481e-02 1.213999999999999968e+00 8.371999999999999886e+00 --2.365850009600594994e+00 6.435232233098839641e-03 5.737746688369579573e+00 2.507895134507404089e-02 -1.800000000000000211e-02 3.292000000000000259e+00 --2.381988725306464882e+00 -1.298163269935558202e-02 5.778580058624194216e+00 1.836399016064297826e-02 1.245999999999999996e+00 1.596400000000000041e+01 --2.364805052551260278e+00 9.243575093656253077e-04 5.709616829169139152e+00 2.097727480887607437e-02 4.480000000000000093e-01 6.520000000000000462e+00 --2.368573118193741500e+00 -1.088972915443654375e-03 5.713966675724969413e+00 1.850657232760834908e-02 1.150000000000000133e+00 8.652000000000001023e+00 --2.368517013651747938e+00 -3.667182722374104278e-03 5.699998390505313317e+00 1.605821671384757496e-02 6.580000000000000293e-01 5.483999999999999986e+00 --2.384088790974073113e+00 5.971092209222708495e-03 5.777534296639961653e+00 1.645816251232258554e-02 1.266000000000000014e+00 1.691600000000000037e+01 --2.373801517137214656e+00 -1.680387579301445772e-03 5.728512277712780154e+00 1.660534606141122332e-02 2.125999999999999890e+00 1.949200000000000088e+01 --2.390868258733401586e+00 5.431600107116130172e-04 5.799414668912505455e+00 1.454847589850587382e-02 1.759999999999999898e-01 9.592000000000000526e+00 --2.369242647236368793e+00 -2.199534024562173860e-03 5.706373775586202512e+00 1.657636718609781235e-02 -1.400000000000000029e-02 1.160000000000000059e-01 --2.380339269749663700e+00 1.591693206950563601e-03 5.789065656958403139e+00 2.171594171195618400e-02 1.552000000000000046e+00 1.420800000000000018e+01 --2.368107353361376344e+00 -1.157033729817517724e-02 5.749292936167554657e+00 2.513382165122816231e-02 3.220000000000000084e-01 8.380000000000000782e+00 --2.374603588102842000e+00 3.238782721090044826e-03 5.751893409631081866e+00 2.006105341422760938e-02 1.987999999999999989e+00 1.120800000000000018e+01 --2.406575438832713409e+00 -2.042006407308314536e-03 5.840286616720483437e+00 8.403310747932790994e-03 1.518000000000000016e+00 1.431600000000000072e+01 --2.368006208956024317e+00 7.999055862212648207e-03 5.725062847177414760e+00 2.093882125426640636e-02 -1.120000000000000023e-01 1.116800000000000104e+01 --2.372847044760856061e+00 4.336952231658263140e-04 5.745028854401499352e+00 2.035825478517334572e-02 -1.340000000000000080e-01 9.083999999999999631e+00 --2.377134013456740025e+00 -9.334926347929079979e-03 5.802538472980779183e+00 2.681121723319433020e-02 -2.708000000000000185e+00 1.745599999999999952e+01 --2.367384077456602398e+00 -5.521525468261474084e-03 5.724186741181418014e+00 2.133746092532733812e-02 -4.899999999999999911e-01 1.047600000000000087e+01 --2.368572305879598439e+00 1.244334420596954986e-03 5.733811328714963906e+00 2.204435688997758921e-02 4.919999999999999929e-01 9.592000000000000526e+00 --2.354336142955489652e+00 -9.878318603769302431e-03 5.675753950500854295e+00 2.391447740430114807e-02 -1.652000000000000135e+00 9.168000000000001037e+00 --2.385012485164415441e+00 2.160421818801027023e-03 5.766228945710677678e+00 1.370012285070624884e-02 6.440000000000000169e-01 4.384000000000000341e+00 --2.378979688411311688e+00 -1.555318417122725011e-03 5.747914354444573881e+00 1.561302829851634287e-02 2.899999999999999800e-01 2.756000000000000227e+00 --2.398095222125526504e+00 -3.161584931236567728e-03 5.795135900382816452e+00 7.693628956992085502e-03 2.540000000000000036e-01 5.331999999999999851e+00 --2.387966888407489829e+00 -4.924626048796495147e-03 5.889049174190095215e+00 3.272107179984208580e-02 9.819999999999999840e-01 1.286800000000000033e+01 --2.363444654438767945e+00 -7.185949472549847845e-03 5.708640565231443809e+00 2.195031405017997331e-02 -1.612000000000000099e+00 7.991999999999999993e+00 --2.375288553242630663e+00 1.792116756792121440e-03 5.792942319997761658e+00 2.675236277092302162e-02 -1.239999999999999991e-01 5.448000000000000398e+00 --2.365305300663176347e+00 -1.467483867224930218e-03 5.715699402694330189e+00 2.163195597243559865e-02 3.519999999999999796e-01 8.168000000000001037e+00 --2.364919377785819954e+00 6.751175084300152463e-04 5.716135707730020776e+00 2.204435779528499117e-02 2.141999999999999904e+00 9.332000000000000739e+00 --2.364976112445117185e+00 -4.831024197669243556e-04 5.708535793473769715e+00 2.063664488896269425e-02 1.626000000000000112e+00 8.763999999999999346e+00 --2.380282965305328791e+00 1.713789022220590886e-03 5.772758169087155444e+00 1.888580563669927520e-02 -1.203999999999999959e+00 1.108800000000000097e+01 --2.367136866805402473e+00 -3.536890384767063804e-04 5.741324621402335460e+00 2.462591345274272106e-02 -5.620000000000000551e-01 1.538799999999999990e+01 --2.366745325559842072e+00 -1.488020901955190191e-02 5.739140539744127523e+00 2.445362267163986303e-02 8.659999999999999920e-01 1.433999999999999986e+01 --2.390705159454355133e+00 -4.757093290027327240e-03 5.808119375277291496e+00 1.619800422390989605e-02 -1.310000000000000053e+00 1.193200000000000038e+01 --2.378004051223863158e+00 1.258195456553706619e-02 5.820237567788824506e+00 2.915090022115223237e-02 -1.223999999999999977e+00 1.473600000000000065e+01 --2.376114389459973442e+00 1.995505732897931428e-03 5.770593396906525285e+00 2.207994520115224082e-02 -2.240000000000000213e+00 1.232000000000000028e+01 --2.374170182020049591e+00 1.039899314221449803e-03 5.750065990151188799e+00 2.011441948154182174e-02 2.860000000000000320e-01 1.458800000000000097e+01 --2.380989652533807455e+00 -7.644722601179672512e-03 5.761674572808931138e+00 1.629614424309976800e-02 -1.201999999999999957e+00 7.491999999999999993e+00 --2.356061645151219519e+00 1.009856497389409642e-02 5.725071028761132830e+00 3.129673907613896716e-02 1.054000000000000048e+00 9.099999999999999645e+00 --2.372006547240690377e+00 1.987519984281845790e-03 5.787295700209032390e+00 2.859164295324943469e-02 1.916000000000000147e+00 1.127200000000000024e+01 --2.392191286828519114e+00 -1.785911889130130034e-03 5.781479789183276985e+00 1.029098382268548752e-02 1.180000000000000077e-01 1.066000000000000014e+01 --2.362927928693926205e+00 -5.451938714758251640e-03 5.705987280454916544e+00 2.193415015303395305e-02 -2.200000000000000011e-01 4.743999999999999773e+00 --2.381214977622930107e+00 -2.634569010728697244e-03 5.787145988903994009e+00 2.062366071985764077e-02 4.060000000000000275e-01 1.609199999999999875e+01 --2.342881665521393320e+00 6.750160862239954623e-04 5.645962360533737012e+00 2.857783846350435766e-02 -6.560000000000000275e-01 8.263999999999999346e+00 --2.377832645267043521e+00 -1.445778342162097369e-04 5.737844143487885518e+00 1.481335091285753379e-02 -4.939999999999999947e-01 3.435999999999999943e+00 --2.381889586724204033e+00 -6.286330528850884222e-04 5.794054563646130696e+00 2.126685797091113286e-02 8.240000000000000657e-01 7.496000000000000441e+00 --2.371295452537317772e+00 -2.661259294677792604e-03 5.726837301087507548e+00 1.845505271649759346e-02 7.860000000000000320e-01 1.109999999999999964e+01 --2.387683041712226117e+00 6.566912995029473772e-06 5.782505598422517323e+00 1.429132739417081008e-02 -6.099999999999999867e-01 1.258000000000000007e+01 --2.370580443288787809e+00 5.927506429449887031e-03 5.720441276387430385e+00 1.791611818841876147e-02 -7.960000000000000409e-01 9.416000000000000369e+00 --2.372701280371104282e+00 -1.824729436557744359e-03 5.750893394308213225e+00 2.152363001232747083e-02 7.259999999999999787e-01 1.241200000000000081e+01 --2.374765986895186920e+00 8.204098388141779731e-04 5.779503585963934320e+00 2.482271286269597046e-02 4.279999999999999916e-01 8.599999999999999645e+00 --2.399420974922992222e+00 -5.024446211346833384e-03 5.825615065754102595e+00 1.186638768021038536e-02 -3.079999999999999960e-01 1.251200000000000045e+01 --2.367169534477154169e+00 -9.770313974651353636e-03 5.764583522767342316e+00 2.869591452912814006e-02 -5.899999999999999689e-01 1.195599999999999952e+01 --2.374828272189518419e+00 -3.369936801114856769e-03 5.732666404867109655e+00 1.645843802969749331e-02 3.200000000000000067e-01 2.415999999999999925e+00 --2.369842441194188520e+00 -2.297765118928346128e-03 5.745919866307150237e+00 2.310308507692590899e-02 4.919999999999999929e-01 1.120000000000000107e+01 --2.376865544541270747e+00 3.179128344841825483e-04 5.786086258016108985e+00 2.417848957705884955e-02 -4.339999999999999969e-01 9.811999999999999389e+00 --2.377788687265312451e+00 -2.802582695794225698e-03 5.742972669238134209e+00 1.575373166556130397e-02 -6.620000000000000329e-01 5.948000000000000398e+00 --2.367882785483844010e+00 -1.504983200719397151e-03 5.705707206132742293e+00 1.762684443939737527e-02 -4.399999999999999745e-02 5.008000000000000007e+00 --2.380889182604652543e+00 3.352959479859644182e-03 5.763150054288509239e+00 1.666759167447054435e-02 9.400000000000000577e-01 8.471999999999999531e+00 --2.357161033516183668e+00 -4.477395576297466678e-03 5.706786094957587707e+00 2.708973144529036592e-02 1.046000000000000041e+00 1.165200000000000102e+01 --2.412323534747611742e+00 5.866261233971195067e-03 5.919860358884933227e+00 1.726159798320033717e-02 2.458000000000000185e+00 1.982000000000000028e+01 --2.371563294285067958e+00 7.505813326965257021e-03 5.758908231026684810e+00 2.390029355046109985e-02 -9.799999999999999822e-01 1.203200000000000003e+01 --2.372794238894933017e+00 -1.038534651117262522e-02 5.748773635404103466e+00 2.101022349995614394e-02 -8.659999999999999920e-01 8.099999999999999645e+00 --2.371827141490814750e+00 -6.538087799293216184e-04 5.728762929302863682e+00 1.834440679501260843e-02 -1.975999999999999979e+00 9.448000000000000398e+00 --2.376864653707094099e+00 -5.160139271283724002e-04 5.796606836350538750e+00 2.604138599144713989e-02 -2.292000000000000259e+00 1.674399999999999977e+01 --2.373790769118293120e+00 -4.665253736579821724e-03 5.727683674906607791e+00 1.645725332842799468e-02 -1.191999999999999948e+00 1.153599999999999959e+01 --2.390930245982668456e+00 -1.334204991511871597e-03 5.794866446611078636e+00 1.369945632254946331e-02 4.780000000000000360e-01 6.588000000000000078e+00 --2.392225070627822525e+00 -1.421955891400398294e-03 5.787540445968363478e+00 1.132211387255639343e-02 -2.840000000000000302e-01 2.792000000000000259e+00 --2.364198633272702743e+00 -7.103036759891838761e-03 5.726043194741189168e+00 2.441265646582975804e-02 6.540000000000000258e-01 6.187999999999999723e+00 --2.369856953974876390e+00 -6.674063311987057760e-04 5.733950987922740161e+00 2.096207053164328427e-02 1.076000000000000068e+00 7.775999999999999801e+00 --2.389197306258096898e+00 8.217898843858239752e-03 5.798265867853422684e+00 1.573093173795877750e-02 7.740000000000000213e-01 1.098000000000000043e+01 --2.354056839627951092e+00 -6.644168441914804005e-03 5.684834599657873966e+00 2.582567531113721601e-02 -1.082000000000000073e+00 7.780000000000000249e+00 --2.376801898367900900e+00 3.005779727014461309e-03 5.761725877458009570e+00 1.991631080800042308e-02 5.819999999999999618e-01 3.971999999999999975e+00 --2.399138632219859346e+00 5.557866669153450380e-03 5.861051248762122690e+00 1.825801827957138773e-02 1.340000000000000080e-01 9.763999999999999346e+00 --2.374944649238063477e+00 -6.414621567952027113e-03 5.756786594903061882e+00 2.061898111863492630e-02 -2.939999999999999836e-01 7.652000000000000135e+00 --2.417982238095864211e+00 3.635947012921597436e-03 5.928763201286153972e+00 1.403967182698099940e-02 1.760000000000000009e+00 1.445599999999999952e+01 --2.404648228480599670e+00 2.198499183867456616e-02 5.884196092693787961e+00 1.736109460010248559e-02 -1.042000000000000037e+00 1.242800000000000082e+01 --2.378981607899461892e+00 1.894173868913544712e-03 5.751778449201322196e+00 1.629351494903688927e-02 -4.160000000000000364e-01 8.519999999999999574e+00 --2.347437252429693810e+00 -2.942923324773138571e-03 5.701981755473191527e+00 3.475084812115605826e-02 -6.139999999999999902e-01 1.301999999999999957e+01 --2.354229600349532880e+00 -2.765060469797028277e-03 5.686540614296283991e+00 2.600320216966543405e-02 -9.199999999999999845e-02 8.247999999999999332e+00 --2.424194789427340790e+00 1.600986787098670691e-02 5.932209962394338731e+00 9.310198545897006850e-03 -1.866000000000000103e+00 1.048399999999999999e+01 --2.376097336553496753e+00 8.636929396422542149e-03 5.791125692605643138e+00 2.569283464105406520e-02 -2.560000000000000053e-01 7.456000000000000405e+00 --2.387246316094417953e+00 -5.072809832193186930e-03 5.777276927628578918e+00 1.373125965548366301e-02 -7.419999999999999929e-01 8.756000000000000227e+00 --2.387811418281090781e+00 -5.188592176738519336e-03 5.761782808925733690e+00 1.053342344583696293e-02 3.900000000000000133e-01 6.315999999999999837e+00 --2.405085829612314541e+00 3.599723946561229210e-02 5.928768638644344335e+00 2.426301070463929288e-02 -3.799999999999999906e-02 1.218800000000000061e+01 --2.392968839039582463e+00 2.701009508773581408e-04 5.813116331468952680e+00 1.516096724330253699e-02 -4.359999999999999987e-01 7.576000000000000512e+00 --2.371690358074560301e+00 -1.061507365436044001e-02 5.750363789616859123e+00 2.224088092098652075e-02 1.439999999999999947e+00 1.479199999999999982e+01 --2.384518898536634346e+00 -1.487532336280040016e-02 5.813618912944541250e+00 2.233756620849181723e-02 1.217999999999999972e+00 2.343599999999999994e+01 --2.390900702134001410e+00 -5.167326457453020640e-03 5.800836245947915693e+00 1.475556315298626187e-02 -5.919999999999999707e-01 1.046400000000000041e+01 --2.389330247894751125e+00 -3.810920619932555570e-03 5.785967475005920235e+00 1.349196819126301759e-02 8.400000000000000522e-02 2.415999999999999925e+00 --2.362205760029053359e+00 -1.326266959922249100e-03 5.701022018632576405e+00 2.168462839387671690e-02 -3.240000000000000102e-01 6.208000000000000185e+00 --2.403488318210420527e+00 -2.894626316714210817e-03 5.815856523127882483e+00 6.764197768398392228e-03 1.074000000000000066e+00 6.932000000000000384e+00 --2.375907890853203419e+00 -3.550215080300909379e-04 5.783852674731204679e+00 2.460859161979786491e-02 -8.960000000000000187e-01 8.160000000000000142e+00 --2.377284562559650372e+00 2.553728811321474747e-03 5.778126573903072938e+00 2.240557113568921593e-02 3.387999999999999901e+00 2.131200000000000117e+01 --2.369506521052892722e+00 2.423473455737974475e-03 5.726784639230607432e+00 1.998473452051563806e-02 5.060000000000000053e-01 6.836000000000000298e+00 --2.398153380582590533e+00 -3.803144575787680611e-03 5.808605154502457069e+00 9.984402434244707761e-03 1.388000000000000123e+00 5.616000000000000547e+00 --2.380407645519039495e+00 -2.018728490211872412e-03 5.777455051741847036e+00 1.960736849837879658e-02 -7.540000000000000036e-01 8.684000000000001052e+00 --2.386357215806221621e+00 2.351884709770872550e-03 5.804247467829301677e+00 1.923363451670314847e-02 -2.668000000000000149e+00 1.468800000000000061e+01 --2.372511215688089425e+00 5.294311007503862444e-04 5.732571179011195284e+00 1.843388990727752585e-02 -1.302000000000000046e+00 5.652000000000000135e+00 --2.364337543921489981e+00 5.959687992388093547e-03 5.690582566564033939e+00 1.795714213984435717e-02 5.720000000000000639e-01 4.336000000000000298e+00 --2.367581015988034387e+00 2.074445408655581878e-03 5.707583572037775888e+00 1.821990102224108760e-02 -1.280000000000000027e-01 6.624000000000000554e+00 --2.396425408565141080e+00 -9.101127281707237920e-03 5.805963485152765280e+00 1.094534564854228453e-02 -8.600000000000000699e-02 1.142800000000000082e+01 --2.387226362206000374e+00 -4.190980141444771226e-03 5.760567327927573977e+00 1.082049244822666859e-02 4.219999999999999862e-01 4.419999999999999929e+00 --2.384973208710113202e+00 2.327119959220942582e-03 5.790802766763520459e+00 1.805331677524252623e-02 5.859999999999999654e-01 1.175600000000000023e+01 --2.380698998454262583e+00 -3.579246049224643362e-03 5.800341071257828496e+00 2.339103507154293576e-02 5.600000000000000533e-01 9.544000000000000483e+00 --2.350366210527230493e+00 4.312811821892467007e-03 5.676361937755111775e+00 2.753026494528767326e-02 1.134000000000000119e+00 8.419999999999999929e+00 --2.354476359601430868e+00 -5.829149854400472730e-03 5.706490273497976773e+00 2.937218053609694929e-02 -7.640000000000000124e-01 7.687999999999999723e+00 --2.361833533712753397e+00 -1.582405214430139496e-03 5.774383342197013214e+00 3.515755953236083392e-02 -1.477999999999999980e+00 1.740399999999999991e+01 --2.371893991048964700e+00 -3.666483277288669351e-03 5.740176403802045968e+00 2.030866782211249513e-02 5.800000000000000294e-02 5.764000000000000234e+00 --2.379431283262131380e+00 5.154862071493558108e-03 5.804152860756556898e+00 2.514758397021578384e-02 -2.400000000000000050e-02 7.496000000000000441e+00 diff --git a/sample/Standard/.gitignore b/samples/Standard/.gitignore similarity index 100% rename from sample/Standard/.gitignore rename to samples/Standard/.gitignore diff --git a/sample/Standard/Hubbard/square/StdFace.def b/samples/Standard/Hubbard/square/StdFace.def similarity index 100% rename from sample/Standard/Hubbard/square/StdFace.def rename to samples/Standard/Hubbard/square/StdFace.def diff --git a/sample/Standard/Hubbard/square/UHF/initial.def b/samples/Standard/Hubbard/square/UHF/initial.def similarity index 100% rename from sample/Standard/Hubbard/square/UHF/initial.def rename to samples/Standard/Hubbard/square/UHF/initial.def diff --git a/sample/Standard/Hubbard/square/UHF/reference/zqp_APOrbital_opt.dat b/samples/Standard/Hubbard/square/UHF/reference/zqp_APOrbital_opt.dat similarity index 100% rename from sample/Standard/Hubbard/square/UHF/reference/zqp_APOrbital_opt.dat rename to samples/Standard/Hubbard/square/UHF/reference/zqp_APOrbital_opt.dat diff --git a/sample/Standard/Hubbard/square/UHF/reference/zvo_check.dat b/samples/Standard/Hubbard/square/UHF/reference/zvo_check.dat similarity index 100% rename from sample/Standard/Hubbard/square/UHF/reference/zvo_check.dat rename to samples/Standard/Hubbard/square/UHF/reference/zvo_check.dat diff --git a/sample/Standard/Hubbard/square/UHF/reference/zvo_eigen.dat b/samples/Standard/Hubbard/square/UHF/reference/zvo_eigen.dat similarity index 100% rename from sample/Standard/Hubbard/square/UHF/reference/zvo_eigen.dat rename to samples/Standard/Hubbard/square/UHF/reference/zvo_eigen.dat diff --git a/sample/Standard/Hubbard/square/UHF/reference/zvo_gap.dat b/samples/Standard/Hubbard/square/UHF/reference/zvo_gap.dat similarity index 100% rename from sample/Standard/Hubbard/square/UHF/reference/zvo_gap.dat rename to samples/Standard/Hubbard/square/UHF/reference/zvo_gap.dat diff --git a/sample/Standard/Hubbard/square/UHF/reference/zvo_result.dat b/samples/Standard/Hubbard/square/UHF/reference/zvo_result.dat similarity index 100% rename from sample/Standard/Hubbard/square/UHF/reference/zvo_result.dat rename to samples/Standard/Hubbard/square/UHF/reference/zvo_result.dat diff --git a/sample/Standard/Hubbard/triangular/StdFace.def b/samples/Standard/Hubbard/triangular/StdFace.def similarity index 100% rename from sample/Standard/Hubbard/triangular/StdFace.def rename to samples/Standard/Hubbard/triangular/StdFace.def diff --git a/sample/Standard/Hubbard/triangular/UHF/initial.def b/samples/Standard/Hubbard/triangular/UHF/initial.def similarity index 100% rename from sample/Standard/Hubbard/triangular/UHF/initial.def rename to samples/Standard/Hubbard/triangular/UHF/initial.def diff --git a/sample/Standard/Hubbard/triangular/UHF/reference/zqp_APOrbital_opt.dat b/samples/Standard/Hubbard/triangular/UHF/reference/zqp_APOrbital_opt.dat similarity index 100% rename from sample/Standard/Hubbard/triangular/UHF/reference/zqp_APOrbital_opt.dat rename to samples/Standard/Hubbard/triangular/UHF/reference/zqp_APOrbital_opt.dat diff --git a/sample/Standard/Hubbard/triangular/UHF/reference/zvo_check.dat b/samples/Standard/Hubbard/triangular/UHF/reference/zvo_check.dat similarity index 100% rename from sample/Standard/Hubbard/triangular/UHF/reference/zvo_check.dat rename to samples/Standard/Hubbard/triangular/UHF/reference/zvo_check.dat diff --git a/sample/Standard/Hubbard/triangular/UHF/reference/zvo_eigen.dat b/samples/Standard/Hubbard/triangular/UHF/reference/zvo_eigen.dat similarity index 100% rename from sample/Standard/Hubbard/triangular/UHF/reference/zvo_eigen.dat rename to samples/Standard/Hubbard/triangular/UHF/reference/zvo_eigen.dat diff --git a/sample/Standard/Hubbard/triangular/UHF/reference/zvo_gap.dat b/samples/Standard/Hubbard/triangular/UHF/reference/zvo_gap.dat similarity index 100% rename from