diff --git a/docs/Manifest.toml b/docs/Manifest.toml
index 2c48725f..4e8209b1 100644
--- a/docs/Manifest.toml
+++ b/docs/Manifest.toml
@@ -756,9 +756,9 @@ uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
 [[deps.SortingAlgorithms]]
 deps = ["DataStructures"]
-git-tree-sha1 = "c60ec5c62180f27efea3ba2908480f8055e17cee"
+git-tree-sha1 = "5165dfb9fd131cf0c6957a3a7605dede376e7b63"
 uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
-version = "1.1.1"
+version = "1.2.0"
 
 [[deps.SparseArrays]]
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
@@ -831,9 +831,9 @@ deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [[deps.TranscodingStreams]]
-git-tree-sha1 = "7c9196c8c83802d7b8ca7a6551a0236edd3bf731"
+git-tree-sha1 = "49cbf7c74fafaed4c529d47d48c8f7da6a19eb75"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
-version = "0.10.0"
+version = "0.10.1"
 weakdeps = ["Random", "Test"]
 
     [deps.TranscodingStreams.extensions]
diff --git a/docs/make.jl b/docs/make.jl
index c9039331..bf63883f 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -4,10 +4,11 @@ using QuantumLattices
 
 makedocs(
     format=     Documenter.HTML(
-                    prettyurls= get(ENV, "CI", "false") == "true",
-                    canonical=  "https://quantum-many-body.github.io/QuantumLattices.jl/latest/",
-                    assets=     ["assets/favicon.ico"],
-                    analytics=  "UA-89508993-1",
+                    prettyurls = get(ENV, "CI", "false") == "true",
+                    canonical = "https://quantum-many-body.github.io/QuantumLattices.jl/latest/",
+                    assets = ["assets/favicon.ico"],
+                    analytics = "UA-89508993-1",
+                    size_threshold_warn = 204800,
                 ),
     sitename=   "QuantumLattices.jl",
     pages=      [
diff --git a/docs/src/unitcell description framework/InternalDegreesOfFreedom.md b/docs/src/unitcell description framework/InternalDegreesOfFreedom.md
index f22d3405..e6e06723 100644
--- a/docs/src/unitcell description framework/InternalDegreesOfFreedom.md	
+++ b/docs/src/unitcell description framework/InternalDegreesOfFreedom.md	
@@ -521,11 +521,9 @@ Operators with 2 Operator
 julia> another = Operator(2, FID{:f}(1, 1//2, 1)) + Operator(3, FID{:f}(1, 1//2, 2));
 
 julia> ops * another 
-Operators with 4 Operator
+Operators with 2 Operator
   Operator(6, FID{:f}(1, 1//2, 1), FID{:f}(1, 1//2, 2))
   Operator(6, FID{:f}(1, 1//2, 2), FID{:f}(1, 1//2, 1))
-  Operator(9, FID{:f}(1, 1//2, 2), FID{:f}(1, 1//2, 2))
-  Operator(4, FID{:f}(1, 1//2, 1), FID{:f}(1, 1//2, 1))
 
 julia> 2 * ops
 Operators with 2 Operator
@@ -537,7 +535,7 @@ Operators with 2 Operator
   Operator(6, FID{:f}(1, 1//2, 2))
   Operator(4, FID{:f}(1, 1//2, 1))
 ```
-It is noted that in the result, the distributive law automatically applies.
+It is noted that in the result, the distributive law automatically applies. Besides, the fermion operator relation $c^2=c\dagger^2=0$ is also used.
 
 As is usual, the Hermitian conjugate of an [`Operators`](@ref) can be obtained by the adjoint operator:
 ```jldoctest
diff --git a/src/QuantumSystems.jl b/src/QuantumSystems.jl
index 04b4a915..cef51a66 100644
--- a/src/QuantumSystems.jl
+++ b/src/QuantumSystems.jl
@@ -218,8 +218,9 @@ end
 Get the multiplication of two fermionic Fock operators.
 """
 const block = quote
-    rank(f₁)>0 && rank(f₂)>0 && f₁[end]==f₂[1] && return 0
-    return invoke(*, Tuple{OperatorProd, OperatorProd}, f₁, f₂)
+    result = invoke(*, Tuple{OperatorProd, OperatorProd}, f₁, f₂)
+    rank(f₁)>0 && rank(f₂)>0 && f₁[end]==f₂[1] && return replace(result, value=zero(valtype(result)))
+    return result
 end
 @eval @inline Base.:*(f₁::Operator{<:Number, <:ID{FID{:f}}}, f₂::Operator{<:Number, <:ID{FID{:f}}}) = $block
 @eval @inline Base.:*(f₁::Operator{<:Number, <:ID{Index{Int, <:FID{:f}}}}, f₂::Operator{<:Number, <:ID{Index{Int, <:FID{:f}}}}) = $block
diff --git a/test/Manifest.toml b/test/Manifest.toml
index c3c0522e..bcc9071a 100644
--- a/test/Manifest.toml
+++ b/test/Manifest.toml
@@ -656,9 +656,9 @@ uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
 [[deps.SortingAlgorithms]]
 deps = ["DataStructures"]
-git-tree-sha1 = "c60ec5c62180f27efea3ba2908480f8055e17cee"
+git-tree-sha1 = "5165dfb9fd131cf0c6957a3a7605dede376e7b63"
 uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
-version = "1.1.1"
+version = "1.2.0"
 
 [[deps.SparseArrays]]
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
@@ -722,9 +722,9 @@ deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [[deps.TranscodingStreams]]
-git-tree-sha1 = "7c9196c8c83802d7b8ca7a6551a0236edd3bf731"
+git-tree-sha1 = "49cbf7c74fafaed4c529d47d48c8f7da6a19eb75"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
-version = "0.10.0"
+version = "0.10.1"
 weakdeps = ["Random", "Test"]
 
     [deps.TranscodingStreams.extensions]
diff --git a/test/QuantumSystems.jl b/test/QuantumSystems.jl
index 00b16e9d..eec33847 100644
--- a/test/QuantumSystems.jl
+++ b/test/QuantumSystems.jl
@@ -103,7 +103,7 @@ end
 
     op₁ = Operator(1.5, id₁, id₂)
     op₂ = Operator(2.0, id₂, id₁)
-    @test op₁*op₂ == 0
+    @test op₁*op₂ == Operator(0.0, id₁, id₂, id₂, id₁)
 
     op₁ = Operator(1.5, id₁, id₂)
     op₂ = Operator(2.0, id₁, id₂)