[SymmetrySectors] Non-abelian fusion

NDTensors/src/lib/Sectors/src/abstractcategory.jl

@@ -93,25 +93,3 @@ function GradedAxes.tensor_product(
 end
 
 GradedAxes.fuse_labels(c1::AbstractCategory, c2::AbstractCategory) = c1 ⊗ c2
-
-# ===============  sum rules ====================
-⊕(c1::C, c2::C) where {C<:AbstractCategory} = GradedAxes.gradedrange([c1 => 1, c2 => 1])
-
-function ⊕(
-  c::C, g::GradedAxes.GradedUnitRange{Vector{LabelledNumbers.LabelledInteger{V,C}}}
-) where {V<:Integer,C<:AbstractCategory}
-  return GradedAxes.gradedrange([c => 1]) ⊕ g
-end
-
-function ⊕(
-  g::GradedAxes.GradedUnitRange{Vector{LabelledNumbers.LabelledInteger{V,C}}}, c::C
-) where {V<:Integer,C<:AbstractCategory}
-  return g ⊕ GradedAxes.gradedrange([c => 1])
-end
-
-function ⊕(
-  g1::GradedAxes.GradedUnitRange{Vector{LabelledNumbers.LabelledInteger{V,C}}},
-  g2::GradedAxes.GradedUnitRange{Vector{LabelledNumbers.LabelledInteger{V,C}}},
-) where {V<:Integer,C<:AbstractCategory}
-  return GradedAxes.axis_cat(g1, g2)
-end

NDTensors/src/lib/Sectors/test/test_category_product.jl

@@ -1,6 +1,6 @@
 @eval module $(gensym())
 using NDTensors.Sectors:
-  ×, ⊕, ⊗, Fib, Ising, SU, SU2, U1, Z, categories, sector, quantum_dimension
+  ×, ⊗, Fib, Ising, SU, SU2, U1, Z, categories, sector, quantum_dimension
 using NDTensors.GradedAxes: dual, gradedrange
 using Test: @test, @testset, @test_throws
 @testset "Test Named Category Products" begin
@@ -60,10 +60,10 @@ using Test: @test, @testset, @test_throws
     q21 = (N=U1(2),) × (J=SU2(1),)
     q22 = (N=U1(2),) × (J=SU2(2),)
 
-    @test q1h ⊗ q1h == q20 ⊕ q21
+    @test q1h ⊗ q1h == gradedrange([q20 => 1, q21 => 1])
     @test q10 ⊗ q1h == gradedrange([q2h => 1])
-    @test q0h ⊗ q1h == q10 ⊕ q11
-    @test q11 ⊗ q11 == q20 ⊕ q21 ⊕ q22
+    @test q0h ⊗ q1h == gradedrange([q10 => 1, q11 => 1])
+    @test q11 ⊗ q11 == gradedrange([q20 => 1, q21 => 1, q22 => 1])
   end
 
   @testset "U(1) × SU(2)" begin
@@ -78,10 +78,10 @@ using Test: @test, @testset, @test_throws
     q21 = (N=U1(2),) × (J=SU{2}(3),)
     q22 = (N=U1(2),) × (J=SU{2}(5),)
 
-    @test q1h ⊗ q1h == q20 ⊕ q21
+    @test q1h ⊗ q1h == gradedrange([q20 => 1, q21 => 1])
     @test q10 ⊗ q1h == gradedrange([q2h => 1])
-    @test q0h ⊗ q1h == q10 ⊕ q11
-    @test q11 ⊗ q11 == q20 ⊕ q21 ⊕ q22
+    @test q0h ⊗ q1h == gradedrange([q10 => 1, q11 => 1])
+    @test q11 ⊗ q11 == gradedrange([q20 => 1, q21 => 1, q22 => 1])
   end
 
   @testset "Comparisons with unspecified labels" begin
@@ -134,17 +134,22 @@ end
 
   @testset "Fusion of SU2 products" begin
     phh = SU2(1//2) × SU2(1//2)
-    @test phh ⊗ phh ==
-      (SU2(0) × SU2(0)) ⊕ (SU2(1) × SU2(0)) ⊕ (SU2(0) × SU2(1)) ⊕ (SU2(1) × SU2(1))
+    @test phh ⊗ phh == gradedrange([
+      1 => (SU2(0) × SU2(0)),
+      1 => (SU2(1) × SU2(0)),
+      1 => (SU2(0) × SU2(1)),
+      1 => (SU2(1) × SU2(1)),
+    ])
   end
 
   @testset "Fusion of mixed U1 and SU2 products" begin
     p2h = U1(2) × SU2(1//2)
     p1h = U1(1) × SU2(1//2)
-    @test p2h ⊗ p1h == (U1(3) × SU2(0)) ⊕ (U1(3) × SU2(1))
+    @test p2h ⊗ p1h == gradedrange([(U1(3) × SU2(0)) => 1, (U1(3) × SU2(1)) => 1])
 
     p1h1 = U1(1) × SU2(1//2) × Z{2}(1)
-    @test p1h1 ⊗ p1h1 == (U1(2) × SU2(0) × Z{2}(0)) ⊕ (U1(2) × SU2(1) × Z{2}(0))
+    @test p1h1 ⊗ p1h1 ==
+      gradedrabge([(U1(2) × SU2(0) × Z{2}(0)) => 1, (U1(2) × SU2(1) × Z{2}(0)) => 1])
   end
 end
 end