sample/Standard/Hubbard/triangular/UHF/reference/zvo_gap.dat rename to samples/Standard/Hubbard/triangular/UHF/reference/zvo_gap.dat diff --git a/sample/Standard/Hubbard/triangular/UHF/reference/zvo_result.dat b/samples/Standard/Hubbard/triangular/UHF/reference/zvo_result.dat similarity index 100% rename from sample/Standard/Hubbard/triangular/UHF/reference/zvo_result.dat rename to samples/Standard/Hubbard/triangular/UHF/reference/zvo_result.dat diff --git a/sample/Standard/Kondo/Chain/StdFace.def b/samples/Standard/Kondo/Chain/StdFace.def similarity index 100% rename from sample/Standard/Kondo/Chain/StdFace.def rename to samples/Standard/Kondo/Chain/StdFace.def diff --git a/sample/Standard/Spin/HeisenbergChain/StdFace.def b/samples/Standard/Spin/HeisenbergChain/StdFace.def similarity index 100% rename from sample/Standard/Spin/HeisenbergChain/StdFace.def rename to samples/Standard/Spin/HeisenbergChain/StdFace.def diff --git a/sample/Standard/Spin/HeisenbergSquare/StdFace.def b/samples/Standard/Spin/HeisenbergSquare/StdFace.def similarity index 100% rename from sample/Standard/Spin/HeisenbergSquare/StdFace.def rename to samples/Standard/Spin/HeisenbergSquare/StdFace.def diff --git a/sample/Standard/Spin/Kagome/StdFace.def b/samples/Standard/Spin/Kagome/StdFace.def similarity index 100% rename from sample/Standard/Spin/Kagome/StdFace.def rename to samples/Standard/Spin/Kagome/StdFace.def diff --git a/sample/Standard/Spin/Kitaev/StdFace.def b/samples/Standard/Spin/Kitaev/StdFace.def similarity index 100% rename from sample/Standard/Spin/Kitaev/StdFace.def rename to samples/Standard/Spin/Kitaev/StdFace.def diff --git a/samples/Wannier/Sr2VO4/README.md b/samples/Wannier/Sr2VO4/README.md new file mode 100644 index 00000000..e3007c14 --- /dev/null +++ b/samples/Wannier/Sr2VO4/README.md @@ -0,0 +1,44 @@ +# Sr2VO4 : Downfolding into 2D three-band Hubbard model + +Compute the Wannier function and effective interaction (U and J) with RESPACK. +Convert that result into HPhi-input. +Compute it as a 2D electron system (4 site * 3 band, 4 electrons). + +First, we compute the charge density with DFT. + +``` bash +$ pw.x -in scf.in +``` +The pseudopotential (UPF file) are downloaded from +[Standard Solid State Pseudopotentials (SSSP)](http://materialscloud.org/sssp/) +http://materialscloud.org/sssp/pseudos/SSSP_eff_PBE.tar.gz + +Then perform non-scf calculation and convert the result into RESPACK format. +``` bash +$ pw.x -in nscf.in +$ qe2respack.sh sr2cuo3.save +``` + +Wannierization +``` bash +$ calc_wannier < respack.in +``` +Dielectric matrix +``` bash +$ calc_chiqw < respack.in +``` +Coulomb potential U and Hund coupling J +``` bash +$ calc_w3d < respack.in +$ calc_j3d < respack.in +``` + +Convert the result into wannier90 format +``` bash +$ respack2wan90.py zvo +``` + +Run HPhi +``` bash +$ HPhi -s stan.in +``` diff --git a/samples/Wannier/Sr2VO4/band.in b/samples/Wannier/Sr2VO4/band.in new file mode 100644 index 00000000..f08980ba --- /dev/null +++ b/samples/Wannier/Sr2VO4/band.in @@ -0,0 +1,82 @@ +&CONTROL + calculation = 'bands' + pseudo_dir = '../pseudo/' + prefix = 'sr2vo4' +/ +&SYSTEM + ibrav = 0 + nat = 7 + ntyp = 3 + ecutwfc = 45.000000 + ecutrho = 360.000000 + nbnd = 57 +/ +&ELECTRONS +/ +CELL_PARAMETERS angstrom + -1.917800 1.917800 6.280100 + 1.917800 -1.917800 6.280100 + 1.917800 1.917800 -6.280100 +ATOMIC_SPECIES + O 15.999400 O_pbe_v1.2.uspp.F.UPF + Sr 87.620000 Sr.pbe-spn-rrkjus_psl.1.0.0.UPF + V 50.941500 V_pbe_v1.uspp.F.UPF +ATOMIC_POSITIONS crystal + Sr 0.644600 0.644600 1.000000 + Sr 0.355400 0.355400 0.000000 + V 0.000000 0.000000 0.000000 + O 0.500000 0.000000 0.500000 + O 0.000000 0.500000 0.500000 + O 0.842000 0.842000 1.000000 + O 0.158000 0.158000 0.000000 +K_POINTS crystal + 49 + 0.5000000000 0.5000000000 -0.5000000000 1.0 + 0.4433287500 0.5566712500 -0.5000000000 1.0 + 0.3866575000 0.6133425000 -0.5000000000 1.0 + 0.3299862500 0.6700137500 -0.5000000000 1.0 + 0.2733150000 0.7266850000 -0.5000000000 1.0 + 0.2166437500 0.7833562500 -0.5000000000 1.0 + 0.1599725000 0.8400275000 -0.5000000000 1.0 + 0.1033012500 0.8966987500 -0.5000000000 1.0 + 0.0466300000 0.9533700000 -0.5000000000 1.0 + 0.0919660000 0.9080340000 -0.4546620000 1.0 + 0.1373020000 0.8626980000 -0.4093240000 1.0 + 0.1826380000 0.8173620000 -0.3639860000 1.0 + 0.2279740000 0.7720260000 -0.3186480000 1.0 + 0.2733100000 0.7266900000 -0.2733100000 1.0 + 0.3186480000 0.6813520000 -0.3186480000 1.0 + 0.3639860000 0.6360140000 -0.3639860000 1.0 + 0.4093240000 0.5906760000 -0.4093240000 1.0 + 0.4546620000 0.5453380000 -0.4546620000 1.0 + 0.5000000000 0.5000000000 -0.5000000000 1.0 + 0.3750000000 0.3750000000 -0.3750000000 1.0 + 0.2500000000 0.2500000000 -0.2500000000 1.0 + 0.1250000000 0.1250000000 -0.1250000000 1.0 + 0.0000000000 0.0000000000 0.0000000000 1.0 + -0.0625000000 0.0625000000 0.0000000000 1.0 + -0.1250000000 0.1250000000 0.0000000000 1.0 + -0.1875000000 0.1875000000 0.0000000000 1.0 + -0.2500000000 0.2500000000 0.0000000000 1.0 + -0.3125000000 0.3125000000 0.0000000000 1.0 + -0.3750000000 0.3750000000 0.0000000000 1.0 + -0.4375000000 0.4375000000 0.0000000000 1.0 + -0.5000000000 0.5000000000 0.0000000000 1.0 + -0.5000000000 0.5000000000 0.0466300000 1.0 + -0.4546620000 0.4546620000 0.0919660000 1.0 + -0.4093240000 0.4093240000 0.1373020000 1.0 + -0.3639860000 0.3639860000 0.1826380000 1.0 + -0.3186480000 0.3186480000 0.2279740000 1.0 + -0.2733100000 0.2733100000 0.2733100000 1.0 + -0.2277583333 0.2277583333 0.2277583333 1.0 + -0.1822066667 0.1822066667 0.1822066667 1.0 + -0.1366550000 0.1366550000 0.1366550000 1.0 + -0.0911033333 0.0911033333 0.0911033333 1.0 + -0.0455516667 0.0455516667 0.0455516667 1.0 + 0.0000000000 0.0000000000 0.0000000000 1.0 + 0.0000000000 0.0833333333 0.0000000000 1.0 + 0.0000000000 0.1666666667 0.0000000000 1.0 + 0.0000000000 0.2500000000 0.0000000000 1.0 + 0.0000000000 0.3333333333 0.0000000000 1.0 + 0.0000000000 0.4166666667 0.0000000000 1.0 + 0.0000000000 0.5000000000 -0.0000000000 1.0 diff --git a/samples/Wannier/Sr2VO4/bands.in b/samples/Wannier/Sr2VO4/bands.in new file mode 100644 index 00000000..b8780925 --- /dev/null +++ b/samples/Wannier/Sr2VO4/bands.in @@ -0,0 +1,4 @@ +&BANDS + prefix = 'sr2vo4' + lsym = .false. +/ diff --git a/samples/Wannier/Sr2VO4/nscf.in b/samples/Wannier/Sr2VO4/nscf.in new file mode 100644 index 00000000..27fc3e4d --- /dev/null +++ b/samples/Wannier/Sr2VO4/nscf.in @@ -0,0 +1,35 @@ +&CONTROL + calculation = 'nscf' + pseudo_dir = '../pseudo/' + wf_collect = .true. + prefix = 'sr2vo4' +/ +&SYSTEM + ibrav = 0 + nat = 7 + ntyp = 3 + ecutwfc = 45.000000 + ecutrho = 360.000000 + occupations = 'tetrahedra_opt' + nbnd = 57 +/ +&ELECTRONS +/ +CELL_PARAMETERS angstrom + -1.917800 1.917800 6.280100 + 1.917800 -1.917800 6.280100 + 1.917800 1.917800 -6.280100 +ATOMIC_SPECIES + O 15.999400 O_pbe_v1.2.uspp.F.UPF + Sr 87.620000 Sr.pbe-spn-rrkjus_psl.1.0.0.UPF + V 50.941500 V_pbe_v1.uspp.F.UPF +ATOMIC_POSITIONS crystal + Sr 0.644600 0.644600 1.000000 + Sr 0.355400 0.355400 0.000000 + V 0.000000 0.000000 0.000000 + O 0.500000 0.000000 0.500000 + O 0.000000 0.500000 0.500000 + O 0.842000 0.842000 1.000000 + O 0.158000 0.158000 0.000000 +K_POINTS automatic + 4 4 4 0 0 0 diff --git a/samples/Wannier/Sr2VO4/respack.in b/samples/Wannier/Sr2VO4/respack.in new file mode 100644 index 00000000..28e48930 --- /dev/null +++ b/samples/Wannier/Sr2VO4/respack.in @@ -0,0 +1,50 @@ +&PARAM_CHIQW +Num_freq_grid = 1 +!Ecut_for_eps = +flg_cRPA = 1 +MPI_num_proc_per_qcomm = 1 +MPI_num_qcomm = 4 +!flg_calc_type = 2 +!n_calc_q = 8 +/ +&PARAM_WANNIER +N_wannier = 3 +Lower_energy_window = 9.865 +Upper_energy_window = 13.35 +N_initial_guess = 3 +/ +dxy 0.2 0.0 0.0 0.0 +dyz 0.2 0.0 0.0 0.0 +dzx 0.2 0.0 0.0 0.0 +&PARAM_INTERPOLATION +N_sym_points = 10 +dense = 12, 12, 12 +/ +0.50000 0.50000 -0.50000 +0.04663 0.95337 -0.50000 +0.27331 0.72669 -0.27331 +0.50000 0.50000 -0.50000 +0.00000 0.00000 0.00000 +-0.50000 0.50000 0.00000 +-0.50000 0.50000 0.04663 +-0.27331 0.27331 0.27331 +0.00000 0.00000 0.00000 +0.00000 0.50000 0.00000 +&PARAM_VISUALIZATION +flg_vis_wannier = 1, +ix_vis_min = -1, +ix_vis_max = 2, +iy_vis_min = -1, +iy_vis_max = 2, +iz_vis_min = -1, +iz_vis_max = 2 +/ +&PARAM_CALC_INT +calc_ifreq = 1 +ix_intJ_min = 0 +ix_intJ_max = 0 +iy_intJ_min = 0 +iy_intJ_max = 0 +iz_intJ_min = 0 +iz_intJ_max = 0 +/ diff --git a/samples/Wannier/Sr2VO4/scf.in b/samples/Wannier/Sr2VO4/scf.in new file mode 100644 index 00000000..4830c987 --- /dev/null +++ b/samples/Wannier/Sr2VO4/scf.in @@ -0,0 +1,34 @@ +&CONTROL + calculation = 'scf' + pseudo_dir = '../pseudo/' + prefix = 'sr2vo4' +/ +&SYSTEM + ibrav = 0 + nat = 7 + ntyp = 3 + ecutwfc = 45.000000 + ecutrho = 360.000000 + occupations = 'tetrahedra_opt' +/ +&ELECTRONS +mixing_beta = 0.3 +/ +CELL_PARAMETERS angstrom + -1.917800 1.917800 6.280100 + 1.917800 -1.917800 6.280100 + 1.917800 1.917800 -6.280100 +ATOMIC_SPECIES + O 15.999400 O_pbe_v1.2.uspp.F.UPF + Sr 87.620000 Sr.pbe-spn-rrkjus_psl.1.0.0.UPF + V 50.941500 V_pbe_v1.uspp.F.UPF +ATOMIC_POSITIONS crystal + Sr 0.644600 0.644600 1.000000 + Sr 0.355400 0.355400 0.000000 + V 0.000000 0.000000 0.000000 + O 0.500000 0.000000 0.500000 + O 0.000000 0.500000 0.500000 + O 0.842000 0.842000 1.000000 + O 0.158000 0.158000 0.000000 +K_POINTS automatic + 4 4 4 0 0 0 diff --git a/samples/Wannier/Sr2VO4/stan.in b/samples/Wannier/Sr2VO4/stan.in new file mode 100644 index 00000000..9168ab84 --- /dev/null +++ b/samples/Wannier/Sr2VO4/stan.in @@ -0,0 +1,18 @@ +model = "Hubbard" +lattice = "wannier90" +a0w = 2 +a0l = 0 +a0h = 2 +a1w = 0 +a1l = 2 +a1h = 2 +a2w = 1 +a2l = 0 +a2h = 0 +method = "CG" +2Sz = 0 +nelec = 4 +exct = 1 +cutoff_t = 0.2 +cutoff_u = 0.4 +cutoff_j = 0.1 From 782054edc24db31dded62959c4633828488d038d Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Fri, 16 Mar 2018 16:20:44 +0900 Subject: [PATCH 16/34] Add English manuals for the RESPACK iterface. --- dist.sh | 7 +-- doc/en/index.rst | 1 + doc/en/wannier/contact.rst | 12 ++++ doc/en/wannier/format.rst | 46 ++++++++++++++ doc/en/wannier/index.rst | 25 ++++++++ doc/en/wannier/overview.rst | 19 ++++++ doc/en/wannier/parameter.rst | 27 ++++++++ doc/en/wannier/tutorial.rst | 116 +++++++++++++++++++++++++++++++++++ doc/jp/wannier/format.rst | 36 ++++++++++- doc/jp/wannier/parameter.rst | 19 +++++- doc/jp/wannier/tutorial.rst | 68 ++++++++++++++++++++ mVMCconfig.sh | 12 ++-- 12 files changed, 371 insertions(+), 17 deletions(-) create mode 100644 doc/en/wannier/contact.rst create mode 100644 doc/en/wannier/format.rst create mode 100644 doc/en/wannier/index.rst create mode 100644 doc/en/wannier/overview.rst create mode 100644 doc/en/wannier/parameter.rst create mode 100644 doc/en/wannier/tutorial.rst diff --git a/dist.sh b/dist.sh index 74b0f553..b93f7450 100755 --- a/dist.sh +++ b/dist.sh @@ -20,11 +20,6 @@ cp -rf * mVMC-${vid} # cd mVMC-${vid}/doc/jp make -f makefile_doc_jp -cp userguide_jp.pdf ../../../ -cd ../en -make -f makefile_doc_en -cp userguide_en.pdf ../../../ -cd ../fourier/ja sed -i -e "s/mathjax/pngmath/g" conf.py make latexpdfja make html @@ -32,7 +27,7 @@ cd ../en sed -i -e "s/mathjax/pngmath/g" conf.py make latexpdfja make html -cd ../../../ +cd ../../ # # Remove some files # diff --git a/doc/en/index.rst b/doc/en/index.rst index 7b909b8f..9e8edad2 100644 --- a/doc/en/index.rst +++ b/doc/en/index.rst @@ -18,6 +18,7 @@ Manual for mVMC algorithm.rst appendix.rst fourier/index + wannier/index acknowledge.rst .. Indices and tables diff --git a/doc/en/wannier/contact.rst b/doc/en/wannier/contact.rst new file mode 100644 index 00000000..9404d730 --- /dev/null +++ b/doc/en/wannier/contact.rst @@ -0,0 +1,12 @@ +Contact +======= + +If you have any comments, questions, bug reports etc. about this utility, +please contact to the main developer (Mitsuaki Kawamura) by +sending the e-mail (the address is shown below). + +:: + + mkawamura_at_issp.u-tokyo.ac.jp + +Please change ``_at_`` into ``@``, when you will send the e-mail. diff --git a/doc/en/wannier/format.rst b/doc/en/wannier/format.rst new file mode 100644 index 00000000..8ee1ebbf --- /dev/null +++ b/doc/en/wannier/format.rst @@ -0,0 +1,46 @@ +File format +=========== + +Standard mode of HPhi/mVMC reads the following files. +We can obtain these files by executing the utility ``respack2wan90.py`` in the directory +where the programs of RESPACK are executed. +``respack2wan90.py`` is included in HPhi/mVMC package. + +Geometry +-------- + +The file name is ``[CDataFileHeat]_geom.dat``. +By editing this file, we can modify the number of orbitals treated in HPhi/mVMC. + +:: + + -1.917800 1.917800 6.280100 + 1.917800 -1.917800 6.280100 + 1.917800 1.917800 -6.280100 + 3 + 0.000000 -0.000000 -0.000000 + -0.000000 -0.000000 -0.000000 + 0.000000 0.000000 0.000000 + +* Lines 1 - 3 + + Unit lattice vectors in the Cartesian coordinate (arbitrary unit). + +* Line 4 + + The number of orbitals par unit cell treated by mVMC/HPhi. + When this file is generated by ``respack2wan90.py``, + this number is the same as the number of Wannier functions in RESPACK. + When we reduce the number by editing this file, + the model including the same number of orbitals from the top. + +* Line 5 - end + + Wannier centres in the fractional coordinate. They are used by the Fourier utility. + +Hopping, Coulomb, exchange integrals +------------------------------------ + +The file name is ``[CDataFileHeat]_hr.dat``, ``[CDataFileHeat]_ur.dat``, +and ``[CDataFileHeat]_jr.dat``, respectively. +They are formatted as the hopping-integral file of Wannier90 is used. diff --git a/doc/en/wannier/index.rst b/doc/en/wannier/index.rst new file mode 100644 index 00000000..aff29f2e --- /dev/null +++ b/doc/en/wannier/index.rst @@ -0,0 +1,25 @@ +.. test documentation master file, created by + sphinx-quickstart on Sat Jan 7 22:10:04 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +.. _wannier: + +Downfolding with Wannier functions +================================== +.. toctree:: + :maxdepth: 3 + + overview + tutorial + parameter + format + contact + +.. Indices and tables +.. ================== + +.. * :ref:`genindex` +.. * :ref:`modindex` +.. * :ref:`search` + diff --git a/doc/en/wannier/overview.rst b/doc/en/wannier/overview.rst new file mode 100644 index 00000000..842b0e57 --- /dev/null +++ b/doc/en/wannier/overview.rst @@ -0,0 +1,19 @@ +Overview +======== + +In this document, we introduce how we compute downfolded models +with mVMC or :math:`{\mathcal H}\Phi` in conjunction to +`RESPACK `_. + +Prerequisite +------------ + +We compute the Kohn-Sham orbitals with +`QuantumESPRESSO `_ +or +`xTAPP `_, +and obtain the Wannier function, the dielectric function, +the effective interaction with RESPACK, +and simulate quantum lattice models with +mVMC or :math:`{\mathcal H}\Phi`. +Therefore, these programs must be available in our machine. diff --git a/doc/en/wannier/parameter.rst b/doc/en/wannier/parameter.rst new file mode 100644 index 00000000..1f1d0dd4 --- /dev/null +++ b/doc/en/wannier/parameter.rst @@ -0,0 +1,27 @@ +Input parameter for Standard mode +================================= + +We show the following example of the input file. + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/stan.in + +The input parameters for the Standard mode to perform calculation +of the downfolded model are as follows: + +* ``lattice = "wannier90"`` + +* ``cutoff_t``, ``cutoff_u``, ``cutoff_j`` + + **Type :** float + + **Default :** ``1.0e-8`` + + The cutoff for the hopping, Coulomb, exchange integrals. + We ignore these integrals smaller than cutoffs. + +* ``W``, ``L``, ``Height`` +* ``a0W``, ``a0L``, ``a0H``, ``a1W``, ``a1L``, ``a1H``, ``a2W``, ``a2L``, ``a2H`` +* ``Wsub``, ``Lsub``, ``Hsub`` +* ``a0Wsub``, ``a0Lsub``, ``a0Hsub``, ``a1Wsub``, ``a1Lsub``, ``a1Hsub``, ``a2Wsub``, ``a2Lsub``, ``a2Hsub`` + + The third dimension appears. diff --git a/doc/en/wannier/tutorial.rst b/doc/en/wannier/tutorial.rst new file mode 100644 index 00000000..02be1397 --- /dev/null +++ b/doc/en/wannier/tutorial.rst @@ -0,0 +1,116 @@ +.. _tutorialwannier: + +Tutorial +======== + +In this tutorial, we downfold Sr\ :sub:`2`\ VO\ :sub:`4` +into three-orbitals 2D Hubbard model, +and simulate that model with HPhi/mVMC. +We employ QuantumESPRESSO for the DFT calculation. + +SCF calculation of charge density +--------------------------------- + +First, we perform the SCF calculation of the charge density. +The input file is as follows: + +:download:`scf.in <../../../samples/Wannier/Sr2VO4/scf.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/scf.in + +The pseudopotential (UPF file) are downloaded from +`Standard Solid State Pseudopotentials (SSSP) `_ +http://materialscloud.org/sssp/pseudos/SSSP_eff_PBE.tar.gz + +We use the program ``pw.x`` in QuantumESPRESSO as follows. + +.. code-block:: bash + + $ pw.x -in scf.in + +(Optional) Band structure +------------------------- + +:download:`band.in <../../../samples/Wannier/Sr2VO4/band.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/band.in + +We use ``pw.x``. + +.. code-block:: bash + + $ pw.x -in band.in + +:download:`bands.in <../../../samples/Wannier/Sr2VO4/bands.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/bands.in + +We use ``bands.x`` QuantumESPRESSO. + +.. code-block:: bash + + $ bands.x -in bands.in + +We can plot the band structure by reading output ``bands.out.gnu`` from +GnuPlot etc. + +Kohn-Sham orbitals for Wannier +------------------------------ + +:download:`nscf.in <../../../samples/Wannier/Sr2VO4/nscf.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/nscf.in + +We use ``pw.x`` as + +.. code-block:: bash + + $ pw.x -in nscf.in + +Then, we use the utility ``qe2respack.sh`` which is included in the RESPACK package. +The command-line argument is the name of ``[prefix].save`` directory. + +.. code-block:: bash + + $ qe2respack.sh sr2cuo3.save + +Wannier function, dielectric function, effective interaction +------------------------------------------------------------ + +:download:`respack.in <../../../samples/Wannier/Sr2VO4/respack.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/respack.in + +We use ``calc_wannier``, ``calc_chiqw``, ``calc_j3d``, +``calc_w3d`` in RESPACK. + +.. code-block:: bash + + $ calc_wannier < respack.in + $ calc_chiqw < respack.in + $ calc_w3d < respack.in + $ calc_j3d < respack.in + +Quantum lattice mode for HPhi/mVMC +---------------------------------- + +First, we translate the hopping file etc. created by RESPACK +into the Wannier90 format. +For this purpose, we use the utility ``respack2wan90.py`` included in HPhi/mVMC. +The command-line argument should be the same as the input parameter ``CDataFileHead`` +for Standard mode of HPhi/mVMC. +If we do not specify that argument, the default value ``zvo`` is used. + +.. code-block:: bash + + $ respack2wan90.py zvo + +Then we can run HPhi/mVMC with the standard mode. + +:download:`respack.in <../../../samples/Wannier/Sr2VO4/stan.in>` + +.. literalinclude:: ../../../samples/Wannier/Sr2VO4/stan.in + +.. code-block:: bash + + $ vmc.out -s stan.in diff --git a/doc/jp/wannier/format.rst b/doc/jp/wannier/format.rst index 7b51bb6c..320372bc 100644 --- a/doc/jp/wannier/format.rst +++ b/doc/jp/wannier/format.rst @@ -1,11 +1,43 @@ ファイルフォーマット ==================== +HPhi/mVMCのスタンダードモードでは以下のファイルを読み込む. +これらのファイルはRESPACKのプログラムを実行したディレクトリで, +HPhi/mVMCに付属のユーティリティー ``respack2wan90.py`` を使うと得られる. + ジオメトリー ------------ +ファイル名は ``[CDataFileHeat]_geom.dat``. +このファイルを必要に応じて修正することで取り扱う軌道数を変更できる. + +:: + + -1.917800 1.917800 6.280100 + 1.917800 -1.917800 6.280100 + 1.917800 1.917800 -6.280100 + 3 + 0.000000 -0.000000 -0.000000 + -0.000000 -0.000000 -0.000000 + 0.000000 0.000000 0.000000 + +* 1 - 3行目 + + 結晶並進ベクトル. デカルト座標系で任意単位. + +* 4行目 + + mVMC/HPhiで取り入れる, ユニットセルあたりの軌道数. + ``respack2wan90.py`` によって生成すると, Wannier関数の数と同じになる. + Wannier関数の数よりも少なくすることも可能であり, + その場合には先頭からこの数の分だけの軌道を取り入れたモデルが構築される. + +* 5行目以降 + + 各軌道のWannier中心 (フラクショナル座標). Fourier変換ツールで使われる. + ホッピング, Coulomb積分, 交換積分 --------------------------------- -Wannier90の形式に従う. -付属のユーティリティーrespack2wan90.pyを使う. +ファイル名は ``[CDataFileHeat]_hr.dat``, ``[CDataFileHeat]_ur.dat``, ``[CDataFileHeat]_jr.dat``. +Wannier90のホッピング積分の形式に従う. diff --git a/doc/jp/wannier/parameter.rst b/doc/jp/wannier/parameter.rst index 4c2182de..80750082 100644 --- a/doc/jp/wannier/parameter.rst +++ b/doc/jp/wannier/parameter.rst @@ -7,5 +7,22 @@ .. literalinclude:: ../../../samples/Wannier/Sr2VO4/stan.in -Wannier関数を用いたダウンフォールディングに特有のパラメーターは次の通りである. +Wannier関数を用いたダウンフォールディングに特有のパラメーター設定は次の通りである. +* ``lattice = "wannier90"`` + +* ``cutoff_t``, ``cutoff_u``, ``cutoff_j`` + + **形式 :** 実数 + + **デフォルト値 :** ``1.0e-8`` + + ホッピング, Coulomb積分, 交換積分に対して, + これより小さい値を無視する. + +* ``W``, ``L``, ``Height`` +* ``a0W``, ``a0L``, ``a0H``, ``a1W``, ``a1L``, ``a1H``, ``a2W``, ``a2L``, ``a2H`` +* ``Wsub``, ``Lsub``, ``Hsub`` +* ``a0Wsub``, ``a0Lsub``, ``a0Hsub``, ``a1Wsub``, ``a1Lsub``, ``a1Hsub``, ``a2Wsub``, ``a2Lsub``, ``a2Hsub`` + + このように3番目の次元が現れる. diff --git a/doc/jp/wannier/tutorial.rst b/doc/jp/wannier/tutorial.rst index d4fb49c6..9c56bc96 100644 --- a/doc/jp/wannier/tutorial.rst +++ b/doc/jp/wannier/tutorial.rst @@ -11,21 +11,47 @@ DFT計算はQuantumESPRESSOで行う. 