fix implementation and support fermions

Author: Jutho

src/fusiontrees/manipulations.jl

@@ -242,6 +242,26 @@ end
 # -> B-move (bendleft, bendright) is simple in standard basis
 # -> A-move (foldleft, foldright) is complicated, needs to be reexpressed in standard form
 
+# flip a duality flag of a fusion tree
+function flip(f₁::FusionTree{I,N₁}, f₂::FusionTree{I,N₂}, i::Int) where {I<:Sector,N₁,N₂}
+    @assert 0 < i ≤ N₁ + N₂
+    if i ≤ N₁
+        a = f₁.uncoupled[i]
+        fs = frobeniusschur(a) * twist(a)
+        factor = f₁.isdual[i] ? fs : one(fs)
+        isdual′ = TupleTools.setindex(f₁.isdual, !f₁.isdual[i], i)
+        f₁′ = FusionTree{I}(f₁.uncoupled, f₁.coupled, isdual′, f₁.innerlines, f₁.vertices)
+        return SingletonDict((f₁′, f₂) => factor)
+    else
+        i -= N₁
+        a = f₂.uncoupled[i]
+        factor = f₂.isdual[i] ? frobeniusschur(a) : twist(a)
+        isdual′ = TupleTools.setindex(f₂.isdual, !f₂.isdual[i], i)
+        f₂′ = FusionTree{I}(f₂.uncoupled, f₂.coupled, isdual′, f₂.innerlines, f₂.vertices)
+        return SingletonDict((f₁, f₂′) => factor)
+    end
+end
+
 # change to N₁ - 1, N₂ + 1
 function bendright(f₁::FusionTree{I,N₁}, f₂::FusionTree{I,N₂}) where {I<:Sector,N₁,N₂}
     # map final splitting vertex (a, b)<-c to fusion vertex a<-(c, dual(b))

src/tensors/indexmanipulations.jl

@@ -8,13 +8,18 @@ Return a new tensor that is isomorphic to `t` but where the arrows on the indice
 """
 function flip(t::AbstractTensorMap, I)
     P = flip(space(t), I)
-    t2 = similar(t, P)
-    for (c, b) in blocks(t)
-        copy!(t2[c], b)
+    t′ = similar(t, P)
+    for (f₁, f₂) in fusiontrees(t)
+        f₁′, f₂′ = f₁, f₂
+        factor = one(scalartype(t))
+        for i in I
+            (f₁′, f₂′), s = only(flip(f₁′, f₂′, i))
+            factor *= s
+        end
+        scale!(t′[f₁′, f₂′], t[f₁, f₂], factor)
     end
-    return t
+    return t′
 end
-flip(t::TensorMap, I) = TensorMap(t.data, flip(space(t), I))
 
 """
     permute!(tdst::AbstractTensorMap, tsrc::AbstractTensorMap, (p₁, p₂)::Index2Tuple)

test/tensors.jl

@@ -326,22 +326,33 @@ for V in spacelist
                 @test HrA12array ≈ convert(Array, HrA12)
             end
         end
-        if BraidingStyle(I) isa Bosonic # TODO: add fermionic tests by including parity tensors
-            @timedtestset "Index flipping: test via contraction" begin
-                t1 = rand(ComplexF64, V1 ⊗ V2 ⊗ V3 ← V4)
-                t2 = rand(ComplexF64, V2' ⊗ V5 ← V4' ⊗ V1)
-                @tensor ta[a, b] := t1[x, y, a, z] * t2[y, b, z, x]
-                @tensor tb[a, b] := flip(t1, 1)[x, y, a, z] * flip(t2, 4)[y, b, z, x]
-                @test ta ≈ tb
-                @tensor tb[a, b] := flip(t1, (2, 4))[x, y, a, z] *
-                                    flip(t2, (1, 3))[y, b, z, x]
-                @test ta ≈ tb
-                @tensor tb[a, b] := flip(t1, (1, 2, 4))[x, y, a, z] *
-                                    flip(t2, (1, 3, 4))[y, b, z, x]
-                @tensor tb[a, b] := flip(t1, (1, 3))[x, y, a, z] *
-                                    flip(t2, (2, 4))[y, b, z, x]
-                @test flip(ta, (1, 2)) ≈ tb
-            end
+        @timedtestset "Index flipping: test via explicit flip" begin
+            t = rand(ComplexF64, V1 ⊗ V1' ← V1' ⊗ V1)
+            F1 = unitary(flip(V1), V1)
+
+            @tensor tf[a, b; c, d] := F1[a, a'] * t[a', b; c, d]
+            @test flip(t, 1) ≈ tf
+            @tensor tf[a, b; c, d] := conj(F1[b, b']) * t[a, b'; c, d]
+            @test twist!(flip(t, 2), 2) ≈ tf
+            @tensor tf[a, b; c, d] := F1[c, c'] * t[a, b; c', d]
+            @test flip(t, 3) ≈ tf
+            @tensor tf[a, b; c, d] := conj(F1[d, d']) * t[a, b; c, d']
+            @test twist!(flip(t, 4), 4) ≈ tf
+        end
+        @timedtestset "Index flipping: test via contraction" begin
+            t1 = rand(ComplexF64, V1 ⊗ V2 ⊗ V3 ← V4)
+            t2 = rand(ComplexF64, V2' ⊗ V5 ← V4' ⊗ V1)
+            @tensor ta[a, b] := t1[x, y, a, z] * t2[y, b, z, x]
+            @tensor tb[a, b] := flip(t1, 1)[x, y, a, z] * flip(t2, 4)[y, b, z, x]
+            @test ta ≈ tb
+            @tensor tb[a, b] := flip(t1, (2, 4))[x, y, a, z] *
+                                flip(t2, (1, 3))[y, b, z, x]
+            @test ta ≈ tb
+            @tensor tb[a, b] := flip(t1, (1, 2, 4))[x, y, a, z] *
+                                flip(t2, (1, 3, 4))[y, b, z, x]
+            @tensor tb[a, b] := flip(t1, (1, 3))[x, y, a, z] *
+                                flip(t2, (2, 4))[y, b, z, x]
+            @test flip(ta, (1, 2)) ≈ tb
         end
         @timedtestset "Multiplication of isometries: test properties" begin
             W2 = V4 ⊗ V5