NDTensors/src/lib/Sectors/test/test_fusion_rules.jl

@@ -1,27 +1,8 @@
 @eval module $(gensym())
 using NDTensors.GradedAxes: fuse_labels, gradedrange
-using NDTensors.Sectors: ⊕, ⊗, Fib, Ising, SU, SU2, U1, Z, quantum_dimension
+using NDTensors.Sectors: ⊗, Fib, Ising, SU, SU2, U1, Z, quantum_dimension
 using Test: @inferred, @test, @testset
 
-@testset "sum rules" begin
-
-  # test abelian
-  q1 = U1(1)
-  q2 = U1(2)
-  @test q1 ⊕ q2 == gradedrange([q1 => 1, q2 => 1])
-  @test q2 ⊕ q1 == gradedrange([q2 => 1, q1 => 1])  # unsorted
-  @test q1 ⊕ q1 == gradedrange([q1 => 1, q1 => 1])
-  @test (@inferred quantum_dimension(gradedrange([q1 => 1, q2 => 2]))) == 3
-
-  # test non-abelian
-  j2 = SU2(1//2)
-  j3 = SU2(1)
-  @test j2 ⊕ j3 == gradedrange([j2 => 1, j3 => 1])
-  @test j3 ⊕ j2 == gradedrange([j3 => 1, j2 => 1])  # unsorted
-  @test j2 ⊕ j2 == gradedrange([j2 => 1, j2 => 1])
-  @test (@inferred quantum_dimension(gradedrange([j2 => 2, j3 => 3]))) == 13
-end
-
 @testset "fusion rules" begin
   @testset "Z{2} fusion rules" begin
     z0 = Z{2}(0)
@@ -54,9 +35,9 @@ end
     j5 = SU2(2)
 
     @test j1 ⊗ j2 == gradedrange([j2 => 1])
-    @test j2 ⊗ j2 == j1 ⊕ j3
-    @test j2 ⊗ j3 == j2 ⊕ j4
-    @test j3 ⊗ j3 == j1 ⊕ j3 ⊕ j5
+    @test j2 ⊗ j2 == gradedrange([j1 => 1, j3 => 1])
+    @test j2 ⊗ j3 == gradedrange([j2 => 1, j4 => 1])
+    @test j3 ⊗ j3 == gradedrange([j1 => 1, j3 => 1, j5 => 1])
     @test (@inferred j1 ⊗ j2) == gradedrange([j2 => 1])
   end
 
@@ -68,9 +49,9 @@ end
     j5 = SU{2}(5)
 
     @test j1 ⊗ j2 == gradedrange([j2 => 1])
-    @test j2 ⊗ j2 == j1 ⊕ j3
-    @test j2 ⊗ j3 == j2 ⊕ j4
-    @test j3 ⊗ j3 == j1 ⊕ j3 ⊕ j5
+    @test j2 ⊗ j2 == gradedrange([j1 => 1, j3 => 1])
+    @test j2 ⊗ j3 == gradedrange([j2 => 1, j4 => 1])
+    @test j3 ⊗ j3 == gradedrange([j1 => 1, j3 => 1, j5 => 1])
     @test (@inferred j1 ⊗ j2) == gradedrange([j2 => 1])
   end
 
@@ -81,9 +62,8 @@ end
     @test ı ⊗ ı == gradedrange([ı => 1])
     @test ı ⊗ τ == gradedrange([τ => 1])
     @test τ ⊗ ı == gradedrange([τ => 1])
-    @test τ ⊗ τ == ı ⊕ τ
-    @test (@inferred τ ⊗ τ) == ı ⊕ τ
-    @test (@inferred quantum_dimension(ı ⊕ ı)) == 2.0
+    @test (@inferred τ ⊗ τ) == gradedrange([ı => 1, τ => 1])
+    @test (@inferred quantum_dimension(gradedrange([ı => 1, ı => 1]))) == 2.0
   end
 
   @testset "Ising fusion rules" begin
@@ -96,12 +76,12 @@ end
     @test σ ⊗ ı == gradedrange([σ => 1])
     @test ı ⊗ ψ == gradedrange([ψ => 1])
     @test ψ ⊗ ı == gradedrange([ψ => 1])
-    @test σ ⊗ σ == ı ⊕ ψ
+    @test σ ⊗ σ == gradedrange([ı => 1, ψ => 1])
     @test σ ⊗ ψ == gradedrange([σ => 1])
     @test ψ ⊗ σ == gradedrange([σ => 1])
     @test ψ ⊗ ψ == gradedrange([ı => 1])
     @test (@inferred ψ ⊗ ψ) == gradedrange([ı => 1])
-    @test (@inferred quantum_dimension(ı ⊕ ψ)) == 2.0
+    @test (@inferred quantum_dimension(σ ⊗ σ)) == 2.0
   end
 end
 end