電荷密度のSCF計算 ----------------- +まず, DFTによる電荷密度のSCF計算を行う. + :download:`scf.in <../../../samples/Wannier/Sr2VO4/scf.in>` .. literalinclude:: ../../../samples/Wannier/Sr2VO4/scf.in +The pseudopotential (UPF file) are downloaded from +`Standard Solid State Pseudopotentials (SSSP) `_ +http://materialscloud.org/sssp/pseudos/SSSP_eff_PBE.tar.gz + +QuantumESPRESSO内のプログラム ``pw.x`` を使う. + +.. code-block:: bash + + $ pw.x -in scf.in + (Optional) バンド計算と描画 --------------------------- :download:`band.in <../../../samples/Wannier/Sr2VO4/band.in>` .. literalinclude:: ../../../samples/Wannier/Sr2VO4/band.in + +ここでも ``pw.x`` を使う. +.. code-block:: bash + + $ pw.x -in band.in + :download:`bands.in <../../../samples/Wannier/Sr2VO4/bands.in>` .. literalinclude:: ../../../samples/Wannier/Sr2VO4/bands.in + +QuantumESPRESSOの ``bands.x`` を使う. +.. code-block:: bash + + $ bands.x -in bands.in + +出力された ``bands.out.gnu`` をGnuPlotなどで読み込んでバンドを描く. + Kohn-Sham軌道の計算 ------------------- @@ -33,6 +59,19 @@ Kohn-Sham軌道の計算 .. literalinclude:: ../../../samples/Wannier/Sr2VO4/nscf.in +ここでも ``pw.x`` を使う. + +.. code-block:: bash + + $ pw.x -in nscf.in + +次にRESPACKに付属のユーティリティー ``qe2respack.sh`` を使う. +引数は ``[prefix].save`` ディレクトリ名. + +.. code-block:: bash + + $ qe2respack.sh sr2cuo3.save + Wannier関数, 誘電関数, 有効相互作用の計算 ----------------------------------------- @@ -40,9 +79,38 @@ Wannier関数, 誘電関数, 有効相互作用の計算 .. literalinclude:: ../../../samples/Wannier/Sr2VO4/respack.in +RESPACKのプログラム ``calc_wannier``, ``calc_chiqw``, ``calc_j3d``, +``calc_w3d`` を使う. + +.. code-block:: bash + + $ calc_wannier < respack.in + $ calc_chiqw < respack.in + $ calc_w3d < respack.in + $ calc_j3d < respack.in + HPhi/mVMCによるモデル計算 ------------------------- +まず, RESPACKによって出力されたホッピング等のファイルを +Wannier90の形式に変換する. +これにはHPhi/mVMCに付属のユーティリティー +respack2wan90.pyを使う. +引数はHPhi/mVMCのスタンダードモードのパラメーター ``CDataFileHead`` と同じにする. +引数を指定しない場合は ``zvo`` (HPhi/mVMCの ``CDataFileHead`` のデフォルト) +が指定されたものとする. + +.. code-block:: bash + + $ respack2wan90.py zvo + +これで, HPhi/mVMCで実行する準備が出来たので, +スタンダードモードを用いて計算する. + :download:`respack.in <../../../samples/Wannier/Sr2VO4/stan.in>` .. literalinclude:: ../../../samples/Wannier/Sr2VO4/stan.in + +.. code-block:: bash + + $ vmc.out -s stan.in diff --git a/mVMCconfig.sh b/mVMCconfig.sh index 966f49be..b51495e5 100644 --- a/mVMCconfig.sh +++ b/mVMCconfig.sh @@ -155,10 +155,8 @@ mvmc: cd tool;make -f makefile_tool userguide: - cd doc/jp/;make -f makefile_doc_jp; - cd doc/en/;make -f makefile_doc_en; - cd doc/fourier/ja; make html latexpdfja - cd doc/fourier/en; make html latexpdfja + cd doc/jp; make html latexpdfja + cd doc/en; make html latexpdfja clean: cd src/mVMC/; make -f makefile_src clean @@ -166,10 +164,8 @@ clean: veryclean: make clean - cd doc/jp; make -f makefile_doc_jp clean - cd doc/en; make -f makefile_doc_en clean - cd doc/fourier/ja; make clean - cd doc/fourier/en; make clean + cd doc/jp; make clean + cd doc/en; make clean rm -f src/make.sys makefile EOF fi From c6fe4546d984fe3452a882ee1dea20f5526f9b6d Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Sat, 17 Mar 2018 18:05:07 +0900 Subject: [PATCH 17/34] Update manual --- doc/en/wannier/tutorial.rst | 5 +++-- doc/jp/wannier/tutorial.rst | 7 ++++--- samples/Wannier/Sr2VO4/README.md | 4 ++-- samples/Wannier/Sr2VO4/band.in | 12 ++++++------ samples/Wannier/Sr2VO4/nscf.in | 14 +++++++------- samples/Wannier/Sr2VO4/respack.in | 5 ----- samples/Wannier/Sr2VO4/scf.in | 14 +++++++------- samples/Wannier/Sr2VO4/stan.in | 6 ++---- 8 files changed, 31 insertions(+), 36 deletions(-) diff --git a/doc/en/wannier/tutorial.rst b/doc/en/wannier/tutorial.rst index 02be1397..0c0888d1 100644 --- a/doc/en/wannier/tutorial.rst +++ b/doc/en/wannier/tutorial.rst @@ -19,8 +19,9 @@ The input file is as follows: .. literalinclude:: ../../../samples/Wannier/Sr2VO4/scf.in The pseudopotential (UPF file) are downloaded from -`Standard Solid State Pseudopotentials (SSSP) `_ -http://materialscloud.org/sssp/pseudos/SSSP_eff_PBE.tar.gz +`The SG15 Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials `_. + +http://www.quantum-simulation.org/potentials/sg15_oncv/sg15_oncv_upf_2015-10-07.tar.gz We use the program ``pw.x`` in QuantumESPRESSO as follows. diff --git a/doc/jp/wannier/tutorial.rst b/doc/jp/wannier/tutorial.rst index 9c56bc96..fc491c3e 100644 --- a/doc/jp/wannier/tutorial.rst +++ b/doc/jp/wannier/tutorial.rst @@ -17,9 +17,10 @@ DFT計算はQuantumESPRESSOで行う. .. literalinclude:: ../../../samples/Wannier/Sr2VO4/scf.in -The pseudopotential (UPF file) are downloaded from -`Standard Solid State Pseudopotentials (SSSP) `_ -http://materialscloud.org/sssp/pseudos/SSSP_eff_PBE.tar.gz +擬ポテンシャル (UPF ファイル) は +`The SG15 Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials `_ のものを使う. + +http://www.quantum-simulation.org/potentials/sg15_oncv/sg15_oncv_upf_2015-10-07.tar.gz QuantumESPRESSO内のプログラム ``pw.x`` を使う. diff --git a/samples/Wannier/Sr2VO4/README.md b/samples/Wannier/Sr2VO4/README.md index e3007c14..7b964d1d 100644 --- a/samples/Wannier/Sr2VO4/README.md +++ b/samples/Wannier/Sr2VO4/README.md @@ -10,8 +10,8 @@ First, we compute the charge density with DFT. $ pw.x -in scf.in ``` The pseudopotential (UPF file) are downloaded from -[Standard Solid State Pseudopotentials (SSSP)](http://materialscloud.org/sssp/) -http://materialscloud.org/sssp/pseudos/SSSP_eff_PBE.tar.gz +[The SG15 Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials](www.quantum-simulation.org/potentials/sg15_oncv/) +http://www.quantum-simulation.org/potentials/sg15_oncv/sg15_oncv_upf_2015-10-07.tar.gz Then perform non-scf calculation and convert the result into RESPACK format. ``` bash diff --git a/samples/Wannier/Sr2VO4/band.in b/samples/Wannier/Sr2VO4/band.in index f08980ba..39678b4e 100644 --- a/samples/Wannier/Sr2VO4/band.in +++ b/samples/Wannier/Sr2VO4/band.in @@ -1,14 +1,14 @@ &CONTROL calculation = 'bands' - pseudo_dir = '../pseudo/' + pseudo_dir = './' prefix = 'sr2vo4' / &SYSTEM ibrav = 0 nat = 7 ntyp = 3 - ecutwfc = 45.000000 - ecutrho = 360.000000 + ecutwfc = 120.0 + ecutrho = 480 nbnd = 57 / &ELECTRONS @@ -18,9 +18,9 @@ CELL_PARAMETERS angstrom 1.917800 -1.917800 6.280100 1.917800 1.917800 -6.280100 ATOMIC_SPECIES - O 15.999400 O_pbe_v1.2.uspp.F.UPF - Sr 87.620000 Sr.pbe-spn-rrkjus_psl.1.0.0.UPF - V 50.941500 V_pbe_v1.uspp.F.UPF + O 15.999400 O_ONCV_PBE-1.0.upf + Sr 87.620000 Sr_ONCV_PBE-1.0.upf + V 50.941500 V_ONCV_PBE-1.0.upf ATOMIC_POSITIONS crystal Sr 0.644600 0.644600 1.000000 Sr 0.355400 0.355400 0.000000 diff --git a/samples/Wannier/Sr2VO4/nscf.in b/samples/Wannier/Sr2VO4/nscf.in index 27fc3e4d..f5607d34 100644 --- a/samples/Wannier/Sr2VO4/nscf.in +++ b/samples/Wannier/Sr2VO4/nscf.in @@ -1,6 +1,6 @@ &CONTROL calculation = 'nscf' - pseudo_dir = '../pseudo/' + pseudo_dir = './' wf_collect = .true. prefix = 'sr2vo4' / @@ -8,10 +8,10 @@ ibrav = 0 nat = 7 ntyp = 3 - ecutwfc = 45.000000 - ecutrho = 360.000000 + ecutwfc = 120.0 + ecutrho = 480 occupations = 'tetrahedra_opt' - nbnd = 57 + nbnd = 100 / &ELECTRONS / @@ -20,9 +20,9 @@ CELL_PARAMETERS angstrom 1.917800 -1.917800 6.280100 1.917800 1.917800 -6.280100 ATOMIC_SPECIES - O 15.999400 O_pbe_v1.2.uspp.F.UPF - Sr 87.620000 Sr.pbe-spn-rrkjus_psl.1.0.0.UPF - V 50.941500 V_pbe_v1.uspp.F.UPF + O 15.999400 O_ONCV_PBE-1.0.upf + Sr 87.620000 Sr_ONCV_PBE-1.0.upf + V 50.941500 V_ONCV_PBE-1.0.upf ATOMIC_POSITIONS crystal Sr 0.644600 0.644600 1.000000 Sr 0.355400 0.355400 0.000000 diff --git a/samples/Wannier/Sr2VO4/respack.in b/samples/Wannier/Sr2VO4/respack.in index 28e48930..f0d36011 100644 --- a/samples/Wannier/Sr2VO4/respack.in +++ b/samples/Wannier/Sr2VO4/respack.in @@ -1,11 +1,6 @@ &PARAM_CHIQW Num_freq_grid = 1 -!Ecut_for_eps = flg_cRPA = 1 -MPI_num_proc_per_qcomm = 1 -MPI_num_qcomm = 4 -!flg_calc_type = 2 -!n_calc_q = 8 / &PARAM_WANNIER N_wannier = 3 diff --git a/samples/Wannier/Sr2VO4/scf.in b/samples/Wannier/Sr2VO4/scf.in index 4830c987..5e834c63 100644 --- a/samples/Wannier/Sr2VO4/scf.in +++ b/samples/Wannier/Sr2VO4/scf.in @@ -1,14 +1,14 @@ &CONTROL calculation = 'scf' - pseudo_dir = '../pseudo/' + pseudo_dir = './' prefix = 'sr2vo4' / &SYSTEM ibrav = 0 nat = 7 ntyp = 3 - ecutwfc = 45.000000 - ecutrho = 360.000000 + ecutwfc = 120.0 + ecutrho = 480 occupations = 'tetrahedra_opt' / &ELECTRONS @@ -19,9 +19,9 @@ CELL_PARAMETERS angstrom 1.917800 -1.917800 6.280100 1.917800 1.917800 -6.280100 ATOMIC_SPECIES - O 15.999400 O_pbe_v1.2.uspp.F.UPF - Sr 87.620000 Sr.pbe-spn-rrkjus_psl.1.0.0.UPF - V 50.941500 V_pbe_v1.uspp.F.UPF + O 15.999400 O_ONCV_PBE-1.0.upf + Sr 87.620000 Sr_ONCV_PBE-1.0.upf + V 50.941500 V_ONCV_PBE-1.0.upf ATOMIC_POSITIONS crystal Sr 0.644600 0.644600 1.000000 Sr 0.355400 0.355400 0.000000 @@ -31,4 +31,4 @@ ATOMIC_POSITIONS crystal O 0.842000 0.842000 1.000000 O 0.158000 0.158000 0.000000 K_POINTS automatic - 4 4 4 0 0 0 + 8 8 8 0 0 0 diff --git a/samples/Wannier/Sr2VO4/stan.in b/samples/Wannier/Sr2VO4/stan.in index 9168ab84..260c4791 100644 --- a/samples/Wannier/Sr2VO4/stan.in +++ b/samples/Wannier/Sr2VO4/stan.in @@ -9,10 +9,8 @@ a1h = 2 a2w = 1 a2l = 0 a2h = 0 -method = "CG" 2Sz = 0 nelec = 4 -exct = 1 -cutoff_t = 0.2 -cutoff_u = 0.4 +cutoff_t = 0.1 +cutoff_u = 1.0 cutoff_j = 0.1 From 8e9f49ddc4142db844eef9a336f61961dbb6f911 Mon Sep 17 00:00:00 2001 From: Mitsuaki Kwamura Date: Sun, 25 Mar 2018 10:44:20 +0900 Subject: [PATCH 18/34] Manual: Add Hamiltonian for downfolding --- doc/en/wannier/overview.rst | 30 ++++++++++++++++++++++++++++++ doc/jp/wannier/overview.rst | 30 ++++++++++++++++++++++++++++++ 2 files changed, 60 insertions(+) diff --git a/doc/en/wannier/overview.rst b/doc/en/wannier/overview.rst index 842b0e57..79891140 100644 --- a/doc/en/wannier/overview.rst +++ b/doc/en/wannier/overview.rst @@ -5,6 +5,36 @@ In this document, we introduce how we compute downfolded models with mVMC or :math:`{\mathcal H}\Phi` in conjunction to `RESPACK `_. +.. math:: + + \begin{aligned} + {\cal H} &= + \sum_{i, j, \alpha, \beta, \sigma} + t_{i \alpha j \beta} c_{i \alpha \sigma}^{\dagger} c_{j \beta \sigma} + \nonumber \\ + &+ \sum_{i, \alpha} + U_{i \alpha i \alpha} n_{i \alpha \uparrow} n_{j \alpha \downarrow} + + \sum_{(i, \alpha) \lt (j, \beta)} + U_{i \alpha j \beta} n_{i \alpha} n_{j \beta} + - \sum_{(i, \alpha) \lt (j, \beta)} + J_{i \alpha j \beta} (n_{i \alpha \uparrow} n_{j \beta \uparrow} + + n_{i \alpha \downarrow} n_{j \beta \downarrow}) + \nonumber \\ + &+ \sum_{(i, \alpha) \lt (j, \beta)} + J_{i \alpha j \beta} ( + c_{i \alpha \uparrow}^{\dagger} c_{j \beta \downarrow}^{\dagger} + c_{i \alpha \downarrow} c_{j \beta \uparrow} + + c_{j \beta \uparrow}^{\dagger} c_{i \alpha \downarrow}^{\dagger} + c_{j \beta \downarrow} c_{j \alpha \uparrow} ) + \nonumber \\ + &+ \sum_{(i, \alpha) \lt (j, \beta)} + J_{i \alpha j \beta} ( + c_{i \alpha \uparrow}^{\dagger} c_{i \alpha \downarrow}^{\dagger} + c_{j \beta \downarrow} c_{j \beta \uparrow} + + c_{j \beta \uparrow}^{\dagger} c_{j \beta \downarrow}^{\dagger} + c_{i \alpha \downarrow} c_{i \alpha \uparrow} ) + \end{aligned} + Prerequisite ------------ diff --git a/doc/jp/wannier/overview.rst b/doc/jp/wannier/overview.rst index 5207c3e0..57d8a557 100644 --- a/doc/jp/wannier/overview.rst +++ b/doc/jp/wannier/overview.rst @@ -6,6 +6,36 @@ mVMC および :math:`{\mathcal H}\Phi` を用いて, ダウンフォールディングをした格子モデルを計算する機能について説明する. +.. math:: + + \begin{aligned} + {\cal H} &= + \sum_{i, j, \alpha, \beta, \sigma} + t_{i \alpha j \beta} c_{i \alpha \sigma}^{\dagger} c_{j \beta \sigma} + \nonumber \\ + &+ \sum_{i, \alpha} + U_{i \alpha i \alpha} n_{i \alpha \uparrow} n_{j \alpha \downarrow} + + \sum_{(i, \alpha) \lt (j, \beta)} + U_{i \alpha j \beta} n_{i \alpha} n_{j \beta} + - \sum_{(i, \alpha) \lt (j, \beta)} + J_{i \alpha j \beta} (n_{i \alpha \uparrow} n_{j \beta \uparrow} + + n_{i \alpha \downarrow} n_{j \beta \downarrow}) + \nonumber \\ + &+ \sum_{(i, \alpha) \lt (j, \beta)} + J_{i \alpha j \beta} ( + c_{i \alpha \uparrow}^{\dagger} c_{j \beta \downarrow}^{\dagger} + c_{i \alpha \downarrow} c_{j \beta \uparrow} + + c_{j \beta \uparrow}^{\dagger} c_{i \alpha \downarrow}^{\dagger} + c_{j \beta \downarrow} c_{j \alpha \uparrow} ) + \nonumber \\ + &+ \sum_{(i, \alpha) \lt (j, \beta)} + J_{i \alpha j \beta} ( + c_{i \alpha \uparrow}^{\dagger} c_{i \alpha \downarrow}^{\dagger} + c_{j \beta \downarrow} c_{j \beta \uparrow} + + c_{j \beta \uparrow}^{\dagger} c_{j \beta \downarrow}^{\dagger} + c_{i \alpha \downarrow} c_{i \alpha \uparrow} ) + \end{aligned} + 要件 ---- From 6a35697f2091c48e26f724a2d13940a8afa5b40a Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Fri, 30 Mar 2018 01:16:24 +0900 Subject: [PATCH 19/34] spelling --- doc/en/fourier/index.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/en/fourier/index.rst b/doc/en/fourier/index.rst index dc15bb4e..05c633b5 100644 --- a/doc/en/fourier/index.rst +++ b/doc/en/fourier/index.rst @@ -5,8 +5,8 @@ .. _fourier: -HPhi/mVMC Fourie-Transformation utility -======================================= +HPhi/mVMC Fourier-Transformation utility +======================================== .. toctree:: :maxdepth: 3 From a5e5c203616517714b2ce554a249e73b14a98244 Mon Sep 17 00:00:00 2001 From: k-yoshimi Date: Fri, 30 Mar 2018 09:53:35 +0900 Subject: [PATCH 20/34] fix spellmiss and add spell-check function for sphinx --- doc/en/appendix.rst | 2 +- doc/en/conf.py | 5 +- doc/en/expert.rst | 4 +- doc/en/output.rst | 4 +- doc/en/spell_check.sh | 1 + doc/en/spelling_wordlist.txt | 224 +++++++++++++++++++++++++++++++++++ doc/en/standard.rst | 6 +- doc/en/wannier/format.rst | 2 +- 8 files changed, 238 insertions(+), 10 deletions(-) create mode 100644 doc/en/spell_check.sh create mode 100644 doc/en/spelling_wordlist.txt diff --git a/doc/en/appendix.rst b/doc/en/appendix.rst index 22685d6d..78223010 100644 --- a/doc/en/appendix.rst +++ b/doc/en/appendix.rst @@ -64,7 +64,7 @@ file ``UHF`` is generated in ``src/ComplexUHF/src``. Input files ~~~~~~~~~~~ -A file for assigning input files (namelsit.def) +A file for assigning input files (namelist.def) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The following files are needed to use the program of UHF. The format diff --git a/doc/en/conf.py b/doc/en/conf.py index b2879e71..dfbd39a9 100644 --- a/doc/en/conf.py +++ b/doc/en/conf.py @@ -30,9 +30,12 @@ # ones. extensions = [ 'sphinx.ext.mathjax', - 'sphinx_numfig' + 'sphinx_numfig', + 'sphinxcontrib.spelling' ] +spelling_word_list_filename='spelling_wordlist.txt' + # Add any paths that contain templates here, relative to this directory. templates_path = ['_templates'] diff --git a/doc/en/expert.rst b/doc/en/expert.rst index 5a5a2fd4..13c36753 100644 --- a/doc/en/expert.rst +++ b/doc/en/expert.rst @@ -574,7 +574,7 @@ Keywords and parameters **Type :** int-type (0 or 1, default value: 0) **Description :** The option of solving :math:`Sx=g` in the SR method - without construting :math:`S` + without constructing :math:`S` matrix [NeuscammanUmrigarChan_ ]. (0: off, 1: on). This reduces the amount of memory usage from :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})` to @@ -989,7 +989,7 @@ Use rules CoulombInter file (coulombinter.def) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -The Hamiltonian for the coulombintrer interactions +The Hamiltonian for the coulombinter interactions .. math:: diff --git a/doc/en/output.rst b/doc/en/output.rst index 2df1d30b..f652b429 100644 --- a/doc/en/output.rst +++ b/doc/en/output.rst @@ -92,7 +92,7 @@ Output file for doublonHolon 2-site factors (\*\*\*\_doublonHolon2site\_opt.dat) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -The optimized 2-site doublon-holon crrelation factors by SR method are +The optimized 2-site doublon-holon correlation factors by SR method are outputted. The file format is same as the ``InDH2`` file defined in Sec. :ref:`InputParam`. @@ -100,7 +100,7 @@ Output file for doublonHolon 4-site factors (\*\*\*\_doublonHolon4site\_opt.dat) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -The optimized 4-site doublon-holon crrelation factors by SR method are +The optimized 4-site doublon-holon correlation factors by SR method are outputted. The file format is same as the ``InDH4`` file defined in Sec. :ref:`InputParam`. diff --git a/doc/en/spell_check.sh b/doc/en/spell_check.sh new file mode 100644 index 00000000..f50abef5 --- /dev/null +++ b/doc/en/spell_check.sh @@ -0,0 +1 @@ +sphinx-build -b spelling -d _build/doctrees . _build_spelling diff --git a/doc/en/spelling_wordlist.txt b/doc/en/spelling_wordlist.txt new file mode 100644 index 00000000..94d6e7e8 --- /dev/null +++ b/doc/en/spelling_wordlist.txt @@ -0,0 +1,224 @@ +bd +ba +fd +yoshimi +bd +ba +fd +ccf +fe +Hidetoshi +Nishimori +Daisuke +Tahara +Lanczos +diagonalization +ver +Yuichi +Motoyama +Yasuyuki +Kato +Takeo +Hoshi +Tomohiro +Sogabe +Krylov +Bogoliubov +doi +JPSJ +subdiagonal +Mersenne +dSFMT +Iwanami +ies +Shoten +Sugiura +Shimizu +wavefunctions +wavefunction +mTPQ +Lett +Takahiro +Misawa +CalcType +CalcModel +Hund +Ising +CalcMod +ModPara +LocSpin +xxx +Kondo +dat +isite +tmp +idim +mem +Flct +doublon +stp +TMcomponents +TimeKeeper +EigenVector +TPQ +spni +spnj +cisajs +OneBodyG +eigen +cisajscktalt +TwoBodyG +eigenvec +Sz +eigenvetor +Nup +Ndown +recalcvec +tmpvec +onsite +Kagome +Offsite +hoppings +offdiagonal +Yamamoto +Zhang +Fujiwara +LOBCG +BiCG +eigenenergy +Eqn +GC +Yamaji +Knyazev +Yamada +Imamura +Machida +OpenMP +MPI +sdry +mpirun +mpiexec +HPhi +gz +sekirei +maki +fortran +CMake +gcc +hamiltonians +Mitsuaki +Kawamura +Kazuyoshi +Youhei +Todo +Naoki +Kawashima +diagonalizations +Dzyaloshinskii +Moriya +Kitaev +Dagotto +Imada +Takahashi +Jaklič +Prelovšek +Raedt +Nomura +Kurita +Arita +namelist +locspn +zTrans +zInterall +greenone +greentwo +antiferromagnetic +eigenenergies +zvo +eigennumber +indices +Acknowledgement +Sugihara +Murota +http +titech +www +jp +nishimori +titpack +html +hiroshima +SFMT +sz +offsite +modpara +DynamicalGreen +countings +Frommer +calcmod +mVMC +Shinaoka +Moyuru +Ryui +Kaneko +Calro +Pfaffian +Hartree +Fock +vmcdry +holon +Defs +Gutzwiller +legendre +coulombintra +coulombinter +hund +jastrow +OrbitalAntiParallel +orbitalidx +qptransidx +Brillouine +corplot +splot +gnuplot +vmc +zqp +kpoint +gp +Satoshi +Ogoe +Kota +Ido +Masatoshi +Kazusyohi +CDataFileHead +yyy +zzz +doublonHolon +CalcTimer +postscripted +acc +hopp +grandcanonical +trianguler +kagome +Sublattice +bogoliubov +intel +cmake +Wannier +Downfolding +downfolded +Kohn +downfold +pseudopotential +sublattice +Malkov +mvmc +gutzwiller +Malkov +Montecarlo +unconserved +gauge +nd + diff --git a/doc/en/standard.rst b/doc/en/standard.rst index 75d9061a..81c55709 100644 --- a/doc/en/standard.rst +++ b/doc/en/standard.rst @@ -506,7 +506,7 @@ Figs. :num:`latticepng` , :num:`honeycombpng` , :num:`kagomepng` **Type :** Double (``0.0`` as defaults) **Description :** We can specify the phase for the hopping through - the cell boundary with these parameter (unit: degree). These fuctor + the cell boundary with these parameter (unit: degree). These factors for the :math:`\vec{a}_0` direction and the :math:`\vec{a}_1` direction can be specified independently. For the one-dimensional system, only ``phase0`` can be used. For example, a fopping from @@ -527,7 +527,7 @@ Parameters for the numerical condition **Type :** int-type (must be specified) - **Description :** The number of itenerant electrons. It is the sum of + **Description :** The number of itinerant electrons. It is the sum of the :math:`\uparrow` and :math:`\downarrow` electrons. - ``NVMCCalMode`` @@ -683,7 +683,7 @@ Parameters for the numerical condition **Type :** int-type (0 or 1, default value: 0) **Description :** The option of solving :math:`Sx=g` in the SR method - without construting :math:`S` + without constructing :math:`S` matrix [NeuscammanUmrigarChan_ ]. (0: off, 1: on). This reduces the amount of memory usage from :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})` to diff --git a/doc/en/wannier/format.rst b/doc/en/wannier/format.rst index 8ee1ebbf..20a34638 100644 --- a/doc/en/wannier/format.rst +++ b/doc/en/wannier/format.rst @@ -36,7 +36,7 @@ By editing this file, we can modify the number of orbitals treated in HPhi/mVMC. * Line 5 - end - Wannier centres in the fractional coordinate. They are used by the Fourier utility. + Wannier centers in the fractional coordinate. They are used by the Fourier utility. Hopping, Coulomb, exchange integrals ------------------------------------ From 43e859395336355acfe84b759e8595a07ddb6963 Mon Sep 17 00:00:00 2001 From: "k.ido" Date: Thu, 5 Apr 2018 11:07:07 +0900 Subject: [PATCH 21/34] #187 debug (makeCandidate in vmcmake_fsz.c) --- src/mVMC/readdef.c | 2 +- src/mVMC/vmcmake_fsz.c | 5 +++-- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/src/mVMC/readdef.c b/src/mVMC/readdef.c index 162bf082..1b03f586 100644 --- a/src/mVMC/readdef.c +++ b/src/mVMC/readdef.c @@ -1959,7 +1959,7 @@ int GetInfoTwoBodyGEx(FILE *fp, int **ArrayIdx, int Nsite, int NArray, char *def ArrayIdx[idx][5] = x5; ArrayIdx[idx][6] = x6; ArrayIdx[idx][7] = x7; - if (CheckQuadSite(x0, x2, x4, x6, Nsite) != 0) { + if (CheckQuadSite(x2, x3, x5, x6, Nsite) != 0) { fprintf(stderr, "Error: Site index is incorrect. \n"); info = 1; break; diff --git a/src/mVMC/vmcmake_fsz.c b/src/mVMC/vmcmake_fsz.c index 3eaadf07..e9a116ea 100644 --- a/src/mVMC/vmcmake_fsz.c +++ b/src/mVMC/vmcmake_fsz.c @@ -515,13 +515,14 @@ void makeCandidate_hopping_fsz(int *mi_, int *ri_, int *rj_, int *s_,int *t_, in do { mi = gen_rand32()%Nsize; s = eleSpn[mi] ; //fsz - t = (genrand_real2()<0.5) ? s : 1-s; //fsz + //t = (genrand_real2()<0.5) ? s : 1-s; //fsz ri = eleIdx[mi]; //fsz } while (LocSpn[ri] == 1); icnt = 0; do { rj = gen_rand32()%Nsite; + t = (genrand_real2()<0.5) ? 