add fermionoperators

fix fermionic creation and annihilation operators (c+, c, n) #7

src/MPSKitModels.jl

@@ -25,6 +25,9 @@ export sigma_xx, sigma_yy, sigma_zz, sigma_plusmin, sigma_minplus, sigma_exchang
 export σˣ, σʸ, σᶻ, σ⁺, σ⁻, σˣˣ, σʸʸ, σᶻᶻ, σ⁺⁻, σ⁻⁺, σσ
 include("operators/spinoperators.jl")
 
+export cc, ccdag, cdagc, cdagcdag, number
+include("operators/fermionoperators.jl")
+
 export @mpoham
 include("mpoham.jl")
 

src/operators/fermionoperators.jl

@@ -0,0 +1,34 @@
+function cc(elt::Type{<:Number}=ComplexF64)
+ pspace = Vect[FermionParity](0=>1, 1=>1)
+ cc = TensorMap(zeros, elt, pspace^2 ← pspace^2)
+ blocks(cc)[fℤ₂(0)][1, 2] = -one(elt)
+ return cc
+end
+
+function ccdag(elt::Type{<:Number}=ComplexF64)
+ pspace = Vect[FermionParity](0 => 1, 1 => 1)
+ ccdag = TensorMap(zeros, elt, pspace^2 ← pspace^2)
+ blocks(ccdag)[fℤ₂(1)][2, 1] = -one(elt)
+ return ccdag
+end
+
+function cdagc(elt::Type{<:Number}=ComplexF64)
+ pspace = Vect[FermionParity](0 => 1, 1 => 1)
+ cdagc = TensorMap(zeros, elt, pspace^2 ← pspace^2)
+ blocks(cdagc)[fℤ₂(1)][1, 2] = one(elt)
+ return cdagc
+end
+
+function cdagcdag(elt::Type{<:Number}=ComplexF64)
+ pspace = Vect[FermionParity](0 => 1, 1 => 1)
+ cdagcdag = TensorMap(zeros, elt, pspace^2 ← pspace^2)
+ blocks(cdagcdag)[fℤ₂(0)][2, 1] = one(elt)
+ return cdagcdag
+end
+
+function number(elt::Type{<:Number}=ComplexF64)
+ pspace = Vect[FermionParity](0 => 1, 1 => 1)
+ n = TensorMap(zeros, elt, pspace, pspace)
+ blocks(n)[fℤ₂(1)] .= one(elt)
+ return n
+end

test/fermionoperators.jl

@@ -0,0 +1,21 @@
+using MPSKitModels
+using TensorKit
+using TensorOperations
+using Test
+using LinearAlgebra: tr
+
+# anticommutation relations
+# {cᵢ†, cⱼ†} = 0 = {cᵢ, cⱼ}
+
+@test cc() ≈ -permute(cc(), (2, 1), (4, 3))
+@test cdagcdag() ≈ -permute(cdagcdag(), (2, 1), (4, 3))
+@test ccdag() ≈ -permute(cdagc(), (2, 1), (4, 3))
+
+@tensor begin
+ term1[a; b] := ccdag()[a, i; i, b]
+ term2[a; b] := cdagc()[a, i; i, b]
+end
+
+@test term1 + term2 ≈ id(domain(term))
+
+@test term2 ≈ number()

test/runtests.jl

@@ -4,6 +4,8 @@ using Test
  include("spinoperators.jl")
 end
 
+@testset "fermion operators" include("fermionoperators.jl")
+
 @testset "transverse field ising model" begin
  include("tfim.jl")
 end