pairing operator for U1SpinlessFermion

Author: qyli

src/LocalSpace/SpinlessFermion.jl

@@ -18,6 +18,9 @@ Two rank-`3` operators of hopping `c^dag c`.
 
      FFdag::NTuple{2, TensorMap}
 Two rank-`3` operators of hopping `c c^dag`.
+
+     ΔdagΔ::NTuple{4, TensorMap}
+Four operators of pairing `Δ^dag Δ`, where `Δᵢⱼ = cᵢcⱼ` is the pairing operator.  Rank = `(3, 4, 4, 3)`. Sign convention: `(i,j,k,l)` gives `cᵢ^dag cⱼ^dag cₖ cₗ = - cⱼ^dag cᵢ^dag cₖ cₗ = - Δᵢⱼ^dag Δₖₗ`.
 """
 module U₁SpinlessFermion
 using TensorKit
@@ -55,6 +58,17 @@ const FFdag = let
      F, Fdag
 end
 
+const ΔdagΔ = let
+     A = FdagF[1]
+     aspace = Rep[U₁](1 => 1)
+     aspace2 = Rep[U₁](2 => 1)
+     iso = isometry(aspace ⊗ aspace, aspace2)
+     @tensor B[d a; b e] := A[a b c] * iso[c d e]
+     C = permute(B', ((2, 1), (4, 3)))
+     D = permute(A', ((2, 1), (3,)))
+     A, B, C, D
+end
+
 end
 
 """

test/mulsiteIntr.jl

@@ -18,7 +18,7 @@ for i in 1:L, j in 1:L
 	if i == j
 		addIntr!(Tree, U1SpinlessFermion.n, i, -Tij[i, i]; name = :n)
 	else
-		addIntr!(Tree, U1SpinlessFermion.FdagF, (i, j), (true, true), 
+		addIntr!(Tree, U1SpinlessFermion.FdagF, (i, j), (true, true),
 			-Tij[i, j]; name = (:Fdag, :F), Z = U1SpinlessFermion.Z)
 	end
 end
@@ -42,6 +42,7 @@ for i in 1:L, j in 1:L, k in 1:L, l in 1:L
 	!duplicated && !allunique([i, j, k, l]) && continue
 	addObs!(Tree, (U1SpinlessFermion.FdagF..., U1SpinlessFermion.FdagF...), (i, j, k, l), (true, true, true, true); Z = U1SpinlessFermion.Z, name = (:Fdag, :F, :Fdag, :F))
 	addObs!(Tree, Tuple(fill(U1SpinlessFermion.n, 4)), (i, j, k, l), (false, false, false, false); name = (:n, :n, :n, :n))
+	addObs!(Tree, U1SpinlessFermion.ΔdagΔ, (i, j, k, l), (true, true, true, true); Z = U1SpinlessFermion.Z, name = (:Fdag, :Fdag, :F, :F))
 end
 # 3-site 
 for i in 1:L, j in 1:L, k in 1:L
@@ -124,7 +125,11 @@ end
 		!duplicated && !allunique([i, j, k, l]) && continue
 		O_ex = ExpectationValue(G, [i, j, k, l], [1, 3])
 		@test haskey(Obs.FdagFFdagF, (i, j, k, l)) && abs(Obs.FdagFFdagF[(i, j, k, l)] - O_ex) < tol
+
+		O_ex = ExpectationValue(G, [i, j, k, l], [1, 2])
+		@test haskey(Obs.FdagFdagFF, (i, j, k, l)) && abs(Obs.FdagFdagFF[(i, j, k, l)] - O_ex) < tol
 	end
+
 end