0 : 1; //fsz if(icnt> icnt_max){ flag = 1; // TRUE break; @@ -668,7 +669,7 @@ void makeCandidate_LocalSpinFlip_localspin(int *mi_, int *ri_, int *rj_, int *s_ void makeCandidate_LocalSpinFlip_conduction(int *mi_, int *ri_, int *rj_, int *s_,int *t_, int *rejectFlag_, const int *eleIdx, const int *eleCfg,const int *eleNum,const int *eleSpn) { const int icnt_max = Nsite*Nsite; - int icnt; + int icnt=0; int mi, ri, rj, s, flag; int t; //fsz From e0a6005998e5b4bd63dff1ebf814adf25b0e4304 Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Mon, 16 Apr 2018 15:11:07 +0900 Subject: [PATCH 22/34] Unify to HPhi 94584d1fa3eeb082ad6658000b3282d35fbbd72b --- src/StdFace/StdFace_ModelUtil.c | 35 +- src/StdFace/StdFace_main.c | 109 ++++-- tool/CMakeLists.txt | 11 +- tool/corplot.F90 | 537 ---------------------------- tool/{fourier.F90 => greenr2k.F90} | 549 +++++++++++++++++------------ tool/makefile_tool | 11 +- tool/respack2wan90.py | 32 +- 7 files changed, 442 insertions(+), 842 deletions(-) delete mode 100644 tool/corplot.F90 rename tool/{fourier.F90 => greenr2k.F90} (52%) diff --git a/src/StdFace/StdFace_ModelUtil.c b/src/StdFace/StdFace_ModelUtil.c index 7483dace..6a19d5da 100644 --- a/src/StdFace/StdFace_ModelUtil.c +++ b/src/StdFace/StdFace_ModelUtil.c @@ -1156,33 +1156,36 @@ void StdFace_InputHopp( */ void StdFace_PrintGeometry(struct StdIntList *StdI) { FILE *fp; - int isite, iCell; + int isite, iCell, ii; fp = fopen("geometry.dat", "w"); - fprintf(fp, "%25.15e %25.15e %25.15e\n", StdI->direct[0][0], StdI->direct[0][1], StdI->direct[0][2]); - fprintf(fp, "%25.15e %25.15e %25.15e\n", StdI->direct[1][0], StdI->direct[1][1], StdI->direct[1][2]); - fprintf(fp, "%25.15e %25.15e %25.15e\n", StdI->direct[2][0], StdI->direct[2][1], StdI->direct[2][2]); - fprintf(fp, "%25.15e %25.15e %25.15e\n", StdI->phase[0], StdI->phase[1], StdI->phase[2]); - fprintf(fp, "%d %d %d\n", StdI->box[0][0], StdI->box[0][1], StdI->box[0][2]); - fprintf(fp, "%d %d %d\n", StdI->box[1][0], StdI->box[1][1], StdI->box[1][2]); - fprintf(fp, "%d %d %d\n", StdI->box[2][0], StdI->box[2][1], StdI->box[2][2]); + for (ii = 0; ii < 3; ii++) + fprintf(fp, "%25.15e %25.15e %25.15e\n", + StdI->direct[ii][0], StdI->direct[ii][1], StdI->direct[ii][2]); + fprintf(fp, "%25.15e %25.15e %25.15e\n", + StdI->phase[0], StdI->phase[1], StdI->phase[2]); + for (ii = 0; ii < 3; ii++) + fprintf(fp, "%d %d %d\n", + StdI->box[ii][0], StdI->box[ii][1], StdI->box[ii][2]); for (iCell = 0; iCell < StdI->NCell; iCell++) { for (isite = 0; isite < StdI->NsiteUC; isite++) { - fprintf(fp, "%25.15e %25.15e %25.15e\n", - StdI->tau[isite][0] + (double)StdI->Cell[iCell][0], - StdI->tau[isite][1] + (double)StdI->Cell[iCell][1], - StdI->tau[isite][2] + (double)StdI->Cell[iCell][2]); + fprintf(fp, "%d %d %d %d\n", + StdI->Cell[iCell][0] - StdI->Cell[0][0], + StdI->Cell[iCell][1] - StdI->Cell[0][1], + StdI->Cell[iCell][2] - StdI->Cell[0][2], + isite); }/*for (isite = 0; isite < StdI->NsiteUC; isite++)*/ }/* for (iCell = 0; iCell < StdI->NCell; iCell++)*/ if (strcmp(StdI->model, "kondo") == 0) { for (iCell = 0; iCell < StdI->NCell; iCell++) { for (isite = 0; isite < StdI->NsiteUC; isite++) { - fprintf(fp, "%25.15e %25.15e %25.15e\n", - StdI->tau[isite][0] + (double)StdI->Cell[iCell][0], - StdI->tau[isite][1] + (double)StdI->Cell[iCell][1], - StdI->tau[isite][2] + (double)StdI->Cell[iCell][2]); + fprintf(fp, "%d %d %d %d\n", + StdI->Cell[iCell][0] - StdI->Cell[0][0], + StdI->Cell[iCell][1] - StdI->Cell[0][1], + StdI->Cell[iCell][2] - StdI->Cell[0][2], + isite + StdI->NsiteUC); }/*for (isite = 0; isite < StdI->NsiteUC; isite++)*/ }/* for (iCell = 0; iCell < StdI->NCell; iCell++)*/ } diff --git a/src/StdFace/StdFace_main.c b/src/StdFace/StdFace_main.c index b4ab6ce5..1f199438 100644 --- a/src/StdFace/StdFace_main.c +++ b/src/StdFace/StdFace_main.c @@ -1320,7 +1320,7 @@ static void PrintModPara(struct StdIntList *StdI) static void Print1Green(struct StdIntList *StdI) { FILE *fp; - int ngreen, igreen, store; + int ngreen, igreen, store, xkondo; int isite, jsite, ispin, jspin, SiMax, SjMax; int **greenindx; /* @@ -1338,24 +1338,60 @@ static void Print1Green(struct StdIntList *StdI) ngreen = 0; }/*if (store == 1)*/ - for (isite = 0; isite < StdI->nsite; isite++) { + if (strcmp(StdI->model, "kondo") == 0) xkondo = 2; + else xkondo = 1; + + if (StdI->ioutputmode == 1) { + for (isite = 0; isite < StdI->NsiteUC*xkondo; isite++) { + + if (isite >= StdI->NsiteUC) isite += StdI->nsite / 2; + + if (StdI->locspinflag[isite] == 0) SiMax = 1; + else SiMax = StdI->locspinflag[isite]; + + for (ispin = 0; ispin <= SiMax; ispin++) { + for (jsite = 0; jsite < StdI->nsite; jsite++) { + + if (StdI->locspinflag[jsite] == 0) SjMax = 1; + else SjMax = StdI->locspinflag[jsite]; + + for (jspin = 0; jspin <= SjMax; jspin++) { + + if (isite != jsite && + (StdI->locspinflag[isite] != 0 && StdI->locspinflag[jsite] != 0)) continue; + + if (ispin == jspin){ + if (store == 1) { + greenindx[ngreen][0] = isite; + greenindx[ngreen][1] = ispin; + greenindx[ngreen][2] = jsite; + greenindx[ngreen][3] = jspin; + } + ngreen++; + } + + }/*for (jspin = 0; jspin <= SjMax; jspin++)*/ + }/*for (jsite = 0; jsite < StdI->nsite; jsite++)*/ + }/*for (ispin = 0; ispin <= SiMax; ispin++)*/ + }/*for (isite = 0; isite < StdI->nsite; isite++)*/ + }/*if (StdI->ioutputmode == 1)*/ + else { + for (isite = 0; isite < StdI->nsite; isite++) { - if (StdI->locspinflag[isite] == 0) SiMax = 1; - else SiMax = StdI->locspinflag[isite]; + if (StdI->locspinflag[isite] == 0) SiMax = 1; + else SiMax = StdI->locspinflag[isite]; - for (ispin = 0; ispin <= SiMax; ispin++) { - for (jsite = 0; jsite < StdI->nsite; jsite++) { + for (ispin = 0; ispin <= SiMax; ispin++) { + for (jsite = 0; jsite < StdI->nsite; jsite++) { - if (StdI->locspinflag[jsite] == 0) SjMax = 1; - else SjMax = StdI->locspinflag[jsite]; + if (StdI->locspinflag[jsite] == 0) SjMax = 1; + else SjMax = StdI->locspinflag[jsite]; - for (jspin = 0; jspin <= SjMax; jspin++) { + for (jspin = 0; jspin <= SjMax; jspin++) { - if (isite != jsite && - (StdI->locspinflag[isite] != 0 && StdI->locspinflag[jsite] != 0)) continue; + if (isite != jsite && + (StdI->locspinflag[isite] != 0 && StdI->locspinflag[jsite] != 0)) continue; - if (StdI->ioutputmode == 2 || ispin == jspin) - { if (store == 1) { greenindx[ngreen][0] = isite; greenindx[ngreen][1] = ispin; @@ -1363,13 +1399,13 @@ static void Print1Green(struct StdIntList *StdI) greenindx[ngreen][3] = jspin; } ngreen++; - } - }/*for (jspin = 0; jspin <= SjMax; jspin++)*/ - }/*for (jsite = 0; jsite < StdI->nsite; jsite++)*/ - }/*for (ispin = 0; ispin <= SiMax; ispin++)*/ - }/*for (isite = 0; isite < StdI->nsite; isite++)*/ - } + }/*for (jspin = 0; jspin <= SjMax; jspin++)*/ + }/*for (jsite = 0; jsite < StdI->nsite; jsite++)*/ + }/*for (ispin = 0; ispin <= SiMax; ispin++)*/ + }/*for (isite = 0; isite < StdI->nsite; isite++)*/ + }/*if (StdI->ioutputmode == 2)*/ + }/*if (StdI->ioutputmode != 0)*/ fp = fopen("greenone.def", "w"); fprintf(fp, "===============================\n"); @@ -1399,7 +1435,7 @@ static void Print1Green(struct StdIntList *StdI) */ static void Print2Green(struct StdIntList *StdI) { FILE *fp; - int ngreen, store, igreen; + int ngreen, store, igreen, xkondo; int site1, site2, site3, site4; int spin1, spin2, spin3, spin4; int S1Max, S2Max, S3Max, S4Max; @@ -1418,7 +1454,12 @@ static void Print2Green(struct StdIntList *StdI) { ngreen = 0; }/*if (store == 1)*/ - for (site1 = 0; site1 < StdI->nsite; site1++) { + if (strcmp(StdI->model, "kondo") == 0) xkondo = 2; + else xkondo = 1; + + for (site1 = 0; site1 < StdI->NsiteUC*xkondo; site1++) { + + if (site1 >= StdI->NsiteUC) site1 += StdI->nsite / 2; if (StdI->locspinflag[site1] == 0) S1Max = 1; else S1Max = StdI->locspinflag[site1]; @@ -2564,12 +2605,12 @@ void StdFace_main( @section sec_stan_proc Overall procedure -If you want to create new lattice file, do as these files. +If you want to create a new lattice file, the following procedures are needed. --# Copy one of laattice files such as Kagome.c +-# Copy one of lattice files such as Kagome.c (Probably the most similar one) and rename it. -# @ref sec_lattice --# Add that function in the header file, StdFace_ModelUtil.h +-# Add the function in the header file, StdFace_ModelUtil.h. -# Add entry at @dontinclude StdFace_main.c @skip StdFace\_main @@ -2581,29 +2622,29 @@ If you want to create new lattice file, do as these files.
@section sec_lattice Modify lattice model file -To create new lattice file, please modify the following part +To create a new lattice file, please modify the following part (Kagome.c as an example): @dontinclude Kagome.c Define function as @skip StdFace\_Kagome( @until { -Lattice parameter used only in geometry.dat and lattice.gp +Lattice parameters are used only in geometry.dat and lattice.gp @skip StdFace\_PrintVal\_d @until Ly -these are unit lattice vectors.\n +These are unit lattice vectors.\n Just call this function to initialize all lattice related parameters @skipline StdFace\_InitSite -where "2" indicates 2D +where "2" indicates 2D. @skip tau @until tau\[2\]\[0\] -These are the fractional coordinate of internal sites. +These are the fractional coordinates of internal sites. Then set parameters of Hamiltonian @skip StdFace\_NotUsed\_J @until @@ -to determine the default value of them and unused parameters. -For more details, please see the description of each functions. -Then Compute the upper limit of the number of Transfer & Interaction and malloc them. +to determine the default values of them and unused parameters. +For more details, please see the description of each function. +Then compute the upper limit of the number of Transfer & Interaction and malloc them. @skip >> @until << Please estimate the number of bonds per site. @@ -2616,9 +2657,7 @@ Probably, it is not necessary to modify this part. The non-local term is as follows: @skip >> @until << -For more details, please see each functions. - -StdFace_Kagome_Boost()? Forget!! +For more details, please see each function. @page page_addstandardval Add new input variable into Standard mode diff --git a/tool/CMakeLists.txt b/tool/CMakeLists.txt index 18b55a25..ae13a4f8 100644 --- a/tool/CMakeLists.txt +++ b/tool/CMakeLists.txt @@ -7,18 +7,13 @@ if(${CMAKE_PROJECT_NAME} STREQUAL "Project") endif(${CMAKE_PROJECT_NAME} STREQUAL "Project") add_library(key2lower STATIC key2lower.c) -add_executable(fourier fourier.F90) -add_executable(corplot corplot.F90) -target_link_libraries(fourier key2lower ${LAPACK_LIBRARIES}) +add_executable(greenr2k greenr2k.F90) +target_link_libraries(greenr2k key2lower ${LAPACK_LIBRARIES}) -install(TARGETS fourier RUNTIME DESTINATION bin) -install(TARGETS corplot RUNTIME DESTINATION bin) +install(TARGETS greenr2k RUNTIME DESTINATION bin) # # Scripts # -configure_file(gen_frmsf.sh gen_frmsf.sh COPYONLY) -install(FILES ${CMAKE_CURRENT_BINARY_DIR}/gen_frmsf.sh DESTINATION bin - PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ GROUP_EXECUTE WORLD_READ WORLD_EXECUTE) configure_file(wout2geom.sh wout2geom.sh COPYONLY) install(FILES ${CMAKE_CURRENT_BINARY_DIR}/wout2geom.sh DESTINATION bin PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ GROUP_EXECUTE WORLD_READ WORLD_EXECUTE) diff --git a/tool/corplot.F90 b/tool/corplot.F90 deleted file mode 100644 index 87460198..00000000 --- a/tool/corplot.F90 +++ /dev/null @@ -1,537 +0,0 @@ -MODULE corplot_val - ! - IMPLICIT NONE - ! - INTEGER,SAVE :: & - & nline, & - & itarget, & - & nwfc, & ! Number of state - & nk_row, & ! number row of total k - & nk ! Number of k to be computed - ! - REAL(8),SAVE :: & - & koff(3), & - & bragg(3,26), & - & braggnorm(26), & - & bz_line(3,2,26*26), & - & recipr(3,3) ! Reciprocal lattice vector - ! - LOGICAL,SAVE :: & - & errbar, & - & rpart - ! - REAL(8),ALLOCATABLE,SAVE :: & - & kvec(:,:) ! (2,nk) k-vector in the 1st BZ - ! - COMPLEX(8),ALLOCATABLE,SAVE :: & - & cor_err(:,:,:), & ! (nk,6,nwfc) Correlation function in the k-space (See below) - & cor_k(:,:,:) ! (nk,6,nwfc) Correlation function in the k-space (See below) - ! - ! Kind of Correlation for cor_k(:,1:6) - ! - ! (1) C_{i up }A_{j up } - ! (2) C_{i down}A_{j down} - ! (3) N_{i}N_{J} = N_{i up}N_{j up} + N_{i up}N_{j down} + N_{i down}N_{j up} + N_{i down}N_{j down} - ! (4) Sz_{i}Sz_{J} = 0.25*(N_{i up}N_{j up} - N_{i up}N_{j down} - N_{i down}N_{j up} + N_{i down}N_{j down}) - ! (5) S_{i + }S_{j - } - ! (6) S.S - ! -END MODULE corplot_val -! -! -! -MODULE corplot_routine - ! - IMPLICIT NONE - ! -CONTAINS -! -! Output Fourier component of Correlation function -! -SUBROUTINE read_cor() - ! -#if defined(FUJITSU) - USE service_routines, ONLY : IARGC -#endif - USE corplot_val, ONLY : nwfc, nk_row, recipr, koff, & - & cor_k, cor_err, kvec, nk - IMPLICIT NONE - ! - INTEGER :: fi = 10, ik, iwfc, nk0, idim - REAL(8) :: rtmp(3) - CHARACTER(256) :: filename, ctmp1, ctmp2 -#if defined(SR) - INTEGER,INTRINSIC :: IARGC -#endif - ! - WRITE(*,*) - WRITE(*,*) "##### Read Files #####" - WRITE(*,*) - ! - nwfc = IARGC() - WRITE(*,*) " Number of Files : ", nwfc - ! - DO iwfc = 1, nwfc - ! - CALL GETARG(iwfc, filename) - ! - OPEN(fi, file = TRIM(filename)) - ! - READ(fi,*) ctmp1, nk0, nk_row - DO idim = 1, 3 - READ(fi,*) ctmp2, recipr(1:3,idim) - END DO - READ(fi,*) ctmp2 - READ(fi,*) ctmp2 - READ(fi,*) ctmp2, koff(1:3) - ! - IF(iwfc == 1) THEN - ! - nk = nk0 - ALLOCATE(cor_k(1:nk,1:6,1:nwfc), cor_err(1:nk,1:6,1:nwfc), kvec(3,nk)) - cor_k(1:nk,1:6,1:nwfc) = CMPLX(0d0, 0d0, KIND(0d0)) - cor_err(1:nk,1:6,1:nwfc) = 0d0 - ! - WRITE(*,*) " Number of k : ", nk - WRITE(*,*) " k-point offset :" - WRITE(*,'(4x3f15.10)') koff(1:3) - ! - END IF - ! - IF(TRIM(ctmp1) == "#HPhi") THEN - WRITE(*,'(a,a,a)') " Read ", TRIM(filename), " as HPhi Correlation File" - DO ik = 1, nk - READ(fi,'(15e15.5)') kvec(1:3, ik), cor_k(ik,1:6,iwfc) - END DO - ELSE ! mVMC - WRITE(*,'(a,a,a)') " Read ", TRIM(filename), " as mVMC Correlation File" - DO ik = 1, nk - READ(fi,'(27e15.5)') kvec(1:3, ik), cor_k(ik,1:6,iwfc), cor_err(ik,1:6,iwfc) - END DO - END IF - ! - CLOSE(fi) - ! - END DO ! iwfc = 1, nwfc - ! -END SUBROUTINE read_cor -! -! Set vectors to difine Bragg's plane -! -SUBROUTINE set_bragg_vector() - ! - USE corplot_val, ONLY : recipr, bragg, braggnorm - IMPLICIT NONE - ! - INTEGER :: i0, i1, i2, ibr - ! - ibr = 0 - ! - DO i0 = -1, 1 - DO i1 = -1, 1 - DO i2 = -1, 1 - ! - IF(ALL((/i0, i1, i2/) == 0)) CYCLE - ! - ibr = ibr + 1 - bragg(1:3,ibr) = MATMUL(recipr(1:3,1:3), DBLE((/i0, i1, i2/))) * 0.5d0 - ! - braggnorm(ibr) = DOT_PRODUCT(bragg(1:3,ibr), bragg(1:3,ibr)) - ! - END DO - END DO - END DO - ! -END SUBROUTINE set_bragg_vector -! -! Solve linear system -! -FUNCTION solve3(a, b) RESULT(det) - ! - IMPLICIT NONE - ! - REAL(8),INTENT(IN) :: a(3,3) - REAL(8),INTENT(INOUT) :: b(3) - ! - REAL(8) :: det, c(3) - ! - det = a(1, 1) * (a(2, 2) * a(3, 3) - a(2, 3) * a(3, 2)) & - & + a(1, 2) * (a(2, 3) * a(3, 1) - a(2, 1) * a(3, 3)) & - & + a(1, 3) * (a(2, 1) * a(3, 2) - a(2, 2) * a(3, 1)) - ! - c(1) = b(1) * (a(2, 2) * a(3, 3) - a(2, 3) * a(3, 2)) & - & + b(2) * (a(1, 3) * a(3, 2) - a(1, 2) * a(3, 3)) & - & + b(3) * (a(1, 2) * a(2, 3) - a(1, 3) * a(2, 2)) - ! - c(2) = b(1) * (a(2, 3) * a(3, 1) - a(2, 1) * a(3, 3)) & - & + b(2) * (a(1, 1) * a(3, 3) - a(1, 3) * a(3, 1)) & - & + b(3) * (a(1, 3) * a(2, 1) - a(1, 1) * a(2, 3)) - ! - c(3) = b(1) * (a(2, 1) * a(3, 2) - a(2, 2) * a(3, 1)) & - & + b(2) * (a(1, 2) * a(3, 1) - a(1, 1) * a(3, 2)) & - & + b(3) * (a(1, 1) * a(2, 2) - a(1, 2) * a(2, 1)) - ! - b(1:3) = c(1:3) / det - ! - RETURN - ! -END FUNCTION solve3 -! -! Judge wheser this line is the edge of 1st BZ -! -FUNCTION bz_corners(ibr, jbr, nbr, corner, corner2) RESULT(lbr) - ! - USE corplot_val, ONLY : bragg, braggnorm - IMPLICIT NONE - ! - INTEGER :: ibr, jbr, nbr - REAL(8) :: corner(3) - REAL(8) :: corner2(3) - ! - INTEGER :: kbr, i, lbr, nbr0 - REAL(8) :: bmat(3,3), rhs(3), prod, thr = 1d-4, det - ! - nbr0 = nbr - ! - DO kbr = nbr0, 26 - ! - bmat(1,1:3) = bragg(1:3,ibr) - bmat(2,1:3) = bragg(1:3,jbr) - bmat(3,1:3) = bragg(1:3,kbr) - ! - rhs(1) = braggnorm(ibr) - rhs(2) = braggnorm(jbr) - rhs(3) = braggnorm(kbr) - ! - ! if Bragg planes do not cross, roop next kbr - ! - det = solve3(bmat, rhs) - IF (ABS(det) < thr) CYCLE - ! - ! if vert0 = vert1, roop next kbr - ! - prod = DOT_PRODUCT(corner2(1:3) - rhs(1:3), corner2(1:3) - rhs(1:3)) - IF (prod < thr) CYCLE - ! - ! is this corner really in 1st BZ ? - ! - i = 0 - DO lbr = 1, 26 - ! - prod = DOT_PRODUCT(bragg(1:3,lbr), rhs(1:3)) - ! - IF (prod > braggnorm(lbr) + thr) THEN - i = 1 - EXIT - END if - ! - END DO - ! - IF(i /= 1) THEN - corner(1:3) = rhs(1:3) - lbr = kbr + 1 - RETURN - END IF - ! - END DO - ! - ! this line is not a BZ boundary - ! - lbr = 1 - RETURN - ! -END FUNCTION bz_corners -! -! Compute Brillouin zone boundariy lines -! -SUBROUTINE set_bz_line() - ! - USE corplot_val, ONLY : bz_line, nline - IMPLICIT NONE - ! - INTEGER :: ibr, jbr, nbr, lvert - REAL(8) :: corner(3,2) - ! - CALL set_bragg_vector() - ! - nline = 0 - ! - DO ibr = 1, 26 - DO jbr = 1, 26 - ! - corner(1:3,1:2) = 0d0 - nbr = 1 - lvert = bz_corners(ibr, jbr, nbr, corner(1:3,1), corner(1:3,2)) - IF(lvert == 1) CYCLE - nbr = lvert - ! - lvert = bz_corners(ibr, jbr, nbr, corner(1:3,2), corner(1:3,1)) - IF(lvert == 1) CYCLE - ! - nline = nline + 1 - ! - ! Sort - ! - IF(corner(1,1) - corner(1,2) > 0.000001) THEN - bz_line(1:3,1:2,nline) = corner(1:3,1:2) - ELSE IF (corner(1,2) - corner(1,1) > 0.000001) THEN - bz_line(1:3,1,nline) = corner(1:3,2) - bz_line(1:3,2,nline) = corner(1:3,1) - ELSE - IF(corner(2,1) - corner(2,2) > 0.000001) THEN - bz_line(1:3,1:2,nline) = corner(1:3,1:2) - ELSE IF (corner(2,2) - corner(2,1) > 0.000001) THEN - bz_line(1:3,1,nline) = corner(1:3,2) - bz_line(1:3,2,nline) = corner(1:3,1) - ELSE - IF(corner(3,1) - corner(3,2) > 0.000001) THEN - bz_line(1:3,1:2,nline) = corner(1:3,1:2) - ELSE - bz_line(1:3,1,nline) = corner(1:3,2) - bz_line(1:3,2,nline) = corner(1:3,1) - END IF - END IF - END IF - ! - END DO - END DO - ! -END SUBROUTINE set_bz_line -! -! Compute Unique BZ line -! -SUBROUTINE uniq_bz_line(minz,maxz,nline2,bz_line2) - ! - USE corplot_val, ONLY : bz_line, nline - IMPLICIT NONE - ! - REAL(8),INTENT(IN) :: minz, maxz - INTEGER,INTENT(OUT) :: nline2 - REAL(8),INTENT(OUT) :: bz_line2(3,2,nline*4) - ! - INTEGER :: iline, jline - REAL(8) :: bz_line0(3,2) - ! - nline2 = 0 - DO iline = 1, nline - ! - bz_line0(1:3,1) = (/bz_line(1,1,iline), bz_line(2,1,iline), maxz/) - bz_line0(1:3,2) = (/bz_line(1,1,iline), bz_line(2,1,iline), minz/) - ! - DO jline = 1, nline2 - IF(ALL(ABS(bz_line0(1:3,1:2) - bz_line2(1:3,1:2,jline)) < 0.000001)) GOTO 10 - END DO - ! - nline2 = nline2 + 1 - bz_line2(1:3,1:2,nline2) = bz_line0(1:3,1:2) - ! -10 CONTINUE - ! - bz_line0(1:3,1) = (/bz_line(1,2,iline), bz_line(2,2,iline), maxz/) - bz_line0(1:3,2) = (/bz_line(1,2,iline), bz_line(2,2,iline), minz/) - ! - DO jline = 1, nline2 - IF(ALL(ABS(bz_line0(1:3,1:2) - bz_line2(1:3,1:2,jline)) < 0.000001)) GOTO 20 - END DO - ! - nline2 = nline2 + 1 - bz_line2(1:3,1:2,nline2) = bz_line0(1:3,1:2) - ! -20 CONTINUE - ! - IF(ALL(ABS(bz_line(1:2,1,iline) - bz_line(1:2,2,iline)) < 0.000001)) CYCLE - ! - bz_line0(1:3,1) = (/bz_line(1,1,iline), bz_line(2,1,iline), minz/) - bz_line0(1:3,2) = (/bz_line(1,2,iline), bz_line(2,2,iline), minz/) - ! - DO jline = 1, nline2 - IF(ALL(ABS(bz_line0(1:3,1:2) - bz_line2(1:3,1:2,jline)) < 0.000001)) GOTO 30 - END DO - ! - nline2 = nline2 + 1 - bz_line2(1:3,1:2,nline2) = bz_line0(1:3,1:2) - ! -30 CONTINUE - ! - bz_line0(1:3,1) = (/bz_line(1,1,iline), bz_line(2,1,iline), maxz/) - bz_line0(1:3,2) = (/bz_line(1,2,iline), bz_line(2,2,iline), maxz/) - ! - DO jline = 1, nline2 - IF(ALL(ABS(bz_line0(1:3,1:2) - bz_line2(1:3,1:2,jline)) < 0.000001)) GOTO 40 - END DO - ! - nline2 = nline2 + 1 - bz_line2(1:3,1:2,nline2) = bz_line0(1:3,1:2) - ! -40 CONTINUE - ! - END DO - ! -END SUBROUTINE uniq_bz_line -! -! Write gnuplot script -! -SUBROUTINE write_gnuplot() - ! - USE corplot_val, ONLY : itarget, rpart, errbar, nwfc, & - & cor_k, nk, nwfc, nline - IMPLICIT NONE - ! - INTEGER :: fo = 20, iwfc, iline, nline2 - REAL(8) :: maxz, minz, bz_line2(3,2,nline*4) - ! - IF(rpart) THEN - maxz = MAXVAL(DBLE( cor_k(1:nk, itarget, 1:nwfc))) - minz = MINVAL(DBLE( cor_k(1:nk, itarget, 1:nwfc))) - ELSE - maxz = MAXVAL(AIMAG(cor_k(1:nk, itarget, 1:nwfc))) - minz = MINVAL(AIMAG(cor_k(1:nk, itarget, 1:nwfc))) - END IF - CALL uniq_bz_line(minz,maxz,nline2,bz_line2) - ! - OPEN(fo, file = "correlation.gp") - ! - WRITE(fo,'(a)') "#set terminal pdf color enhanced \" !" - WRITE(fo,'(a)') "#dashed dl 1.0 size 20.0cm, 20.0cm" - WRITE(fo,'(a)') "#set output 'correlation.pdf'" - WRITE(fo,'(a)') "#set view 60.0, 30.0" - ! - WRITE(fo,*) - WRITE(fo,'(a)') "#set view equal xy" - WRITE(fo,'(a)') "set ticslevel 0" - WRITE(fo,'(a)') "set hidden3d" - WRITE(fo,'(a)') "set xlabel 'kx'" - WRITE(fo,'(a)') "set ylabel 'ky'" - WRITE(fo,'(a,e15.5,a,e15.5,a)') "set zrange [", minz, ":", maxz, "]" - WRITE(fo,*) - WRITE(fo,'(a)') "set pm3d" - WRITE(fo,'(a)') "set pm3d interpolate 5, 5" - WRITE(fo,'(a)') "#set contour" - WRITE(fo,'(a)') "set view 0.0, 0.0" - WRITE(fo,*) - WRITE(fo,*) "##### Set Brillouin-Zone Boundary #####" - WRITE(fo,*) - DO iline = 1, nline2 - WRITE(fo,'(a,e15.5,a,e15.5,a,e15.5,a,e15.5,a,e15.5,a,e15.5,a)') & - & "set arrow from ", bz_line2(1,1,iline), ",", bz_line2(2,1,iline), ",", bz_line2(3,1,iline), & - & " to ", bz_line2(1,2,iline), ",", bz_line2(2,2,iline), ",", bz_line2(3,2,iline), " nohead front" - END DO ! iline = 1, nline - ! - WRITE(fo,*) - WRITE(fo,*) "##### End Set Brillouin-Zone Boundary #####" - WRITE(fo,*) - WRITE(fo,'(a)') "splot \" !" - IF(errbar) THEN - DO iwfc = 1, nwfc - ! - WRITE(fo, '(a,i0,a,i0,a,i0,a)',advance='no') & - & "'correlation.dat' u 1:2:($", iwfc+2, "-$", iwfc+2+nwfc, ") w l tit '", iwfc, "-', " - WRITE(fo, '(a,i0,a,i0,a,i0,a)',advance='no') & - & "'correlation.dat' u 1:2:($", iwfc+2, "+$", iwfc+2+nwfc, ") w l tit '", iwfc, "+'" - ! - IF(iwfc /= nwfc) WRITE(fo,'(a)') ", \" !" - ! - END DO - ELSE - DO iwfc = 1, nwfc - ! - WRITE(fo, '(a,i0,a,i0,a)',advance='no') & - & "'correlation.dat' u 1:2:", iwfc+2, " w l tit '", iwfc, "'" - ! - IF(iwfc /= nwfc) WRITE(fo,'(a)') ", \" !" - ! - END DO - END IF - WRITE(fo,*) - WRITE(fo,*) "pause -1" - ! - CLOSE(fo) - ! -END SUBROUTINE write_gnuplot -! -! Output data to be plotted -! -SUBROUTINE write_data() - ! - USE corplot_val, ONLY : itarget, rpart, nwfc, nk_row, & - & cor_k, cor_err, kvec, koff, nk - IMPLICIT NONE - ! - INTEGER :: fo = 20, ik - REAL(8) :: koff2(2) - CHARACTER(100) :: form - ! - OPEN(fo, file = "correlation.dat") - WRITE(form,'(a,i0,a)') "(", 2 + nwfc*2, "e15.5)" - ! - IF(itarget <= 2) THEN - koff2(1:2) = koff(1:2) - ELSE - koff2(1:2) = 0d0 - END IF - ! - DO ik = 1, nk - ! - IF(rpart) THEN - WRITE(fo,TRIM(form)) kvec(1:2,ik) + koff2(1:2), & - & DBLE(cor_k( ik, itarget, 1:nwfc)), & - & DBLE(cor_err(ik, itarget, 1:nwfc)) - ELSE - WRITE(fo,TRIM(form)) kvec(1:2,ik) + koff2(1:2), & - & AIMAG(cor_k( ik, itarget, 1:nwfc)), & - & AIMAG(cor_err(ik, itarget, 1:nwfc)) - END IF - ! - IF(MOD(ik, nk_row) == 0) WRITE(fo,*) - ! - END DO - ! - CLOSE(fo) - ! -END SUBROUTINE write_data -! -END MODULE corplot_routine -! -! Main routine -! -PROGRAM corplot - ! - USE corplot_routine, ONLY : set_bz_line, read_cor, write_gnuplot, write_data - USE corplot_val, ONLY : itarget, errbar, rpart - IMPLICIT NONE - ! - CALL read_cor() - CALL set_bz_line() - ! - WRITE(*,*) - WRITE(*,*) "##### Plot Start #####" - WRITE(*,*) - WRITE(*,*) " Please specify target number from below (0 or Ctrl-C to exit): " - WRITE(*,*) - WRITE(*,*) " Real Part Without ErrorBar" - WRITE(*,*) " [ 1] Up-Up [ 2] Down-Down [ 3] Density-Density [ 4] SzSz [ 5] S+S- [ 6] S.S" - WRITE(*,*) " Imaginary Part Without ErrorBar" - WRITE(*,*) " [11] Up-Up [12] Down-Down [13] Density-Density [14] SzSz [15] S+S- [16] S.S" - WRITE(*,*) " Real Part With ErrorBar" - WRITE(*,*) " [21] Up-Up [22] Down-Down [23] Density-Density [24] SzSz [25] S+S- [26] S.S" - WRITE(*,*) " Imaginary Part With ErrorBar" - WRITE(*,*) " [31] Up-Up [32] Down-Down [33] Density-Density [34] SzSz [35] S+S- [36] S.S" - WRITE(*,*) - ! - DO - WRITE(*,'(a)',ADVANCE='NO') " Target : " - READ(*,*) itarget - errbar = itarget / 20 >= 1 - rpart = MOD(itarget / 10, 2) == 0 - itarget = MOD(itarget, 10) - IF(itarget < 1 .OR. 6 < itarget) EXIT - CALL write_data() - CALL write_gnuplot() - CALL SYSTEM("gnuplot correlation.gp") - END DO - ! - WRITE(*,*) - WRITE(*,*) "##### Done #####" - WRITE(*,*) - ! -END PROGRAM corplot diff --git a/tool/fourier.F90 b/tool/greenr2k.F90 similarity index 52% rename from tool/fourier.F90 rename to tool/greenr2k.F90 index 46a0148b..cc0a3438 100644 --- a/tool/fourier.F90 +++ b/tool/greenr2k.F90 @@ -3,22 +3,22 @@ MODULE fourier_val IMPLICIT NONE ! INTEGER,SAVE :: & + & nkg(3), & ! k-grid for momentum ditribution + & nk_line, & ! Numberof along each k line + & nnode, & ! Number of node of k-path & calctype, & ! (0) Lanczos (1) TPQ (2) FullDiag (3) LOBCG (4) mVMC & nwfc, & ! Number of state + & nr, & ! Number of R-vector + & norb, & ! Number of orbitals per unit cell & box(3,3), & ! Supercell index - & rbox(3,3), & ! Reciplocal Superlattice Vector times nk - & nsite, & ! Number of sites - & ncor1, & ! Nomber of One-body Correlation function - & ncor2, & ! Number of Two-body Correlation function - & ncor(8), & ! Number of Correlation function for each index(See below) - & nk_row, & ! number row of total k - & ncell, & ! number of unit cell - & nk ! Number of k to be computed + & nsite, & ! Number of sites + & ncor1, & ! Nomber of One-body Correlation function + & ncor2, & ! Number of Two-body Correlation function + & ncor(8), & ! Number of Correlation function for each index(See below) + & nk ! Number of k to be computed ! REAL(8),SAVE :: & - & direct(3,3), & ! Direct lattice vector - & recipr(3,3), & ! Reciprocal lattice vector - & koff(3) ! k-point offset for the boundary phase + & recipr(3,3) ! Reciprocal lattice vector ! CHARACTER(256),SAVE :: & & filehead, & ! Filename header for correlation functions @@ -26,17 +26,23 @@ MODULE fourier_val & file_two ! Filename for Two-body Correlation ! INTEGER,ALLOCATABLE,SAVE :: & - & indx(:,:,:) ! (nsite:nsite,8) Mapping index for each Correlation function + & nreq(:), & ! (nr) Number of equivalent R-vector for each R + & irv(:,:,:), & ! (3,125,nr) R-vector + & rindx(:), & ! (nsite) Index of R + & orb(:), & ! (nsite) Index of orbital + & indx(:,:,:,:) ! (nr,8,norb,norb) Mapping index for each Correlation function ! REAL(8),ALLOCATABLE,SAVE :: & - & kvec(:,:), & ! (3,nk) k-vector in the 1st BZ - & site(:,:) ! (3,nsite) Site geometry in the fractional coordinate + & knode(:,:), & ! (3,nnode) Nodes of k path + & phase(:,:), & ! (125,nr) Boundary phase + & kvec(:,:) ! (3,nk) k-vector in the 1st BZ ! COMPLEX(8),ALLOCATABLE,SAVE :: & - & cor(:,:,:,:), & ! (nsite,nsite,6,nwfc) Correlation function in real space (See below) - & cor_k(:,:,:) ! (nk,6,nwfc) Correlation function in the k-space (See below) + & cor(:,:,:,:,:), & ! (nr,6,norb,norb,nwfc) Correlation function in real space (See below) + & cor_k(:,:,:,:,:) ! (nk,6,norb,norb,nwfc) Correlation function in the k-space (See below) ! CHARACTER(256),ALLOCATABLE :: & + & kname(:), & ! (nnode) Label of k-point node & filetail(:) ! (nwfc) Index (run, step, etc.) in a file name ! ! Kind of Correlation for ncor(1:8) and index(:,:,1:8) @@ -278,14 +284,14 @@ END SUBROUTINE read_filename ! SUBROUTINE read_geometry() ! - USE fourier_val, ONLY : direct, recipr, box, rbox, nsite, site, ncell, koff + USE fourier_val, ONLY : recipr, box, nsite, phase, irv, rindx, orb, & + & nr, nreq, norb, nnode, knode, nk_line, kname, nkg IMPLICIT NONE ! - INTEGER :: fi = 10, isite, ii, jj - REAL(8) :: det, phase(3), pi180 = ACOS(-1d0)/180d0 + INTEGER :: fi = 10, isite, ii, ir, ipiv(3), irv0(3), i1, i2, i3, inode + REAL(8) :: phase0(3), work(10), direct(3,3), rrv(3), lenrv, lenrv0 CHARACTER(256) :: filename - ! - ALLOCATE(site(3,nsite)) + INTEGER,ALLOCATABLE :: irv1(:,:) ! WRITE(*,*) WRITE(*,*) "##### Read Geometry Input File #####" @@ -308,9 +314,10 @@ SUBROUTINE read_geometry() ! ! Bondary phase ! - READ(fi,*) phase(1:3) + READ(fi,*) phase0(1:3) WRITE(*,*) " Boundary phase[degree] : " - WRITE(*,'(4x3f15.10)') phase(1:3) + WRITE(*,'(4x3f15.10)') phase0(1:3) + phase0(1:3) = phase0(1:3) * ACOS(-1.0d0) / 180.0d0 ! ! Supercell index (a0w, a0l, a1w, a1l) ! @@ -320,116 +327,129 @@ SUBROUTINE read_geometry() WRITE(*,*) " Supercell Index :" WRITE(*,'(3i8)') box(1:3, 1:3) ! - DO isite = 1, nsite - READ(fi,*) site(1:3,isite) - END DO - ! - CLOSE(fi) + ! R-vector and orbital index ! - ! The number of unit cell + ALLOCATE(irv1(3,nsite), orb(nsite), rindx(nsite)) ! - ncell = 0 - DO ii = 1, 3 - ncell = ncell & - & + box(ii,1) * box(MOD(ii, 3) + 1, 2) * box(MOD(ii + 1, 3) + 1, 3) & - & - box(ii,1) * box(MOD(ii + 1, 3) + 1, 2) * box(MOD(ii, 3) + 1, 3) - END DO - ! - ! Compute reciprocal SuperLattice Vector - ! - DO ii = 1, 3 - DO jj = 1, 3 - rbox(jj, ii) = & - & box(MOD(jj, 3) + 1, MOD(ii, 3) + 1) * box(MOD(jj + 1, 3) + 1, MOD(ii + 1, 3) + 1) & - & - box(MOD(jj + 1, 3) + 1, MOD(ii, 3) + 1) * box(MOD(jj, 3) + 1, MOD(ii + 1, 3) + 1) + nr = 0 + DO isite = 1, nsite + READ(fi,*) irv0(1:3), orb(isite) + DO ir = 1, nr + IF(ALL(irv1(1:3,ir) == irv0(1:3))) THEN + rindx(isite) = ir + GOTO 10 + END IF END DO + nr = nr + 1 + irv1(1:3, nr) = irv0(1:3) + rindx(isite) = nr + ! +10 CONTINUE + ! END DO + orb(1:nsite) = orb(1:nsite) + 1 + norb = MAXVAL(orb) + WRITE(*,*) " Number of orbitals :", norb + ! + ! k-point + ! + READ(fi,*) nnode, nk_line + ALLOCATE(knode(3,nnode), kname(nnode)) + WRITE(*,*) " Number of k-node, and k-points along lines :", nnode, nk_line + WRITE(*,*) " k-node :" + DO inode = 1, nnode + READ(fi,*) kname(inode), knode(1:3,inode) + WRITE(*,'(a,a,3f10.5)') " ", TRIM(kname(inode)), knode(1:3,inode) + END DO + READ(fi,*) nkg(1:3) + WRITE(*,'(a,3i3)') "k-grid for momentum distribution :", nkg(1:3) ! - IF(ncell < 0) THEN - ncell = -ncell - rbox(1:3,1:3) = - rbox(1:3,1:3) - END IF - WRITE(*,*) " Number of Unit Cell : ", ncell - WRITE(*,*) " Reciprocal superlattice vector (times ncell) :" - WRITE(*,'(3i8)') rbox(1:3, 1:3) + CLOSE(fi) ! ! Compute Reciprocal Lattice Vector ! - det = 0d0 - DO ii = 1, 3 - det = det & - & + direct(ii,1) * direct(MOD(ii, 3) + 1, 2) * direct(MOD(ii + 1, 3) + 1, 3) & - & - direct(ii,1) * direct(MOD(ii + 1, 3) + 1, 2) * direct(MOD(ii, 3) + 1, 3) - END DO + recipr(1:3,1:3) = direct(1:3,1:3) + CALL dgetrf(3, 3, recipr, 3, Ipiv, ii) + CALL dgetri(3, recipr, 3, ipiv, work, 10, ii) + WRITE(*,*) " Reciplocal lattice vector :" + WRITE(*,'(4x3f15.10)') recipr(1:3, 1:3) ! - ! + ! Move original R-vector to the nearest one with periodic boundary cond. ! - DO ii = 1, 3 - DO jj = 1, 3 - recipr(jj, ii) = & - & direct(MOD(jj, 3) + 1, MOD(ii, 3) + 1) * direct(MOD(jj + 1, 3) + 1, MOD(ii + 1, 3) + 1) & - & - direct(MOD(jj + 1, 3) + 1, MOD(ii, 3) + 1) * direct(MOD(jj, 3) + 1, MOD(ii + 1, 3) + 1) + ALLOCATE(nreq(nsite), irv(3,125,nsite), phase(125,nsite)) + ! + WRITE(*,*) " Number of R-vector :", nr + DO ir = 1, nr + lenrv0 = 1.0d10 + DO i1 = -2, 2 + DO i2 = -2, 2 + DO i3 = -2, 2 + ! + irv0(1:3) = irv1(1:3,ir) + MATMUL(box(1:3,1:3), (/i1,i2,i3/)) + rrv(1:3) = MATMUL(direct(1:3,1:3), DBLE(irv0(1:3))) + lenrv = SQRT(DOT_PRODUCT(rrv, rrv)) + IF(lenrv < lenrv0 - 1.0d-6) THEN + lenrv0 = lenrv + nreq(ir) = 1 + ELSE IF(ABS(lenrv - lenrv0) < 1.0d-6) THEN + nreq(ir) = nreq(ir) + 1 + ELSE + CYCLE + END IF + ! + irv(1:3, nreq(ir), ir) = irv0(1:3) + phase(nreq(ir), ir) = DOT_PRODUCT(DBLE((/i1,i2,i3/)), phase0(1:3)) + ! + END DO ! i3 = -2, 2 + END DO ! i2 = -2, 2 + END DO ! i1 = -2, 2 + ! + DO i1 = 1, nreq(ir) + WRITE(*,'(3i5,f7.2,a)',advance="no") irv(1:3, i1, ir), phase(i1, ir), ", " END DO - END DO - recipr(1:3, 1:3) = recipr(1:3, 1:3) / det - WRITE(*,*) " Reciplocal lattice vector :" - WRITE(*,'(4x3f15.10)') recipr(1:3, 1:3) + WRITE(*,*) + ! + END DO ! ir = 1, nr ! - ! k-point offset for the boundary phase + DEALLOCATE(irv1) ! - phase(1:3) = phase(1:3) * pi180 - koff(1:3) = MATMUL(DBLE(rbox(1:3,1:3)), phase(1:3)) - koff(1:3) = koff(1:3) / DBLE(ncell) - koff(1:3) = MATMUL(recipr(1:3,1:3), koff(1:3)) - WRITE(*,*) " k-point offset :" - WRITE(*,'(4x3f15.10)') koff(1:3) - ! END SUBROUTINE read_geometry ! ! Set k points ! SUBROUTINE set_kpoints() ! - USE fourier_val, ONLY : box, rbox, nk, kvec, nk_row, ncell + USE fourier_val, ONLY : nk, kvec, nnode, nk_line, knode, nkg ! IMPLICIT NONE ! - INTEGER :: imax(3), imin(3), i1, i2, i3, ii, edge(3,8), ik, jk, idim, ikvec(3) + INTEGER :: inode, ik, i1, i2, i3 + REAL(8) :: xx ! - ! Define range of k-grid index spanning [-1:1] in fractional BZ + nk = nk_line * (nnode - 1) + 1 + PRODUCT(nkg(1:3)) + WRITE(*,*) " Number of k : ", nk + ALLOCATE(kvec(3,nk)) ! - ii = 0 - DO i3 = -1, 1, 2 - DO i2 = -1, 1, 2 - DO i1 = -1, 1, 2 - ii = ii + 1 - edge(1:3,ii) = MATMUL((/i1, i2, i3/), box(1:3,1:3)) - END DO + kvec(1:3,1) = knode(1:3,1) + nk = 1 + DO inode = 1, nnode - 1 + DO ik = 1, nk_line + xx = DBLE(ik) / DBLE(nk_line) + nk = nk + 1 + kvec(1:3,nk) = (1d0 - xx)*knode(1:3,inode) + xx*knode(1:3,inode+1) END DO END DO ! - DO idim = 1, 3 - imin(idim) = MINVAL(edge(idim,1:8)) - imax(idim) = MAXVAL(edge(idim,1:8)) - END DO + ! k-grid for momentum distribution ! - nk = PRODUCT(imax(1:3) - imin(1:3) + 1) - nk_row = imax(1) - imin(1) + 1 - ALLOCATE(kvec(3,nk)) - ! - nk = 0 - DO i3 = imin(3), imax(3) - DO i2 = imin(2), imax(2) - DO i1 = imin(1), imax(1) - ! - ikvec(1:3) = MATMUL(rbox(1:3,1:3), (/i1, i2, i3/)) + DO i1 = 1, nkg(1) + DO i2 = 1, nkg(2) + DO i3 = 1, nkg(3) nk = nk + 1 - kvec(1:3, nk) = DBLE(ikvec(1:3)) / DBLE(ncell) - ! + kvec(1:3,nk) = DBLE((/i1,i2,i3/)-1) / DBLE(nkg(1:3)) END DO END DO END DO - WRITE(*,*) " Number of k : ", nk ! END SUBROUTINE set_kpoints ! @@ -437,7 +457,8 @@ END SUBROUTINE set_kpoints ! SUBROUTINE read_corrindx() ! - USE fourier_val, ONLY : file_one, file_two, ncor1, ncor2, ncor, indx, nsite, calctype + USE fourier_val, ONLY : file_one, file_two, ncor1, ncor2, ncor, indx, & + & calctype, nr, rindx, orb, norb IMPLICIT NONE ! INTEGER :: fi = 10, itmp(8), icor @@ -447,8 +468,8 @@ SUBROUTINE read_corrindx() WRITE(*,*) "##### Read Correlation Index File #####" WRITE(*,*) ! - ALLOCATE(indx(nsite,nsite,8)) - indx(1:nsite,1:nsite,1:8) = 0 + ALLOCATE(indx(nr,8,norb,norb)) + indx(1:nr,1:8,1:norb,1:norb) = 0 ! ! Read index for the One-Body Correlation ! @@ -470,17 +491,17 @@ SUBROUTINE read_corrindx() ! ! Up-Up correlation ! - indx(itmp(1) + 1, itmp(3) + 1, 1) = icor + indx(rindx(itmp(3) + 1), 1, orb(itmp(1) + 1), orb(itmp(3) + 1)) = icor ELSE IF (itmp(2) == 1 .AND. itmp(4) == 1) THEN ! ! Down-Down correlation ! - indx(itmp(1) + 1, itmp(3) + 1, 2) = icor + indx(rindx(itmp(3) + 1), 2, orb(itmp(1) + 1), orb(itmp(3) + 1)) = icor END IF END DO ! - WRITE(*,*) " Number of Up-Up Index : ", COUNT(indx(1:nsite, 1:nsite, 1) /= 0) - WRITE(*,*) " Number of Down-Down Index : ", COUNT(indx(1:nsite, 1:nsite, 2) /= 0) + WRITE(*,*) " Number of Up-Up Index : ", COUNT(indx(1:nr, 1, 1:norb, 1:norb) /= 0) + WRITE(*,*) " Number of Down-Down Index : ", COUNT(indx(1:nr, 2, 1:norb, 1:norb) /= 0) ! CLOSE(fi) ! @@ -510,12 +531,12 @@ SUBROUTINE read_corrindx() ! ! UpUpUpUp ! - indx(itmp(1) + 1, itmp(5) + 1, 3) = icor + indx(rindx(itmp(5) + 1), 3, orb(itmp(1) + 1), orb(itmp(5) + 1)) = icor ELSE IF(itmp(6) == 1 .AND. itmp(8) == 1) THEN ! ! UpUpDownDown ! - indx(itmp(1) + 1, itmp(5) + 1, 4) = icor + indx(rindx(itmp(5) + 1), 4, orb(itmp(1) + 1), orb(itmp(5) + 1)) = icor END IF ! ELSE IF(itmp(2) == 1 .AND. itmp(4) == 1) THEN @@ -524,12 +545,12 @@ SUBROUTINE read_corrindx() ! ! DownDownUpUp ! - indx(itmp(1) + 1, itmp(5) + 1, 5) = icor + indx(rindx(itmp(5) + 1), 5, orb(itmp(1) + 1), orb(itmp(5) + 1)) = icor ELSE IF(itmp(6) == 1 .AND. itmp(8) == 1) THEN ! ! DownDownDownDown ! - indx(itmp(1) + 1, itmp(5) + 1, 6) = icor + indx(rindx(itmp(5) + 1), 6, orb(itmp(1) + 1), orb(itmp(5) + 1)) = icor END IF ! ELSE IF(calctype /= 4) THEN @@ -540,12 +561,12 @@ SUBROUTINE read_corrindx() ! ! Up-Down-Down-Up = S+S- ! - indx(itmp(1) + 1, itmp(5) + 1, 7) = icor + indx(rindx(itmp(5) + 1), 7, orb(itmp(1) + 1), orb(itmp(5) + 1)) = icor ELSE IF((itmp(2) == 1 .AND. itmp(4) == 0) .AND. (itmp(6) == 0 .AND. itmp(8) == 1)) THEN ! ! Down-Up-Up-Down = S-S+ ! - indx(itmp(1) + 1, itmp(5) + 1, 8) = icor + indx(rindx(itmp(5) + 1), 8, orb(itmp(1) + 1), orb(itmp(5) + 1)) = icor END IF ! END IF ! (calctype /= 4) @@ -560,24 +581,24 @@ SUBROUTINE read_corrindx() ! ! Up-Down-Down-Up = S+S- ! - indx(itmp(1) + 1, itmp(5) + 1, 7) = icor + indx(rindx(itmp(5) + 1), 7, orb(itmp(1) + 1), orb(itmp(5) + 1)) = icor ELSE IF((itmp(2) == 1 .AND. itmp(4) == 1) .AND. (itmp(6) == 0 .AND. itmp(8) == 0)) THEN ! ! Down-Up-Up-Down = S-S+ ! - indx(itmp(1) + 1, itmp(5) + 1, 8) = icor + indx(rindx(itmp(5) + 1), 8, orb(itmp(1) + 1), orb(itmp(5) + 1)) = icor END IF ! END IF ! (calctype == 4 .AND. (itmp(1) == itmp(7) .AND. itmp(3) == itmp(5))) ! END DO ! - WRITE(*,*) " Number of UpUpUpUp Index : ", COUNT(indx(1:nsite, 1:nsite, 3) /= 0) - WRITE(*,*) " Number of UpUpDownDown Index : ", COUNT(indx(1:nsite, 1:nsite, 4) /= 0) - WRITE(*,*) " Number of DownDownUpUp Index : ", COUNT(indx(1:nsite, 1:nsite, 5) /= 0) - WRITE(*,*) " Number of DownDownDownDown Index : ", COUNT(indx(1:nsite, 1:nsite, 6) /= 0) - WRITE(*,*) " Number of Plus-Minus Index : ", COUNT(indx(1:nsite, 1:nsite, 7) /= 0) - WRITE(*,*) " Number of Minus-Plus Index : ", COUNT(indx(1:nsite, 1:nsite, 8) /= 0) + WRITE(*,*) " Number of UpUpUpUp Index : ", COUNT(indx(1:nr, 3, 1:norb, 1:norb) /= 0) + WRITE(*,*) " Number of UpUpDownDown Index : ", COUNT(indx(1:nr, 4, 1:norb, 1:norb) /= 0) + WRITE(*,*) " Number of DownDownUpUp Index : ", COUNT(indx(1:nr, 5, 1:norb, 1:norb) /= 0) + WRITE(*,*) " Number of DownDownDownDown Index : ", COUNT(indx(1:nr, 6, 1:norb, 1:norb) /= 0) + WRITE(*,*) " Number of Plus-Minus Index : ", COUNT(indx(1:nr, 7, 1:norb, 1:norb) /= 0) + WRITE(*,*) " Number of Minus-Plus Index : ", COUNT(indx(1:nr, 8, 1:norb, 1:norb) /= 0) ! CLOSE(fi) ! @@ -588,17 +609,17 @@ END SUBROUTINE read_corrindx SUBROUTINE read_corrfile() ! USE fourier_val, ONLY : filehead, filetail, nwfc, calctype, & - & ncor1, ncor2, indx, cor, nsite + & ncor1, ncor2, indx, cor, norb, nr IMPLICIT NONE ! - INTEGER :: fi = 10, icor, itmp(8), ii, iwfc, isite, jsite + INTEGER :: fi = 10, icor, itmp(8), iwfc, iorb, jorb, ir COMPLEX(8),ALLOCATABLE :: cor0(:) - REAL(8),ALLOCATABLE :: cor0_r(:,:) + REAL(8) :: cor0_r(2) CHARACTER(256) :: filename ! - ALLOCATE(cor(nsite,nsite,6,nwfc)) - ALLOCATE(cor0(0:MAX(ncor1,ncor2)), cor0_r(2,MAX(ncor1,ncor2))) - cor(1:nsite,1:nsite,1:6,1:nwfc) = CMPLX(0d0, 0d0, KIND(1d0)) + ALLOCATE(cor(nr,6,norb,norb,nwfc)) + ALLOCATE(cor0(0:MAX(ncor1,ncor2))) + cor(1:nr,1:6,1:norb,1:norb,1:nwfc) = CMPLX(0d0, 0d0, KIND(1d0)) cor0(0) = CMPLX(0d0, 0d0, KIND(1d0)) ! DO iwfc = 1, nwfc @@ -609,19 +630,18 @@ SUBROUTINE read_corrfile() OPEN(fi, file = TRIM(filename)) ! DO icor = 1, ncor1 - READ(fi,*) itmp(1:4), cor0_r(1:2, icor) + READ(fi,*) itmp(1:4), cor0_r(1:2) + cor0(icor) = CMPLX(cor0_r(1), cor0_r(2), KIND(1d0)) END DO ! CLOSE(fi) ! - cor0(1:ncor1) = CMPLX(cor0_r(1,1:ncor1), cor0_r(2,1:ncor1), KIND(1d0)) - ! ! Map it into Up-Up(1) and Down-Down(2) Correlation ! - DO ii = 1, 2 - DO jsite = 1, nsite - DO isite = 1, nsite - cor(isite, jsite, ii, iwfc) = cor0(indx(isite,jsite,ii)) + DO iorb = 1, norb + DO jorb = 1, norb + DO ir = 1, nr + cor(ir, 1:2, jorb, iorb, iwfc) = cor0(indx(ir, 1:2, jorb, iorb)) END DO END DO END DO @@ -632,68 +652,66 @@ SUBROUTINE read_corrfile() OPEN(fi, file = TRIM(filename)) ! DO icor = 1, ncor2 - READ(fi,*) itmp(1:8), cor0_r(1:2, icor) + READ(fi,*) itmp(1:8), cor0_r(1:2) + cor0(icor) = CMPLX(cor0_r(1), cor0_r(2), KIND(1d0)) END DO ! CLOSE(fi) ! - cor0(1:ncor2) = CMPLX(cor0_r(1,1:ncor2), cor0_r(2,1:ncor2), KIND(1d0)) - ! ! Map it into Density-Density(3), Sz-Sz(4), S+S-(5), S-S+(6) Correlation ! ! Up-Up-Up-Up and Down-Down-Down-Down into Density-Density & Sz-Sz ! - DO jsite = 1, nsite - DO isite = 1, nsite - ! - cor(isite, jsite, 3, iwfc) = cor0(indx(isite,jsite,3)) & - & + cor0(indx(isite,jsite,4)) & - & + cor0(indx(isite,jsite,5)) & - & + cor0(indx(isite,jsite,6)) & - & - SUM(cor(isite, isite, 1:2, iwfc)) & - & * SUM(cor(jsite, jsite, 1:2, iwfc)) - ! - cor(isite, jsite, 4, iwfc) = cor0(indx(isite,jsite,3)) & - & - cor0(indx(isite,jsite,4)) & - & - cor0(indx(isite,jsite,5)) & - & + cor0(indx(isite,jsite,6)) - ! - END DO - END DO + DO iorb = 1, norb + DO jorb = 1, norb + DO ir = 1, nr + ! + cor(ir, 3, jorb, iorb, iwfc) = cor0(indx(ir, 3, jorb, iorb)) & + & + cor0(indx(ir, 4, jorb, iorb)) & + & + cor0(indx(ir, 5, jorb, iorb)) & + & + cor0(indx(ir, 6, jorb, iorb)) + ! + cor(ir, 3, jorb, iorb, iwfc) = cor(ir, 3, jorb, iorb, iwfc) & + & - SUM(cor(ir, 1:2, jorb, iorb, iwfc)) & + & * SUM(cor(ir, 1:2, jorb, iorb, iwfc)) + ! + cor(ir, 4, jorb, iorb, iwfc) = cor0(indx(ir, 3, jorb, iorb)) & + & - cor0(indx(ir, 4, jorb, iorb)) & + & - cor0(indx(ir, 5, jorb, iorb)) & + & + cor0(indx(ir, 6, jorb, iorb)) + ! + cor(ir, 4, jorb, iorb, iwfc) = cor(ir, 4, jorb, iorb, iwfc) * 0.25d0 + ! + ! Up-Down-Down-Up(S+S-) and Down-Up-Up-Down(S-S+) + ! + cor(ir, 5:6, jorb, iorb, iwfc) = cor0(indx(ir, 7:8, jorb, iorb)) + ! + END DO ! ir = 1, nr + END DO ! jorb = 1, norb + END DO ! iorb = 1, norb ! - cor(1:nsite,1:nsite, 4, iwfc) = cor(1:nsite,1:nsite, 4, iwfc) * 0.25d0 + ! For mVMC ! - ! Up-Down-Down-Up(S+S-) and Down-Up-Up-Down(S-S+) + ! Ciu+ Cid Cjd+ Cju = delta_{ij} Ciu+ Ciu - Ciu+ Cju Cjd+ Cid + ! Cid+ Ciu Cju+ Cjd = delta_{ij} Cid+ Cid - Cid+ Cjd Cju+ Ciu ! - DO ii = 5, 6 - DO jsite = 1, nsite - DO isite = 1, nsite - cor(isite, jsite, ii, iwfc) = cor0(indx(isite,jsite,ii + 2)) - END DO - ! - ! For mVMC - ! - ! Ciu+ Cid Cjd+ Cju = delta_{ij} Ciu+ Ciu - Ciu+ Cju Cjd+ Cid - ! Cid+ Ciu Cju+ Cjd = delta_{ij} Cid+ Cid - Cid+ Cjd Cju+ Ciu - ! - IF (calctype == 4) THEN - cor(1:nsite, jsite, ii, iwfc) = - cor(1:nsite, jsite, ii, iwfc) - cor( jsite, jsite, ii, iwfc) = cor(jsite, jsite, ii, iwfc) & - & + cor(jsite, jsite, ii - 4, iwfc) - END IF - ! + IF (calctype == 4) THEN + cor(1:nr, 5:6, 1:norb, 1:norb, iwfc) = - cor(1:nr, 5:6, 1:norb, 1:norb, iwfc) + DO iorb = 1, norb + cor(1, 5:6, iorb, iorb, iwfc) = cor(1, 5:6, iorb, iorb, iwfc) & + & + cor(1, 1:2, iorb, iorb, iwfc) END DO - END DO + END IF ! ! S.S = Sz Sz + 0.5 * (S+S- + S-S+) ! - cor(1:nsite,1:nsite, 6, iwfc) = cor(1:nsite,1:nsite, 4, iwfc) & - & + 0.5d0 * ( cor(1:nsite,1:nsite, 5, iwfc) & - & + cor(1:nsite,1:nsite, 6, iwfc) ) + cor(1:nr, 6, 1:norb, 1:norb, iwfc) = cor(1:nr, 4, 1:norb, 1:norb, iwfc) & + & + 0.5d0 * ( cor(1:nr, 5, 1:norb, 1:norb, iwfc) & + & + cor(1:nr, 6, 1:norb, 1:norb, iwfc) ) ! END DO ! iwfc = 1, nwfc ! - DEALLOCATE(cor0, cor0_r, indx) + DEALLOCATE(cor0, indx) ! END SUBROUTINE read_corrfile ! @@ -701,33 +719,36 @@ END SUBROUTINE read_corrfile ! SUBROUTINE fourier_cor() ! - USE fourier_val, ONLY : nsite, cor, cor_k, site, kvec, nwfc, nk, ncell + USE fourier_val, ONLY : cor, cor_k, kvec, nwfc, nk, nr, nreq, norb, irv, phase IMPLICIT NONE ! - INTEGER :: isite, jsite, ik + INTEGER :: ik, ir, ireq REAL(8) :: tpi = 2.0 * ACOS(-1d0), theta - COMPLEX(8),ALLOCATABLE :: fmat(:,:,:) + COMPLEX(8),ALLOCATABLE :: fmat(:,:) ! - ALLOCATE(fmat(nk,nsite,nsite), cor_k(nk,6,nwfc)) + ALLOCATE(fmat(nk,nr), cor_k(nk,6,norb,norb,nwfc)) ! ! Matirx for Fourier trans. exp(-i k R) ! - DO jsite = 1, nsite - DO isite = 1, nsite - DO ik = 1, nk - theta = - tpi * DOT_PRODUCT(kvec(1:3,ik), (site(1:3,isite) - site(1:3,jsite))) - fmat(ik,isite,jsite) = CMPLX(COS(theta), SIN(theta), KIND(1d0)) + DO ik = 1, nk + DO ir = 1, nr + fmat(ik,ir) = CMPLX(0d0, 0d0, KIND(1d0)) + DO ireq = 1, nreq(ir) + theta = - tpi * DOT_PRODUCT(kvec(1:3,ik), DBLE(irv(1:3,ireq,ir))) & + & + tpi * phase(ireq,ir) + fmat(ik,ir) = fmat(ik,ir) + CMPLX(COS(theta), SIN(theta), KIND(1d0)) END DO - END DO - END DO + fmat(ik,ir) = fmat(ik,ir) / DBLE(nreq(ir)) + END DO ! ir = 1, nr + END DO ! ik = 1, nk ! - CALL zgemm('N', 'N', nk, 6*nwfc, nsite*nsite, CMPLX(1d0, 0d0, KIND(1d0)), fmat, nk, & - & cor, nsite*nsite, CMPLX(0d0,0d0,KIND(1d0)), cor_k, nk) + CALL zgemm('N', 'N', nk, 6*norb*norb*nwfc, nr, CMPLX(1d0, 0d0, KIND(1d0)), fmat, nk, & + & cor, nr, CMPLX(0d0,0d0,KIND(1d0)), cor_k, nk) ! - cor_k(1:nk,1:2,1:nwfc) = cor_k(1:nk,1:2,1:nwfc) / dble(ncell) - cor_k(1:nk,3:6,1:nwfc) = cor_k(1:nk,3:6,1:nwfc) / dble(ncell*ncell) + cor_k(1:nk,1:2,1:norb,1:norb,1:nwfc) = cor_k(1:nk,1:2,1:norb,1:norb,1:nwfc) + cor_k(1:nk,3:6,1:norb,1:norb,1:nwfc) = cor_k(1:nk,3:6,1:norb,1:norb,1:nwfc) / dble(nr) ! - DEALLOCATE(fmat, cor, site) + DEALLOCATE(fmat, cor) ! END SUBROUTINE fourier_cor ! @@ -735,14 +756,31 @@ END SUBROUTINE fourier_cor ! SUBROUTINE output_cor() ! - USE fourier_val, ONLY : cor_k, nk, nk_row, kvec, koff, & - & nwfc, recipr, filehead, filetail, calctype + USE fourier_val, ONLY : cor_k, nk, nnode, knode, nk_line, kname, norb, & + & nwfc, recipr, filehead, filetail, calctype, nkg IMPLICIT NONE ! - INTEGER :: fo = 20, ik, iwfc, idim - REAL(8) :: tpi = 2.0 * ACOS(-1d0) + INTEGER :: fo = 20, ik, iwfc, inode, iorb, jorb, ii, ikk + REAL(8) :: dk(3), dk_cart(3), xk(nk), & + & xk_label(nnode), klength CHARACTER(256) :: filename - COMPLEX(8),ALLOCATABLE :: cor_ave(:,:), cor_err(:,:) + COMPLEX(8),ALLOCATABLE :: cor_ave(:,:,:,:), cor_err(:,:,:,:) + ! + ! Compute x-position for plotting band + ! + xk(1) = 0.0 + ikk = 1 + DO inode = 1, nnode - 1 + dk(1:3) = knode(1:3, inode+1) - knode(1:3, inode) + dk_cart(1:3) = MATMUL(recipr(1:3,1:3), dk(1:3)) + klength = SQRT(DOT_PRODUCT(dk_cart, dk_cart)) / DBLE(nk_line) + xk_label(inode) = xk(ikk) + DO ik = 1, nk_line + xk(ikk+1) = xk(ikk) + klength + ikk = ikk + 1 + END DO + END DO + xk_label(nnode) = xk(ikk) ! ! Output Correlation function in the 1st BZ ! @@ -756,46 +794,54 @@ SUBROUTINE output_cor() ! ! mVMC ! - ALLOCATE(cor_ave(nk,6), cor_err(nk,6)) + ALLOCATE(cor_ave(ikk,6,norb,norb), cor_err(ikk,6,norb,norb)) ! ! Average ! - cor_ave(1:nk,1:6) = SUM(cor_k(1:nk,1:6,1:nwfc), 3) / DBLE(nwfc) + cor_ave(1:ikk,1:6,1:norb,1:norb) = SUM(cor_k(1:ikk,1:6,1:norb,1:norb,1:nwfc), 5) / DBLE(nwfc) ! ! Variance ! - cor_err(1:nk,1:6) = 0d0 + cor_err(1:ikk,1:6,1:norb,1:norb) = 0d0 DO iwfc = 1, nwfc - cor_err(1:nk,1:6) = cor_err(1:nk,1:6) & - & + CMPLX( DBLE(cor_k(1:nk,1:6,iwfc) - cor_ave(1:nk,1:6))**2, & - & AIMAG(cor_k(1:nk,1:6,iwfc) - cor_ave(1:nk,1:6))**2, & - & KIND(0d0)) + cor_err(1:ikk,1:6,1:norb,1:norb) = cor_err(1:ikk,1:6,1:norb,1:norb) & + & + CMPLX( DBLE(cor_k(1:ikk,1:6,1:norb,1:norb,iwfc) - cor_ave(1:ikk,1:6,1:norb,1:norb))**2, & + & AIMAG(cor_k(1:ikk,1:6,1:norb,1:norb,iwfc) - cor_ave(1:ikk,1:6,1:norb,1:norb))**2, & + & KIND(0d0)) END DO ! ! Standard Error ! IF(nwfc == 1) THEN - cor_err(1:nk,1:6) = CMPLX(0d0, 0d0, KIND(0d0)) + cor_err(1:ikk,1:6,1:norb,1:norb) = CMPLX(0d0, 0d0, KIND(0d0)) ELSE - cor_err(1:nk,1:6) = CMPLX(SQRT( DBLE(cor_err(1:nk,1:6))), & - & SQRT(AIMAG(cor_err(1:nk,1:6))), KIND(0d0)) & - & / SQRT(DBLE(nwfc * (nwfc - 1))) + cor_err(1:ikk,1:6,1:norb,1:norb) = CMPLX(SQRT( DBLE(cor_err(1:ikk,1:6,1:norb,1:norb))), & + & SQRT(AIMAG(cor_err(1:ikk,1:6,1:norb,1:norb))), KIND(0d0)) & + & / SQRT(DBLE(nwfc * (nwfc - 1))) END IF ! filename = TRIM(filehead) // "_corr.dat" OPEN(fo, file = TRIM(filename)) ! - WRITE(fo,*) "#mVMC", nk, nk_row - DO idim = 1, 3 - WRITE(fo,*) "# ", tpi * recipr(1:3, idim) + WRITE(fo,*) "# k-length[1]" + ii = 1 + DO iorb = 1, norb + DO jorb = 1, norb + WRITE(fo,'(a,i3,a,i3)') "# Orbital", iorb, " to Orbital", jorb + WRITE(fo,'(a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a)') & + & "# UpUp[", ii+1, ",", ii+2, ",", ii+13, ",", ii+14, & + & "] (Re. Im. Err.) DownDown[", ii+3, ",", ii+4, ",", ii+15, ",", ii+16, "]" + WRITE(fo,'(a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a)') & + & "# Density[", ii+5, ",", ii+6, ",", ii+17, ",", ii+18, & + & "] SzSz[", ii+7, ",", ii+8, ",", ii+19, ",", ii+20, & + & "] S+S-[", ii+9, ",", ii+10, ",", ii+21, ",", ii+22, & + & "] S.S[", ii+11, ",", ii+12, ",", ii+23, ",", ii+24, "]" + ii = ii+24 + END DO END DO - WRITE(fo,*) "# kx[1] ky[2] kz[3](Cart.) UpUp[4,5,16,17] (Re. Im. Err.) DownDown[6,7,18,19]" - WRITE(fo,*) "# Density[8,9,20,21] SzSz[10,11,22,23] S+S-[12,13,24,25] S.S[14,15,26.27]" - WRITE(fo,'(a,3f15.7)') " #k-offset", koff(1:3) ! - DO ik = 1, nk - WRITE(fo,'(27e15.5)') tpi * MATMUL(recipr(1:3,1:3), kvec(1:3,ik)), & - & cor_ave(ik,1:6), cor_err(ik,1:6) + DO ik = 1, ikk + WRITE(fo,'(1000e15.5)') cor_ave(ik,1:6, 1:norb, 1:norb), cor_err(ik,1:6, 1:norb, 1:norb) END DO ! CLOSE(fo) @@ -811,16 +857,22 @@ SUBROUTINE output_cor() filename = TRIM(filehead) // "_corr" // TRIM(filetail(iwfc)) OPEN(fo, file = TRIM(filename)) ! - WRITE(fo,*) "#HPhi", nk, nk_row - DO idim = 1, 3 - WRITE(fo,*) "# ", tpi * recipr(1:3, idim) + WRITE(fo,*) "# k-length[1]" + ii = 1 + DO iorb = 1, norb + DO jorb = 1, norb + WRITE(fo,'(a,i3,a,i3)') "# Orbital", iorb, " to Orbital", jorb + WRITE(fo,'(a,i4,a,i4,a,i4,a,i4,a)') & + & "# UpUp[", ii+1, ",", ii+2, "] (Re. Im.) DownDown[", ii+3, ",", ii+4, "]" + WRITE(fo,'(a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a,i4,a)') & + & "# Density[", ii+5, ",", ii+6, "] SzSz[", ii+7, ",", ii+8, & + & "] S+S-[", ii+9, ",", ii+10, "] S.S[", ii+11, ",", ii+12, "]" + ii = ii+12 + END DO END DO - WRITE(fo,*) "# kx[1] ky[2] kz[3](Cart.) UpUp[4,5] (Re. Im.) DownDown[6,7]" - WRITE(fo,*) "# Density[8,9] SzSz[10,11] S+S-[12,13] S.S[14,15]" - WRITE(fo,'(a,3f15.7)') " #k-offset", koff(1:3) ! - DO ik = 1, nk - WRITE(fo,'(15e15.5)') tpi * MATMUL(recipr(1:3,1:3), kvec(1:3,ik)), cor_k(ik,1:6,iwfc) + DO ik = 1, ikk + WRITE(fo,'(1000e15.5)') xk(ik), cor_k(ik, 1:6, 1:norb, 1:norb, iwfc) END DO ! CLOSE(fo) @@ -829,7 +881,46 @@ SUBROUTINE output_cor() ! END IF ! IF(calctype == 4) ! - DEALLOCATE(cor_k,kvec) + OPEN(fo, file = "kpath.gp") + ! + WRITE(fo,'(a)',advance="no") "set xtics (" + DO inode = 1, nnode - 1 + WRITE(fo,'(a,a,a,f10.5,a)',advance="no") "'", TRIM(kname(inode)), "' ", xk_label(inode), ", " + END DO + WRITE(fo,'(a,a,a,f10.5,a)') "'", TRIM(kname(nnode)), "' ", xk_label(nnode), ")" + WRITE(fo,'(a)') "set ylabel 'Correlation function'" + WRITE(fo,'(a)') "set grid xtics lt 1 lc 0" + ! + CLOSE(fo) + ! + ! FermiSuerfer file + ! + DO iwfc = 1, nwfc + ! + filename = TRIM(filehead) // "_corr" // TRIM(filetail(iwfc)) // ".frmsf" + OPEN(fo, file = TRIM(filename)) + ! + WRITE(fo,*) nkg(1:3) + WRITE(fo,*) 1 + WRITE(fo,*) norb + WRITE(fo,*) REAL(recipr(1:3,1)) + WRITE(fo,*) REAL(recipr(1:3,2)) + WRITE(fo,*) REAL(recipr(1:3,3)) + DO iorb = 1, norb + DO ik = ikk+1, nk + WRITE(fo,*) SUM(REAL(cor_k(ik, 1:2, iorb, iorb, iwfc))) + END DO + END DO + DO iorb = 1, norb + DO ik = ikk+1, nk + WRITE(fo,*) REAL(iorb) + END DO + END DO + CLOSE(fo) + ! + END DO ! iwfc = 1, nwfc + ! + DEALLOCATE(cor_k) ! END SUBROUTINE output_cor ! diff --git a/tool/makefile_tool b/tool/makefile_tool index b7cae3d4..1d2a177b 100644 --- a/tool/makefile_tool +++ b/tool/makefile_tool @@ -4,13 +4,10 @@ include ../src/make.sys .SUFFIXES : .o .F90 .SUFFIXES : .o .c -all:fourier corplot +all:greenr2k -fourier:fourier.o key2lower.o - $(F90) fourier.o key2lower.o $(LIBS) -o $@ - -corplot:corplot.o - $(F90) corplot.o $(LIBS) -o $@ +greenr2k:greenr2k.o key2lower.o + $(F90) greenr2k.o key2lower.o $(LIBS) -o $@ .F90.o: $(F90) -c $< $(FFLAGS) @@ -19,4 +16,4 @@ corplot:corplot.o $(CC) $(CFLAGS) -c $< clean: - rm -f *.o *.mod fourier corplot + rm -f *.o *.mod greenr2k diff --git a/tool/respack2wan90.py b/tool/respack2wan90.py index f2246ab3..9e4eb0ad 100644 --- a/tool/respack2wan90.py +++ b/tool/respack2wan90.py @@ -38,7 +38,7 @@ def res2wan(name_in, name_out): temp1 = [[]] nr = 0 for iline in range(len(line)): - if line[iline] == "\n": + if line[iline] == "\n" or line[iline] == " \n": temp1.append([]) nr += 1 else: @@ -125,15 +125,27 @@ def ref2geom(filename): print("%f %f %f" % (centre[iwan, 0], centre[iwan, 1], centre[iwan, 2]), file=fo) -args = sys.argv +def respack2wan90(seedname): -if len(args) != 2: - print("\nUsage:\n") - print(" $ respack2wan90.py seedname\n") - exit(-1) + res2wan("./dir-wan/dat.h_mat_r", seedname + "_hr.dat") + res2wan("./dir-intW/dat.Wmat", seedname + "_ur.dat") + res2wan("./dir-intJ/dat.Jmat", seedname + "_jr.dat") -res2wan("./dir-wan/dat.h_mat_r", args[1] + "_hr.dat") -res2wan("./dir-intW/dat.Wmat", args[1] + "_ur.dat") -res2wan("./dir-intJ/dat.Jmat", args[1] + "_jr.dat") + ref2geom(seedname + "_geom.dat") -ref2geom(args[1] + "_geom.dat") + +if __name__ == '__main__': + + args = sys.argv + seedname = "zvo" + + if len(args) == 1: + seedname = "zvo" + elif len(args) == 2: + seedname = args[1] + else: + print("\nUsage:\n") + print(" $ respack2wan90.py [seedname]\n") + exit(-1) + + respack2wan90(seedname) From 52fcb2ac0d3da24bf8623f7f1cd968adf693113c Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Tue, 17 Apr 2018 13:06:43 +0900 Subject: [PATCH 23/34] The documantaion of the Fourier tools are updated. fourier and corplot are integrated into greenr2k which can plot corr. function along k-path. The file format is changed largely. --- doc/en/fourier/format.rst | 235 ++++++++++++---------------------- doc/en/fourier/overview.rst | 37 +++--- doc/en/fourier/tutorial.rst | 95 +++++++------- doc/en/fourier/util.rst | 24 +--- doc/figs/corplot.png | Bin 20340 -> 22657 bytes doc/jp/fourier/format.rst | 242 ++++++++++++------------------------ doc/jp/fourier/overview.rst | 39 +++--- doc/jp/fourier/tutorial.rst | 92 ++++++++------ doc/jp/fourier/util.rst | 23 +--- 9 files changed, 307 insertions(+), 480 deletions(-) diff --git a/doc/en/fourier/format.rst b/doc/en/fourier/format.rst index df29ac48..95aedfe3 100644 --- a/doc/en/fourier/format.rst +++ b/doc/en/fourier/format.rst @@ -10,42 +10,44 @@ Geometry The file name in the :ref:`tutorial` is ``geometry.dat``. When we use Standard mode of mVMC/:math:`{\mathcal H}\Phi`, -this file is generated automatically. -Therefore we do not have to care it. +the information of the cell and geometry is generated automatically. :: - 1.000000 0.000000 0.000000 (1) - 0.000000 1.000000 0.000000 (1) - 0.000000 0.000000 1.000000 (1) - 0.000000 0.000000 0.000000 (2) - 4 0 0 (3) - 0 4 0 (3) - 0 0 1 (3) - 0.000000 0.000000 0.000000 (4) - 1.000000 0.000000 0.000000 (4) - 2.000000 0.000000 0.000000 (4) - 3.000000 0.000000 0.000000 (4) - 0.000000 1.000000 0.000000 (4) - 1.000000 1.000000 0.000000 (4) - 2.000000 1.000000 0.000000 (4) - 3.000000 1.000000 0.000000 (4) - 0.000000 2.000000 0.000000 (4) - 1.000000 2.000000 0.000000 (4) - 2.000000 2.000000 0.000000 (4) - 3.000000 2.000000 0.000000 (4) - 0.000000 3.000000 0.000000 (4) - 1.000000 3.000000 0.000000 (4) - 2.000000 3.000000 0.000000 (4) - 3.000000 3.000000 0.000000 (4) - -#. The unit lattice vectors. Arbitrary unit. -#. The phase for the one-body term across boundaries of the simulation cell (degree unit). + 1.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00 (1) + 0.000000000000000e+00 1.000000000000000e+00 0.000000000000000e+00 (1) + 0.000000000000000e+00 0.000000000000000e+00 1.000000000000000e+00 (1) + 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00 (2) + 2 2 0 (3) + -2 2 0 (3) + 0 0 1 (3) + 0 0 0 0 (4) + -1 1 0 0 (4) + 0 1 0 0 (4) + 1 1 0 0 (4) + -1 2 0 0 (4) + 0 2 0 0 (4) + 1 2 0 0 (4) + 0 3 0 0 (4) + 4 20 (5) + G 0 0 0 (6) + X 0.5 0 0 (6) + M 0.5 0.5 0 (6) + G 0 0 0 (6) + 16 16 1 (7) + +#. The unit lattice vectors. Arbitrary unit (Generated by Standard mode). +#. The phase for the one-body term across boundaries of the simulation cell (degree unit, + Generated by Standard mode). #. Three integer vector specifying the shape of the simulation cell. They are the same as the input parameters ``a0W``, ``a0L``, ``a0H``, ``a1W``... - in Standard mode. -#. The position of each site. The fractional coordinate is used. - + in Standard mode (Generated by standard mode). +#. The index of the lattice vector and the orbital each site + (Generated by standard mode). +#. The number of *k* node (high-symmetry point) and the number of *k* + along high symmetry line. +#. Fractional coordinate of *k* nodes. +#. The *k* grid to plot the isosurface of the momentum distribution function. One- and Two-body correlation function in the site representation ----------------------------------------------------------------- @@ -64,33 +66,40 @@ The file names in the :ref:`tutorial` are ``greenone.def`` (one body) and ``gree For calculating correlation functions in :ref:`supported`, indices must be specified as follows: -- :math:`\langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle` +- :math:`\langle {\hat c}_{{\bf k}\alpha\uparrow}^{\dagger} {\hat c}_{{\bf k}\beta\uparrow}\rangle` - :math:`\langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle` - with :math:`(i, j)` ranging on the whole site. + :math:`\langle {\hat c}_{{\bf 0}\alpha\uparrow}^{\dagger} {\hat c}_{{\bf R}\beta\uparrow}\rangle` + with + :math:`{\bf R}` ranging on the all unit cell, and + :math:`(\alpha, \beta)` ranging on the all orbitals in the unit cell. -- :math:`\langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle` +- :math:`\langle {\hat c}_{{\bf k}\alpha\downarrow}^{\dagger} {\hat c}_{{\bf k}\beta\downarrow}\rangle` - :math:`\langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle` - with :math:`(i, j)` ranging on the whole site. + :math:`\langle {\hat c}_{{\bf 0}\alpha\downarrow}^{\dagger} {\hat c}_{{\bf R}\beta\downarrow}\rangle` + with + :math:`{\bf R}` ranging on the all unit cell, and + :math:`(\alpha, \beta)` ranging on the all orbitals in the unit cell. -- :math:`\langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle` and - :math:`\langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle` +- :math:`\langle {\hat \rho}_{{\bf k}\alpha} {\hat \rho}_{{\bf k}\beta}\rangle` and + :math:`\langle {\hat S}_{{\bf k}\alpha}^{z} {\hat S}_{{\bf k}\beta}^{z} \rangle` - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i \sigma} {\hat c}_{j \sigma'}^{\dagger} {\hat c}_{j \sigma'}\rangle` - with :math:`(i, j)` ranging on the whole site and + :math:`\langle {\hat c}_{{\bf 0}\alpha\sigma}^{\dagger} {\hat c}_{{\bf 0}\alpha\sigma} {\hat c}_{{\bf R}\beta \sigma'}^{\dagger} {\hat c}_{{\bf R}\beta \sigma'}\rangle` + with :math:`{\bf R}` ranging on the all unit cell, + :math:`(\alpha, \beta)` ranging on the all orbitals in the unit cell, and :math:`(\sigma, \sigma')` ranging from :math:`\uparrow` to :math:`\downarrow`. -- :math:`\langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle` and - :math:`\langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle` +- :math:`\langle {\hat S}_{{\bf k}\alpha}^{+} {\hat S}_{{\bf k}\beta}^{-} \rangle` and + :math:`\langle {\hat {\bf S}}_{{\bf k}\alpha} \cdot {\hat {\bf S}}_{{\bf k}\beta} \rangle` For :math:`{\mathcal H}\Phi`, - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{i -\sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{j \sigma}\rangle` - with :math:`(i, j)` ranging on the whole site and + :math:`\langle {\hat c}_{{\bf 0}\alpha\sigma}^{\dagger} {\hat c}_{{\bf 0}\alpha-\sigma} {\hat c}_{{\bf R}\beta -\sigma}^{\dagger} {\hat c}_{{\bf R}\beta \sigma}\rangle` + with :math:`{\bf R}` ranging on the all unit cell, + :math:`(\alpha, \beta)` ranging on the all orbitals in the unit cell, and :math:`\sigma` ranging from :math:`\uparrow` to :math:`\downarrow`. For mVMC, - :math:`\langle {\hat c}_{i \sigma}^{\dagger} {\hat c}_{j \sigma} {\hat c}_{j -\sigma}^{\dagger} {\hat c}_{i -\sigma}\rangle` - with :math:`(i, j)` ranging on the whole site and + :math:`\langle {\hat c}_{{\bf 0}\alpha\sigma}^{\dagger} {\hat c}_{{\bf R}\beta \sigma} {\hat c}_{{\bf R}\beta -\sigma}^{\dagger} {\hat c}_{{\bf 0}\alpha-\sigma}\rangle` + with :math:`{\bf R}` ranging on the all unit cell, + :math:`(\alpha, \beta)` ranging on the all orbitals in the unit cell, and :math:`\sigma` ranging from :math:`\uparrow` to :math:`\downarrow`. In the both cases, please care the order of operators. @@ -118,8 +127,8 @@ this utility assume them as 0. .. _zvocorr: -Correlation functions in the primitive Brillouin zone ------------------------------------------------------ +Correlation functions on the *k* path +------------------------------------- This file contains the Fourier-transformed correlation function and generated by the utility ``fourier``. @@ -127,126 +136,38 @@ The file name in the :ref:`tutorial` is ``output/zvo_corr.dat``. :: - #HPhi 16 (1) - # kx[1] ky[2] kz[3](Cart.) UpUp[4,5] (Re. Im.) DownDown[6,7] (2) - # Density[8,9] SzSz[10,11] S+S-[12,13] S-S+[14,15] (2) - #k-offset 0.0000000 0.0000000 0.0000000 (3) - 0.00000E+00 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) - 0.15708E+01 0.00000E+00 0.00000E+00 0.31250E-01 .... (4) + # k-length[1] + # Orbital 1 to Orbital 1 + # UpUp[ 2, 3] (Re. Im.) DownDown[ 4, 5] + # Density[ 6, 7] SzSz[ 8, 9] S+S-[ 10, 11] S.S[ 12, 13] + 0.00000E+00 0.88211E+00 -0.50000E-09 0.88211E+00 0.40000E-09 ... + 0.25000E-01 0.87976E+00 -0.46625E-09 0.87976E+00 0.42882E-09 ... + 0.50000E-01 0.87276E+00 -0.42841E-09 0.87276E+00 0.45201E-09 ... : : -#. ``"#HPhi"`` for the output of ``HPhi``, - ``"#mVMC"`` for the output of ``vmc.out`` - The subsequent integer indicate the number of :math:`k` points in the primitive Brillouine zone. -#. The description of the quantities in each column. -#. The :math:`k` offset for the one-body correlation function. - That is to say, the one-body correlation function in the 4-7 columns are those - at the :math:`k` point shifted from that point in the 1-3 column. -#. The :math:`k` point (Cartesian) and correlation functions. - The real- and the imaginary-part of each correlation function are written. - -.. _kpoint: - -*k*\-point file for corplot ---------------------------- - -This file is generated by ``fourier`` and -read by ``corplot`` when the correlation function is plotted. -The file name is ``kpoint.dat``. +First, the information of the quantities at each column is written, and +then the *k* coordinate along the path and the real- and imaginary- part +of the correlation function are written. -:: - - 81 9 (1) - 0.62832E+01 0.00000E+00 0.00000E+00 (2) - 0.00000E+00 0.62832E+01 0.00000E+00 (2) - 0.00000E+00 0.00000E+00 0.62832E+01 (2) - -0.62832E+01 -0.62832E+01 0.00000E+00 1 (3) - -0.47124E+01 -0.62832E+01 0.00000E+00 2 (3) - -0.31416E+01 -0.62832E+01 0.00000E+00 3 - -0.15708E+01 -0.62832E+01 0.00000E+00 4 - 0.00000E+00 -0.62832E+01 0.00000E+00 1 - 0.15708E+01 -0.62832E+01 0.00000E+00 2 - 0.31416E+01 -0.62832E+01 0.00000E+00 3 - 0.47124E+01 -0.62832E+01 0.00000E+00 4 - -#. The total number of :math:`k` points plotted by ``corplot`` and - the number of columns for displaying by splot of gnuplot. -#. Reciprocal lattice vectors (Cartesian coordinate). -#. The :math:`k` vector (Cartesian) and - the index of the equivalent :math:`k` point in the primitive Brillouin zone. - This number is the same as that in :ref:`zvocorr` - .. _gnuplot: gnuplot script -------------- -This file is generated by ``corplot``, -and read from gnuplot launched automatically. -We also can launch gnuplot independently and ``load`` this script. -The file name is ``correlation.gp``. +This file is generated by ``greenr2k``. +This script is used for displaying the *k* labels in gnuplot. +The file name is ``kpath.gp``. .. code-block:: gnuplot - #set terminal pdf color enhanced \ (1) - #dashed dl 1.0 size 20.0cm, 20.0cm (1) - #set output 'correlation.pdf' (1) - #set view 60.0, 30.0 (1) - - set view equal xy - set ticslevel 0 - set hidden3d - set xlabel 'kx' - set ylabel 'ky' - set zrange [ 0.25000E-10: 0.18435E+00] - - set pm3d - set pm3d interpolate 5, 5 - set view 0.0, 0.0 - - ##### Set Brillouin-Zone Boundary ##### - - set arrow from -0.31416E+01, -0.31416E+01, ... - set arrow from -0.31416E+01, 0.31416E+01, ... - : - ##### End Set Brillouin-Zone Boundary ##### - - splot \ - 'correlation.dat' u 1:2:3 w l tit '1' (2) - pause -1 - -#. When we want to write the figure to a file, - this line is uncommented. - For pasting this figure on the paper etc., - we write the setting of font, line-color, and so on. - For more details, please see the manual of gnuplot. -#. Plotting the file in :ref:`correlation`. + set xtics ('G' 0.00000, 'X' 0.50000, 'M' 1.00000, 'G' 1.70711) + set ylabel 'Correlation function' + set grid xtics lt 1 lc 0 .. _correlation: -Correlation function at wide range of *k* ------------------------------------------ - -This file is generated by ``corplot``, and -read from gnuplot through :ref:`gnuplot`. -The file name is ``correlation.dat``. - -:: +FermiSurfer file to display the isosurface of the momentum distribution +----------------------------------------------------------------------- - -0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 - -0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - -0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 - -0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.00000E+00 -0.62832E+01 0.18435E+00 0.00000E+00 - 0.15708E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.31416E+01 -0.62832E+01 0.20921E-01 0.00000E+00 - 0.47124E+01 -0.62832E+01 0.36159E-01 0.00000E+00 - 0.62832E+01 -0.62832E+01 0.18435E+00 0.00000E+00 - - -0.62832E+01 -0.47124E+01 0.36159E-01 0.00000E+00 - -0.47124E+01 -0.47124E+01 0.20921E-01 0.00000E+00 - -0.31416E+01 -0.47124E+01 0.11372E-01 0.00000E+00 - : - -The 1st and the 2nd column contains the :math:`k` vector (Cartesian). -3rd and the 4th column contains the correlation function and its standard error, respectively. +This file is generated by ``greenr2k``. +The file name in the tutorial is ``output/zvo_corr_eigen0.dat.frmsf``. diff --git a/doc/en/fourier/overview.rst b/doc/en/fourier/overview.rst index 63c2bc91..782cfdbc 100644 --- a/doc/en/fourier/overview.rst +++ b/doc/en/fourier/overview.rst @@ -23,13 +23,13 @@ One-body correlations :nowrap: \begin{align} - \langle {\hat c}_{{\bf k} \uparrow}^{\dagger} {\hat c}_{{\bf k} \uparrow}\rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat c}_{i \uparrow}^{\dagger} {\hat c}_{j \uparrow}\rangle + \langle {\hat c}_{{\bf k} \alpha \uparrow}^{\dagger} {\hat c}_{{\bf k} \beta \uparrow}\rangle + &\equiv \sum_{\bf R}^{N_{\bf R}} e^{-i {\bf k}\cdot{\bf R}} + \langle {\hat c}_{{\bf 0} \alpha \uparrow}^{\dagger} {\hat c}_{{\bf R} \beta \uparrow}\rangle \\ - \langle {\hat c}_{{\bf k} \downarrow}^{\dagger} {\hat c}_{{\bf k} \downarrow}\rangle - &\equiv \frac{1}{N_{\rm cell}} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat c}_{i \downarrow}^{\dagger} {\hat c}_{j \downarrow}\rangle + \langle {\hat c}_{{\bf k} \alpha \downarrow}^{\dagger} {\hat c}_{{\bf k} \beta \downarrow}\rangle + &\equiv \sum_{\bf R}^{N_{\bf R}} e^{-i {\bf k}\cdot {\bf R}} + \langle {\hat c}_{{\bf 0} \alpha \downarrow}^{\dagger} {\hat c}_{{\bf R} \beta \downarrow}\rangle \end{align} Density-density correlation @@ -37,9 +37,10 @@ Density-density correlation .. math:: \begin{align} - \langle {\hat \rho}_{\bf k} {\hat \rho}_{\bf k}\rangle - \equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat \rho}_{i} {\hat \rho}_{j}\rangle + \langle {\hat \rho}_{{\bf k}\alpha} {\hat \rho}_{{\bf k}\beta}\rangle + \equiv \frac{1}{N_{\bf R}} \sum_{\bf R}^{N_{\bf R}} e^{-i {\bf k}\cdot{\bf R}} + \langle ({\hat \rho}_{{\bf 0}\alpha} - \langle {\hat \rho}_{{\bf 0}\alpha} \rangle) + ({\hat \rho}_{{\bf R}\beta} - \langle {\hat \rho}_{{\bf R}\beta} \rangle) \rangle \end{align} Spin-Spin correlations @@ -48,16 +49,16 @@ Spin-Spin correlations :nowrap: \begin{align} - \langle {\hat S}_{\bf k}^{z} {\hat S}_{\bf k}^{z} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat S}_{i}^{z} {\hat S}_{j}^{z} \rangle + \langle {\hat S}_{{\bf k}\alpha}^{z} {\hat S}_{{\bf k}\beta}^{z} \rangle + &\equiv \frac{1}{N_{\bf R}} \sum_{\bf R}^{N_{\bf R}} e^{-i {\bf k}\cdot{\bf R}} + \langle {\hat S}_{{\bf 0}\alpha}^{z} {\hat S}_{{\bf R}\beta}^{z} \rangle \\ - \langle {\hat S}_{\bf k}^{+} {\hat S}_{\bf k}^{-} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat S}_{i}^{+} {\hat S}_{j}^{-} \rangle + \langle {\hat S}_{{\bf k}\alpha}^{+} {\hat S}_{{\bf k}\beta}^{-} \rangle + &\equiv \frac{1}{N_{\bf R}} \sum_{\bf R}^{N_{\bf R}} e^{-i {\bf k}\cdot{\bf R}} + \langle {\hat S}_{{\bf 0}\alpha}^{+} {\hat S}_{{\bf R}\beta}^{-} \rangle \\ - \langle {\hat {\bf S}}_{\bf k} \cdot {\hat {\bf S}}_{\bf k} \rangle - &\equiv \frac{1}{N_{\rm cell}^2} \sum_{i j}^{N_{\rm site}} e^{-i {\bf k}\cdot({\bf R}_i - {\bf R}_j)} - \langle {\hat {\bf S}}_{i} \cdot {\hat {\bf S}}_{j} \rangle + \langle {\hat {\bf S}}_{{\bf k}\alpha} \cdot {\hat {\bf S}}_{{\bf k}\beta} \rangle + &\equiv \frac{1}{N_{\bf R}} \sum_{\bf R}^{N_{\bf R}} e^{-i {\bf k}\cdot{\bf R}} + \langle {\hat {\bf S}}_{{\bf 0}\alpha} \cdot {\hat {\bf S}}_{{\bf R}\beta} \rangle \end{align} diff --git a/doc/en/fourier/tutorial.rst b/doc/en/fourier/tutorial.rst index 7fd36760..182ce641 100644 --- a/doc/en/fourier/tutorial.rst +++ b/doc/en/fourier/tutorial.rst @@ -3,29 +3,57 @@ Tutorial ======== -This tutorial is done by using the input file -in ``sample/Standard/Spin/HeisenbergSquare/``. +In this tutorial, we explain through a sample calculation of +the 8-site Hubbard model on the square lattice. Run HPhi/vmc.out ---------------- - For :math:`{\mathcal H}\Phi` - Calculate the ground state and the correlation function at that state. + We calculate the ground state and the correlation function with + the following input file + + :: + + a0w = 2 + a0l = 2 + a1w = -2 + a1l = 2 + model="Hubbard" + method="CG" + lattice="square" + t=1.0 + U=8.0 + nelec = 8 + 2Sz=0 .. code-block:: bash - $ ../../../../src/HPhi -s StdFace.def + $ HPhi -s input - For mVMC - Optimize the trial wavefunction. + First, we optimize the trial wavefunction with the following input + + :: + + a0w = 2 + a0l = 2 + a1w = -2 + a1l = 2 + model="Hubbard" + lattice="square" + t=1.0 + U=8.0 + nelec = 8 + 2Sz=0 .. code-block:: bash - $ ../../../../src/vmc.out -s StdFace.def + $ vmc.out -s input - Add the following line in ``StdFace.def`` to compute the correlation function. + We add the following line to the input file to compute the correlation function. :: @@ -35,7 +63,7 @@ Run HPhi/vmc.out .. code-block:: bash - $ ../../../../src/vmc.out -s StdFace.def output/zqp_opt.dat + $ vmc.out -s input output/zqp_opt.dat Then the one- and two-body correlation function are written to files in the ``output/`` directory. @@ -51,11 +79,17 @@ Fourier transformation of correlation functions ----------------------------------------------- Perform the Fourier transformation of the correlation function -by using the utility ``fourier``. +by using the utility ``greenr2k``. .. code-block:: bash - $ ../../../../tool/fourier namelist.def geometry.dat + $ echo "4 20 + G 0 0 0 + X 0.5 0 0 + M 0.5 0.5 0 + G 0 0 0 + 16 16 1" >> geometry.dat + $ greenr2k namelist.def geometry.dat Then the Fourier-transformed correlation functions are written to a file in ``output/``. @@ -72,45 +106,22 @@ Related files Display correlation functions ----------------------------- -Plot the correlation function in the :math:`k` space -by using the utility ``corplot``. - -.. code-block:: bash - - $ ../../../../tool/corplot output/zvo_corr.dat +Plot the correlation function in the *k* space +by using gnuplot. -Then the following message appears in the terminal. +.. code-block:: gnuplot -:: - - ##### Plot Start ##### - - Please specify target number from below (0 or Ctrl-C to exit): - - Real Part Without ErrorBar - [ 1] Up-Up [ 2] Down-Down [ 3] Density-Density [ 4] SzSz [ 5] S+S- [ 6] S-S+ - Imaginary Part Without ErrorBar - [11] Up-Up [12] Down-Down [13] Density-Density [14] SzSz [15] S+S- [16] S-S+ - Real Part With ErrorBar - [21] Up-Up [22] Down-Down [23] Density-Density [24] SzSz [25] S+S- [26] S-S+ - Imaginary Part With ErrorBar - [31] Up-Up [32] Down-Down [33] Density-Density [34] SzSz [35] S+S- [36] S-S+ - - Target : - -Type a number corresponding to the quantity to be plotted (for example ``4``) -and press ``Enter``, -then gnuplot is launched and the 3D figure is displayed (Fig. :num:`corplotpng`). + load "kpath.gp" + plot "output/zvo_corr_eigen0.dat" u 1:12 w l .. _corplotpng: .. figure:: ../../figs/corplot.png - The 3D picture when ``Target : 4``. - The solid black lines indicate the Brillouin zone. + The spin-spin correlation :math:`\langle{\bf S}_{\bf k}\cdot{\bf S}_{\bf k}\rangle` + (Column 12). Related files -- kpoint.dat (:ref:`kpoint`) -- correlation.gp (:ref:`gnuplot`) -- correlation.dat (:ref:`correlation`) +- kpath.gp (:ref:`gnuplot`) +- output/zvo_corr.dat (:ref:`zvocorr`) diff --git a/doc/en/fourier/util.rst b/doc/en/fourier/util.rst index 858e5418..93fd440e 100644 --- a/doc/en/fourier/util.rst +++ b/doc/en/fourier/util.rst @@ -1,14 +1,11 @@ -Behavior of each utility -======================== - -Utility ``fourier`` -------------------- +Behavior of ``greenr2k`` utility +================================ This utility is used as follows: .. code-block:: bash - $ ${PATH}/fourier ${NAMELIST} ${GEOMETRY} + $ ${PATH}/greenr2k ${NAMELIST} ${GEOMETRY} where ``${PATH}`` is the path to the directory where the executable ``fourier`` exists, @@ -77,18 +74,3 @@ and the standard error of the real- and imaginary-part of each correlation function, and writes them to a file ``zvo_corr_eigen*.dat`` in ``output/`` directory. - -Utility ``corplot`` -------------------- - -This utility is 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zyL+wP8#|xNRZi)*(nVKOH0(=ocRGHIbFnk-asCVU*q^*x$g2EzmgxU{=nr+-w|{>d zpbaZ-7O-0V-O#{1jo*f>#)d0X<&fgO&h_DRSJY+C z2gnD9h9WJ_0X{w}V4)I2)r4`eybc3W-TWYIrB{|Yq?q{u&x=WLwT`MPXj=OE`I$6> zWDJ6K3i4vrGMnhx`5**NJ0vu86yGGpT> geometry.dat + $ greenr2k namelist.def geometry.dat これにより, カレントディレクトリの ``output/`` 以下に フーリエ変換された相関関数が出力される. @@ -67,49 +101,27 @@ HPhi/vmc.out の実行 - output/zvo_cisajscktalt_001.dat (:ref:`zvocisajs`) - output/zvo_cisajscktalt.dat (:ref:`zvocisajs`) - geometry.dat (:ref:`geometry`) -- output/zvo_corr.dat (:ref:`zvocorr`) +- output/zvo_corr*.dat (:ref:`zvocorr`) 相関関数のプロット ------------------ -ユーティリティプログラム ``corplot`` を使って, +gnuplotを使って, 相関関数を :math:`k` 空間でプロットする. -.. code-block:: bash - - $ ../../../../tool/corplot output/zvo_corr.dat - -この時, ターミナルには次のように標準入力を促すメッセージが現れる. - -:: - - ##### Plot Start ##### - - Please specify target number from below (0 or Ctrl-C to exit): - - Real Part Without ErrorBar - [ 1] Up-Up [ 2] Down-Down [ 3] Density-Density [ 4] SzSz [ 5] S+S- [ 6] S-S+ - Imaginary Part Without ErrorBar - [11] Up-Up [12] Down-Down [13] Density-Density [14] SzSz [15] S+S- [16] S-S+ - Real Part With ErrorBar - [21] Up-Up [22] Down-Down [23] Density-Density [24] SzSz [25] S+S- [26] S-S+ - Imaginary Part With ErrorBar - [31] Up-Up [32] Down-Down [33] Density-Density [34] SzSz [35] S+S- [36] S-S+ - - Target : +.. code-block:: gnuplot -プロットしたい量に対応する数字(例えば4)を入力し, -``Enter`` キーを押すと gnuplot が起動して3Dグラフが表示される(図 :num:`corplotpng` ). + load "kpath.gp" + plot "output/zvo_corr_eigen0.dat" u 1:12 w l .. _corplotpng: .. figure:: ../../figs/corplot.png - Target : 4 としてプロットした図. - 黒線は第一ブリルアンゾーンを表す. + 相関関数 :math:`\langle{\bf S}_{\bf k}\cdot{\bf S}_{\bf k}\rangle` (12列目)を + プロットした図. 関連するファイル -- kpoint.dat (:ref:`kpoint`) -- correlation.gp (:ref:`gnuplot`) -- correlation.dat (:ref:`correlation`) +- kpath.gp (:ref:`gnuplot`) +- output/zvo_corr*.dat (:ref:`zvocorr`) diff --git a/doc/jp/fourier/util.rst b/doc/jp/fourier/util.rst index fe995e6f..c57afb47 100644 --- a/doc/jp/fourier/util.rst +++ b/doc/jp/fourier/util.rst @@ -1,14 +1,11 @@ -各ユーティリティの動作について -============================== - -``fourier`` ユーティリティ --------------------------- +``greenr2k`` ユーティリティの動作について +========================================= このユーティリティーは, 次のようにして使う. .. code-block:: bash - $ ${PATH}/fourier ${NAMELIST} ${GEOMETRY} + $ ${PATH}/greenr2k ${NAMELIST} ${GEOMETRY} ここで, ``${PATH}`` は ``fourier`` ユーティリティのバイナリのあるディレクトリのパス, ${NAMELIST}は :math:`{\mathcal H}\Phi`/mVMC の NameList インプットファイル名, @@ -78,17 +75,3 @@ mVMC を計算し, 平均値と誤差を含んだ単一のファイル ``zvo_corr_eigen*.dat`` を ``output/`` ディレクトリに出力する. -``corplot`` ユーティリティ --------------------------- - -このユーティリティーは, 次のようにして使う. - -.. code-block:: bash - - $ ${PATH}/corplot ${CORR1} ${CORR2} ${CORR3} ... - -ここで, ``${PATH}`` は ``corplot`` ユーティリティのバイナリのあるディレクトリのパス, -${CORR1}, ${CORR2}, ${CORR3}, ...は ``fourier`` ルーチンによって生成された -:ref:`zvocorr` ファイルへのパスである. -すなわち, このユーティリティーでは, (TPQ計算による温度依存性を調べる等の用途で) -複数の相関関数ファイルを読み込み, それらを同時にプロットすることができる. From 91a0dd35d175dbab8084371c4c5a96869ae768bd Mon Sep 17 00:00:00 2001 From: tmisawa Date: Thu, 19 Apr 2018 11:17:08 +0900 Subject: [PATCH 24/34] #191 fixed bug in GetInfoOpt --- src/mVMC/readdef.c | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/mVMC/readdef.c b/src/mVMC/readdef.c index 1b03f586..e097494b 100644 --- a/src/mVMC/readdef.c +++ b/src/mVMC/readdef.c @@ -1748,7 +1748,9 @@ int GetInfoOpt(FILE *fp, int *ArrayOpt, int iComplxFlag, int *iTotalOptCount, in int iLocalOptCount = 0; while (fscanf(fp, "%d ", &i) != EOF) { fscanf(fp, "%d\n", &(ArrayOpt[2 * fidx])); // TBC real - ArrayOpt[2 * fidx + 1] = iComplxFlag; // TBC imaginary + if(iComplxFlag>0){ + ArrayOpt[2 * fidx + 1] = 1; // TBC imaginary + } fidx++; (iLocalOptCount)++; (*iTotalOptCount)++; From dfe0ec72bb3492f625d25db4d9f4f333b4a497ef Mon Sep 17 00:00:00 2001 From: tmisawa Date: Thu, 19 Apr 2018 11:21:23 +0900 Subject: [PATCH 25/34] #191 mod GetInfoOpt --- src/mVMC/readdef.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/mVMC/readdef.c b/src/mVMC/readdef.c index e097494b..903fcdd3 100644 --- a/src/mVMC/readdef.c +++ b/src/mVMC/readdef.c @@ -1749,7 +1749,7 @@ int GetInfoOpt(FILE *fp, int *ArrayOpt, int iComplxFlag, int *iTotalOptCount, in while (fscanf(fp, "%d ", &i) != EOF) { fscanf(fp, "%d\n", &(ArrayOpt[2 * fidx])); // TBC real if(iComplxFlag>0){ - ArrayOpt[2 * fidx + 1] = 1; // TBC imaginary + ArrayOpt[2 * fidx + 1] = ArrayOpt[2 * fidx]; // TBC imaginary } fidx++; (iLocalOptCount)++; From 0a4adf92e5db78d99660def1225b73a1e33b04ad Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Mon, 14 May 2018 15:01:18 +0900 Subject: [PATCH 26/34] cubic and fcc become available; they are equivalent to orthprhombic and fco, respectively. [BugFix] The first column (k-length) of output corr_k was absent. --- src/StdFace/StdFace_main.c | 7 +++++-- tool/greenr2k.F90 | 24 ++++++++++++------------ 2 files changed, 17 insertions(+), 14 deletions(-) diff --git a/src/StdFace/StdFace_main.c b/src/StdFace/StdFace_main.c index 1f199438..a5236b6e 100644 --- a/src/StdFace/StdFace_main.c +++ b/src/StdFace/StdFace_main.c @@ -2515,7 +2515,9 @@ void StdFace_main( || strcmp(StdI->lattice, "chainlattice") == 0) StdFace_Chain(StdI); else if (strcmp(StdI->lattice, "face-centeredorthorhombic") == 0 || strcmp(StdI->lattice, "fcorthorhombic") == 0 - || strcmp(StdI->lattice, "fco") == 0) StdFace_FCOrtho(StdI); + || strcmp(StdI->lattice, "fco") == 0 + || strcmp(StdI->lattice, "face-centeredcubic") == 0 + || strcmp(StdI->lattice, "fcc") == 0) StdFace_FCOrtho(StdI); else if (strcmp(StdI->lattice, "honeycomb") == 0 || strcmp(StdI->lattice, "honeycomblattice") == 0) StdFace_Honeycomb(StdI); else if (strcmp(StdI->lattice, "kagome") == 0 @@ -2523,7 +2525,8 @@ void StdFace_main( else if (strcmp(StdI->lattice, "ladder") == 0 || strcmp(StdI->lattice, "ladderlattice") == 0) StdFace_Ladder(StdI); else if (strcmp(StdI->lattice, "orthorhombic") == 0 - || strcmp(StdI->lattice, "simpleorthorhombic") == 0) StdFace_Orthorhombic(StdI); + || strcmp(StdI->lattice, "simpleorthorhombic") == 0 + || strcmp(StdI->lattice, "cubic") == 0) StdFace_Orthorhombic(StdI); else if (strcmp(StdI->lattice, "pyrochlore") == 0) StdFace_Pyrochlore(StdI); else if (strcmp(StdI->lattice, "tetragonal") == 0 || strcmp(StdI->lattice, "tetragonallattice") == 0 diff --git a/tool/greenr2k.F90 b/tool/greenr2k.F90 index cc0a3438..08568699 100644 --- a/tool/greenr2k.F90 +++ b/tool/greenr2k.F90 @@ -764,7 +764,7 @@ SUBROUTINE output_cor() REAL(8) :: dk(3), dk_cart(3), xk(nk), & & xk_label(nnode), klength CHARACTER(256) :: filename - COMPLEX(8),ALLOCATABLE :: cor_ave(:,:,:,:), cor_err(:,:,:,:) + COMPLEX(8),ALLOCATABLE :: cor_mvmc(:,:,:,:,:) ! ! Compute x-position for plotting band ! @@ -794,29 +794,29 @@ SUBROUTINE output_cor() ! ! mVMC ! - ALLOCATE(cor_ave(ikk,6,norb,norb), cor_err(ikk,6,norb,norb)) + ALLOCATE(cor_mvmc(ikk,6,2,norb,norb)) ! ! Average ! - cor_ave(1:ikk,1:6,1:norb,1:norb) = SUM(cor_k(1:ikk,1:6,1:norb,1:norb,1:nwfc), 5) / DBLE(nwfc) + cor_mvmc(1:ikk,1:6,1,1:norb,1:norb) = SUM(cor_k(1:ikk,1:6,1:norb,1:norb,1:nwfc), 5) / DBLE(nwfc) ! ! Variance ! - cor_err(1:ikk,1:6,1:norb,1:norb) = 0d0 + cor_mvmc(1:ikk,1:6,2,1:norb,1:norb) = 0d0 DO iwfc = 1, nwfc - cor_err(1:ikk,1:6,1:norb,1:norb) = cor_err(1:ikk,1:6,1:norb,1:norb) & - & + CMPLX( DBLE(cor_k(1:ikk,1:6,1:norb,1:norb,iwfc) - cor_ave(1:ikk,1:6,1:norb,1:norb))**2, & - & AIMAG(cor_k(1:ikk,1:6,1:norb,1:norb,iwfc) - cor_ave(1:ikk,1:6,1:norb,1:norb))**2, & + cor_mvmc(1:ikk,1:6,2,1:norb,1:norb) = cor_mvmc(1:ikk,1:6,2,1:norb,1:norb) & + & + CMPLX( DBLE(cor_k(1:ikk,1:6,1:norb,1:norb,iwfc) - cor_mvmc(1:ikk,1:6,1,1:norb,1:norb))**2, & + & AIMAG(cor_k(1:ikk,1:6,1:norb,1:norb,iwfc) - cor_mvmc(1:ikk,1:6,1,1:norb,1:norb))**2, & & KIND(0d0)) END DO ! ! Standard Error ! IF(nwfc == 1) THEN - cor_err(1:ikk,1:6,1:norb,1:norb) = CMPLX(0d0, 0d0, KIND(0d0)) + cor_mvmc(1:ikk,1:6,2,1:norb,1:norb) = CMPLX(0d0, 0d0, KIND(0d0)) ELSE - cor_err(1:ikk,1:6,1:norb,1:norb) = CMPLX(SQRT( DBLE(cor_err(1:ikk,1:6,1:norb,1:norb))), & - & SQRT(AIMAG(cor_err(1:ikk,1:6,1:norb,1:norb))), KIND(0d0)) & + cor_mvmc(1:ikk,1:6,2,1:norb,1:norb) = CMPLX(SQRT( DBLE(cor_mvmc(1:ikk,1:6,2,1:norb,1:norb))), & + & SQRT(AIMAG(cor_mvmc(1:ikk,1:6,2,1:norb,1:norb))), KIND(0d0)) & & / SQRT(DBLE(nwfc * (nwfc - 1))) END IF ! @@ -841,12 +841,12 @@ SUBROUTINE output_cor() END DO ! DO ik = 1, ikk - WRITE(fo,'(1000e15.5)') cor_ave(ik,1:6, 1:norb, 1:norb), cor_err(ik,1:6, 1:norb, 1:norb) + WRITE(fo,'(1000e15.5)') xk(ik), cor_mvmc(ik, 1:6, 1:2, 1:norb, 1:norb) END DO ! CLOSE(fo) ! - DEALLOCATE(cor_ave, cor_err) + DEALLOCATE(cor_mvmc) ! ELSE ! From f11e38ad036ddd981d29aa149786200c12faee0c Mon Sep 17 00:00:00 2001 From: mitsuaki1987 Date: Tue, 15 May 2018 16:12:27 +0900 Subject: [PATCH 27/34] It failed when there is no on-site U. --- src/StdFace/Wannier90.c | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/StdFace/Wannier90.c b/src/StdFace/Wannier90.c index a0eec352..8e5600c7 100644 --- a/src/StdFace/Wannier90.c +++ b/src/StdFace/Wannier90.c @@ -394,11 +394,11 @@ void StdFace_Wannier90( if (strcmp(StdI->model, "spin") == 0 ) { ntransMax = StdI->nsite * (StdI->S2 + 1/*h*/ + 2 * StdI->S2/*Gamma*/); nintrMax = StdI->NCell * (StdI->NsiteUC/*D*/ + n_t/*J*/ + n_u + n_j) - * (3 * StdI->S2 + 1) * (3 * StdI->S2 + 1); + * (3 * StdI->S2 + 1) * (3 * StdI->S2 + StdI->NsiteUC); } else if (strcmp(StdI->model, "hubbard") == 0) { ntransMax = StdI->NCell * 2/*spin*/ * (2 * StdI->NsiteUC/*mu+h+Gamma*/ + n_t * 2/*t*/); - nintrMax = StdI->NCell * (n_u + n_j + 1); + nintrMax = StdI->NCell * (n_u + n_j + StdI->NsiteUC); } /**/ StdFace_MallocInteractions(StdI, ntransMax, nintrMax); From 6bbcf80705e5de82230863d2ac8d00ee38e32bbf Mon Sep 17 00:00:00 2001 From: k-yoshimi Date: Mon, 4 Jun 2018 14:33:42 +0900 Subject: [PATCH 28/34] add CMakeLists to test --- CMakeLists.txt | 10 ++++++++++ test/CMakeLists.txt | 4 ++++ test/python/CMakeLists.txt | 22 ++++++++++++++++++++++ test/python/data/CMakeLists.txt | 26 ++++++++++++++++++++++++++ 4 files changed, 62 insertions(+) create mode 100644 test/CMakeLists.txt create mode 100644 test/python/CMakeLists.txt create mode 100644 test/python/data/CMakeLists.txt diff --git a/CMakeLists.txt b/CMakeLists.txt index 8141dae2..532a80ca 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -61,3 +61,13 @@ add_subdirectory(src/ComplexUHF) add_subdirectory(src/pfapack) add_subdirectory(src/mVMC) add_subdirectory(tool) + +# Build and enable tests +# testing setup +# enable_testing() must be called in the top-level CMakeLists.txt before any add_subdirectory() is called. +option(Testing "Enable testing" OFF) + +if (Testing) + enable_testing(test) + add_subdirectory(test) +endif() diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt new file mode 100644 index 00000000..a5e1e568 --- /dev/null +++ b/test/CMakeLists.txt @@ -0,0 +1,4 @@ +foreach(datafile ${DATA_FILES}) + configure_file(${datafile} ${CMAKE_BINARY_DIR}/test/ COPYONLY) +endforeach() +add_subdirectory(python) diff --git a/test/python/CMakeLists.txt b/test/python/CMakeLists.txt new file mode 100644 index 00000000..60639a11 --- /dev/null +++ b/test/python/CMakeLists.txt @@ -0,0 +1,22 @@ +file(COPY ${CMAKE_SOURCE_DIR}/python/ DESTINATION ${CMAKE_BINARY_DIR}/test/python FILES_MATCHING PATTERN "*.py") +function(add_python_test test) + add_test(NAME python_${test} COMMAND ${PYTHON_EXECUTABLE} ${test}.py) + set_tests_properties(python_${test} PROPERTIES ENVIRONMENT "PYTHONPATH=${CMAKE_BINARY_DIR}/test/python") +endfunction(add_python_test) + +find_package(PythonInterp REQUIRED) + +file(GLOB_RECURSE TEST_FILES "${CMAKE_CURRENT_SOURCE_DIR}/*.py") +foreach(testfile ${TEST_FILES}) + configure_file(${testfile} ${CMAKE_BINARY_DIR}/test/python COPYONLY) +endforeach() + +set(python_test_src + test_Spin +) + +foreach(test ${python_test_src}) + add_python_test(${test}) +endforeach(test) + +add_subdirectory(data) diff --git a/test/python/data/CMakeLists.txt b/test/python/data/CMakeLists.txt new file mode 100644 index 00000000..b8214710 --- /dev/null +++ b/test/python/data/CMakeLists.txt @@ -0,0 +1,26 @@ +FILE(GLOB children RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/*) +SET(dirlist "") +FOREACH(child ${children}) + IF(IS_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${child}) + LIST(APPEND dirlist ${child}) + FILE(GLOB children2 RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_SOURCE_DIR}/${child}/*) + FOREACH(child2 ${children2}) + IF(IS_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${child2}) + LIST(APPEND dirlist ${child2}) + ENDIF() + ENDFOREACH() + ENDIF() +ENDFOREACH() + +FOREACH(dir ${dirlist}) + IF(NOT EXISTS "${CMAKE_BINARY_DIR}/test/python/data/${dir}") + MAKE_DIRECTORY(${CMAKE_BINARY_DIR}/test/python/data/${dir}) + ENDIF() + file(GLOB TEST_FILES "${CMAKE_CURRENT_SOURCE_DIR}/${dir}/*") + foreach(testfile ${TEST_FILES}) + IF(NOT IS_DIRECTORY ${testfile}) + configure_file(${testfile} ${CMAKE_BINARY_DIR}/test/python/data/${dir} COPYONLY) + ENDIF() + endforeach() +ENDFOREACH() + From b496ad8d2a0e606b6b33e00496c5b79e0f0dd37b Mon Sep 17 00:00:00 2001 From: "k.ido" Date: Mon, 4 Jun 2018 15:12:59 +0900 Subject: [PATCH 29/34] #195 del omp --- src/mVMC/stcopt.c | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/mVMC/stcopt.c b/src/mVMC/stcopt.c index d375b2b3..e8581103 100644 --- a/src/mVMC/stcopt.c +++ b/src/mVMC/stcopt.c @@ -171,7 +171,7 @@ int StochasticOpt(MPI_Comm comm) { /* update variational parameters */ if(info==0 && rank==0) { - #pragma omp parallel for default(shared) private(si,pi) + //#pragma omp parallel for default(shared) private(si,pi) #pragma loop noalias #pragma loop norecurrence para for(si=0;si Date: Mon, 4 Jun 2018 19:10:30 +0900 Subject: [PATCH 30/34] upload test tools --- test/python/CMakeLists.txt | 2 +- test/python/data/HeisenbergChain/StdFace.def | 10 + .../data/HeisenbergChain/ref/ref_mean.dat | 216 ++++++++++++++++++ .../data/HeisenbergChain/ref/ref_std.dat | 216 ++++++++++++++++++ test/python/test_HeisenbergChain.py | 28 +++ test/tool/StdFace_org.def | 8 + test/tool/make_ref.py | 23 ++ test/tool/make_ref.sh | 17 ++ 8 files changed, 519 insertions(+), 1 deletion(-) create mode 100644 test/python/data/HeisenbergChain/StdFace.def create mode 100644 test/python/data/HeisenbergChain/ref/ref_mean.dat create mode 100644 test/python/data/HeisenbergChain/ref/ref_std.dat create mode 100644 test/python/test_HeisenbergChain.py create mode 100644 test/tool/StdFace_org.def create mode 100644 test/tool/make_ref.py create mode 100644 test/tool/make_ref.sh diff --git a/test/python/CMakeLists.txt b/test/python/CMakeLists.txt index 60639a11..ec32165d 100644 --- a/test/python/CMakeLists.txt +++ b/test/python/CMakeLists.txt @@ -12,7 +12,7 @@ foreach(testfile ${TEST_FILES}) endforeach() set(python_test_src - test_Spin + test_HeisenbergChain ) foreach(test ${python_test_src}) diff --git a/test/python/data/HeisenbergChain/StdFace.def b/test/python/data/HeisenbergChain/StdFace.def new file mode 100644 index 00000000..3ae2e466 --- /dev/null +++ b/test/python/data/HeisenbergChain/StdFace.def @@ -0,0 +1,10 @@ +L = 16 +Lsub = 2 +model = "Spin" +lattice = "chain" +J = 1.0 +NSROptItrStep = 300 +NVMCSample = 100 +2Sz = 0 +//NVMCCalMode = 1 +RndSeed = 12345 diff --git a/test/python/data/HeisenbergChain/ref/ref_mean.dat b/test/python/data/HeisenbergChain/ref/ref_mean.dat new file mode 100644 index 00000000..1d5e1e77 --- /dev/null +++ b/test/python/data/HeisenbergChain/ref/ref_mean.dat @@ -0,0 +1,216 @@ +-6.843955854471633238e+00 +0.000000000000000000e+00 +5.844000286464069716e-02 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test_HeisenbergChain(self): + # run + #self.assertIs(0, os.system("../../src/mVMC/vmc.out -s %s/StdFace.def" %dir)) + + # get results + array_calc = read_out("./output/zqp_opt.dat")[0:2] + ref_ave = read_out("%s/ref/ref_mean.dat" %dir)[0:2] + ref_std = read_out("%s/ref/ref_std.dat" %dir)[0:2] + testFalse = (ref_std < abs(array_calc - ref_ave)) + print(abs(array_calc[testFalse]) < 1e-8) + print(abs(array_calc[testFalse]), abs(ref_ave[testFalse]), abs(ref_std[testFalse])) + + +if __name__ == '__main__': + unittest.main() diff --git a/test/tool/StdFace_org.def b/test/tool/StdFace_org.def new file mode 100644 index 00000000..951c2d11 --- /dev/null +++ b/test/tool/StdFace_org.def @@ -0,0 +1,8 @@ +L = 16 +Lsub = 2 +model = "Spin" +lattice = "chain" +J = 1.0 +NSROptItrStep = 300 +NVMCSample = 100 +2Sz = 0 diff --git a/test/tool/make_ref.py b/test/tool/make_ref.py new file mode 100644 index 00000000..ef74d44d --- /dev/null +++ b/test/tool/make_ref.py @@ -0,0 +1,23 @@ +import subprocess +import filecmp +import numpy as np +import os + +def read_out(filename): + # drop the first two columns + array = np.loadtxt(filename, dtype='float').astype('float') + return array + +if __name__ == '__main__': + cdir = os.getcwd() + #subprocess.call("sh "+cdir+"/make_ref.sh", shell = True) + array = read_out("output1/zqp_opt.dat") + for i in range(2, 11): + filename = "output{0}/zqp_opt.dat".format(i) + array = np.append(array, read_out(filename)) + array = array.reshape(5, array.shape[0]/5) + std = np.std( array, axis = 0 ) + ave = np.mean( array, axis = 0 ) + np.savetxt("ref_std.dat", X = std) + np.savetxt("ref_mean.dat", X = ave) + #subprocess.call("rm -rf "+cdir+"/output*", shell = True) diff --git a/test/tool/make_ref.sh b/test/tool/make_ref.sh new file mode 100644 index 00000000..f2cba774 --- /dev/null +++ b/test/tool/make_ref.sh @@ -0,0 +1,17 @@ +x=1 +end=10 +while [ $x -lt $end ] +do + cp ./StdFace_org.def ./StdFace.def + echo "RndSeed = $x" >> StdFace.def + ./vmc.out -s ./StdFace.def + x=`expr $x + 12345` + mv ./output ./output$x +done + +cp ./StdFace_org.def ./StdFace_org.def.bak +rm ./*.def +rm ./*.dat +rm ./*.gp +mv ./StdFace_org.def.bak ./StdFace_org.def + From a568d9dc0fe2819f159107f1325c04b9192aebaa Mon Sep 17 00:00:00 2001 From: k-yoshimi Date: Mon, 4 Jun 2018 22:50:29 +0900 Subject: [PATCH 31/34] update test tool --- test/tool/StdFace_org.def | 4 ++-- test/tool/make_ref.py | 4 ++-- test/tool/make_ref.sh | 8 +++++--- 3 files changed, 9 insertions(+), 7 deletions(-) diff --git a/test/tool/StdFace_org.def b/test/tool/StdFace_org.def index 951c2d11..758b2080 100644 --- a/test/tool/StdFace_org.def +++ b/test/tool/StdFace_org.def @@ -1,8 +1,8 @@ L = 16 -Lsub = 2 +Lsub = 4 model = "Spin" lattice = "chain" J = 1.0 -NSROptItrStep = 300 +NSROptItrStep = 400 NVMCSample = 100 2Sz = 0 diff --git a/test/tool/make_ref.py b/test/tool/make_ref.py index ef74d44d..b112b334 100644 --- a/test/tool/make_ref.py +++ b/test/tool/make_ref.py @@ -10,12 +10,12 @@ def read_out(filename): if __name__ == '__main__': cdir = os.getcwd() - #subprocess.call("sh "+cdir+"/make_ref.sh", shell = True) +# subprocess.call("sh "+cdir+"/make_ref.sh", shell = True) array = read_out("output1/zqp_opt.dat") for i in range(2, 11): filename = "output{0}/zqp_opt.dat".format(i) array = np.append(array, read_out(filename)) - array = array.reshape(5, array.shape[0]/5) + array = array.reshape(10, array.shape[0]/10) std = np.std( array, axis = 0 ) ave = np.mean( array, axis = 0 ) np.savetxt("ref_std.dat", X = std) diff --git a/test/tool/make_ref.sh b/test/tool/make_ref.sh index f2cba774..866b24bc 100644 --- a/test/tool/make_ref.sh +++ b/test/tool/make_ref.sh @@ -1,12 +1,14 @@ x=1 -end=10 +end=11 +rm -r ./output* while [ $x -lt $end ] do + x0=`expr 5 \* $x + 12345` cp ./StdFace_org.def ./StdFace.def - echo "RndSeed = $x" >> StdFace.def + echo "RndSeed = $x0" >> StdFace.def ./vmc.out -s ./StdFace.def - x=`expr $x + 12345` mv ./output ./output$x + x=`expr $x + 1` done cp ./StdFace_org.def ./StdFace_org.def.bak From 2df338f7a43eefabfccaed00c65e4250d1527008 Mon Sep 17 00:00:00 2001 From: Kazuyoshi Yoshimi Date: Tue, 5 Jun 2018 08:38:59 +0900 Subject: [PATCH 32/34] update test --- test/python/data/HeisenbergChain/StdFace.def | 4 +- .../data/HeisenbergChain/ref/ref_mean.dat | 276 +++++++++--------- .../data/HeisenbergChain/ref/ref_std.dat | 276 +++++++++--------- test/python/test_HeisenbergChain.py | 11 +- 4 files changed, 271 insertions(+), 296 deletions(-) diff --git a/test/python/data/HeisenbergChain/StdFace.def b/test/python/data/HeisenbergChain/StdFace.def index 3ae2e466..99ccc29b 100644 --- a/test/python/data/HeisenbergChain/StdFace.def +++ b/test/python/data/HeisenbergChain/StdFace.def @@ -3,8 +3,8 @@ Lsub = 2 model = "Spin" lattice = "chain" J = 1.0 -NSROptItrStep = 300 +NSROptItrStep = 400 NVMCSample = 100 2Sz = 0 //NVMCCalMode = 1 -RndSeed = 12345 +RndSeed = 1 diff --git a/test/python/data/HeisenbergChain/ref/ref_mean.dat 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@@ def read_out(filename): class TestAtomic(unittest.TestCase): def test_HeisenbergChain(self): # run - #self.assertIs(0, os.system("../../src/mVMC/vmc.out -s %s/StdFace.def" %dir)) - +# self.assertIs(0, os.system("../../src/mVMC/vmc.out -s %s/StdFace.def" %dir)) # get results array_calc = read_out("./output/zqp_opt.dat")[0:2] ref_ave = read_out("%s/ref/ref_mean.dat" %dir)[0:2] ref_std = read_out("%s/ref/ref_std.dat" %dir)[0:2] - testFalse = (ref_std < abs(array_calc - ref_ave)) - print(abs(array_calc[testFalse]) < 1e-8) - print(abs(array_calc[testFalse]), abs(ref_ave[testFalse]), abs(ref_std[testFalse])) - + testTrue = (ref_std > abs(array_calc - ref_ave)) + testArray = abs(array_calc[testTrue] < 1e-8) + for _test in testArray: + self.assertTrue(_test) if __name__ == '__main__': unittest.main() From ee8f2a0bba8ca0e3b5360362509cd9500edf13b7 Mon Sep 17 00:00:00 2001 From: "k.ido" Date: Fri, 20 Jul 2018 10:49:19 +0900 Subject: [PATCH 33/34] #200 add Error --- src/mVMC/readdef.c | 19 ++++++++++++------- 1 file changed, 12 insertions(+), 7 deletions(-) diff --git a/src/mVMC/readdef.c b/src/mVMC/readdef.c index 903fcdd3..bd0c555a 100644 --- a/src/mVMC/readdef.c +++ b/src/mVMC/readdef.c @@ -556,21 +556,26 @@ int ReadDefFileNInt(char *xNameListFile, MPI_Comm comm) { } } - } + }//rank 0 - if (info != 0) { - if (rank == 0) { - fprintf(stderr, "Error: Definition files(*.def) are incomplete.\n"); - } - MPI_Abort(MPI_COMM_WORLD, EXIT_FAILURE); - } if (rank == 0) { AllComplexFlag = iComplexFlgGutzwiller + iComplexFlgJastrow + iComplexFlgDH2; //TBC AllComplexFlag += iComplexFlgDH4 + iComplexFlgOrbital;//TBC //AllComplexFlag = 1;//DEBUG // AllComplexFlag= 0 -> All real, !=0 -> complex + if(AllComplexFlag == 0 && iFlgOrbitalGeneral == 1){ + fprintf(stderr, "Error: Variational parameters should be complex when orbital is general in this version.\n"); + info = 1; + } } + if (info != 0) { + if (rank == 0) { + fprintf(stderr, "Error: Definition files(*.def) are incomplete.\n"); + } + MPI_Abort(MPI_COMM_WORLD, EXIT_FAILURE); + } + #ifdef _mpi_use MPI_Bcast(bufInt, nBufInt, MPI_INT, 0, comm); MPI_Bcast(&NStoreO, 1, MPI_INT, 0, comm); // for NStoreO From ff0662764c16c4c09e46e95e5ca5f78bd315e88b Mon Sep 17 00:00:00 2001 From: "k.ido" Date: Sat, 21 Jul 2018 21:04:14 +0900 Subject: [PATCH 34/34] change ver --- doc/en/chap01_en.tex | 2 ++ doc/en/conf.py | 2 +- doc/en/intro.rst | 4 ++++ doc/en/userguide_en.tex | 2 +- doc/jp/chap01_jp.tex | 2 ++ doc/jp/conf.py | 2 +- doc/jp/intro.rst | 4 ++++ doc/jp/userguide_jp.tex | 2 +- src/mVMC/include/version.h | 2 +- 9 files changed, 17 insertions(+), 5 deletions(-) diff --git a/doc/en/chap01_en.tex b/doc/en/chap01_en.tex index 866a1a95..36bb858f 100644 --- a/doc/en/chap01_en.tex +++ b/doc/en/chap01_en.tex @@ -81,6 +81,8 @@ \section{Contributors} \label{subsec:developers} This software is developed by following contributors. \begin{itemize} +\item{ver.1.0.3 (released at 2018/7/23)} +\item{ver.1.0.2 (released at 2017/8/25)} \item{ver.1.0.1 (released at 2017/6/8)} \item{ver.1.0.0 (released at 2017/5/23)} \item{ver.0.2.0 (released at 2017/3/16)} diff --git a/doc/en/conf.py b/doc/en/conf.py index dfbd39a9..70991bf8 100644 --- a/doc/en/conf.py +++ b/doc/en/conf.py @@ -59,7 +59,7 @@ # The short X.Y version. version = '1.0' # The full version, including alpha/beta/rc tags. -release = '1.0.2' +release = '1.0.3' # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. diff --git a/doc/en/intro.rst b/doc/en/intro.rst index 16d8a083..ec2e0006 100644 --- a/doc/en/intro.rst +++ b/doc/en/intro.rst @@ -98,6 +98,10 @@ Contributors This software is developed by following contributors. +- ver.1.0.3 (released at 2018/7/23) + +- ver.1.0.2 (released at 2017/8/25) + - ver.1.0.1 (released at 2017/6/8) - ver.1.0.0 (released at 2017/5/23) diff --git a/doc/en/userguide_en.tex b/doc/en/userguide_en.tex index 00a9ffb6..bcfb0a0b 100644 --- a/doc/en/userguide_en.tex +++ b/doc/en/userguide_en.tex @@ -98,7 +98,7 @@ % \mytitlepage{% Manual for mVMC \\ -ver. 1.0.2% +ver. 1.0.3% } { \includegraphics[width=6cm]{../figs/mVMC_logo1.pdf} diff --git a/doc/jp/chap01_jp.tex b/doc/jp/chap01_jp.tex index 78d50278..4f7d39e4 100644 --- a/doc/jp/chap01_jp.tex +++ b/doc/jp/chap01_jp.tex @@ -78,6 +78,8 @@ \subsection{開発貢献者} \label{subsec:developers} 本ソフトウェアは以下の開発貢献者により開発されています。 \begin{itemize} +\item{ver.1.0.3 (2018/7/23リリース)} +\item{ver.1.0.2 (2017/8/25リリース)} \item{ver.1.0.1 (2017/6/8リリース)} \item{ver.1.0.0 (2017/5/23リリース)} \item{ver.0.2.0 (2017/3/16リリース)} diff --git a/doc/jp/conf.py b/doc/jp/conf.py index e984163c..c646f390 100644 --- a/doc/jp/conf.py +++ b/doc/jp/conf.py @@ -56,7 +56,7 @@ # The short X.Y version. version = '1.0' # The full version, including alpha/beta/rc tags. -release = '1.0.2' +release = '1.0.3' # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. diff --git a/doc/jp/intro.rst b/doc/jp/intro.rst index 9fa14364..e6b9b586 100644 --- a/doc/jp/intro.rst +++ b/doc/jp/intro.rst @@ -92,6 +92,10 @@ Public License version 3（GPL v3）に準じて配布されています。 本ソフトウェアは以下の開発貢献者により開発されています。 +- ver.1.0.3 (2018/7/23リリース) + +- ver.1.0.2 (2017/8/25リリース) + - ver.1.0.1 (2017/6/8リリース) - ver.1.0.0 (2017/5/23リリース) diff --git a/doc/jp/userguide_jp.tex b/doc/jp/userguide_jp.tex index 35d89d93..65ba678d 100644 --- a/doc/jp/userguide_jp.tex +++ b/doc/jp/userguide_jp.tex @@ -99,7 +99,7 @@ \vspace{-3cm} \mytitlepage{% 汎用多変数変分モンテカルロ mVMC \\ -マニュアル ver. 1.0.2% +マニュアル ver. 1.0.3% } { \includegraphics[width=6cm]{../figs/mVMC_logo1.pdf} diff --git a/src/mVMC/include/version.h b/src/mVMC/include/version.h index 6208339f..960a71dd 100644 --- a/src/mVMC/include/version.h +++ b/src/mVMC/include/version.h @@ -29,7 +29,7 @@ along with this program. If not, see http://www.gnu.org/licenses/. /* ..- */ #define VERSION_MAJOR 1 #define VERSION_MINOR 0 -#define VERSION_PATCH 2 +#define VERSION_PATCH 3 #define VERSION_PRERELEASE "" /* "alpha", "beta.1", etc. */