refactor label_fusion_rule

Author: ogauthe

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

@@ -54,13 +54,14 @@ function fusion_rule(c1::AbstractCategory, c2::AbstractCategory)
 end
 
 function fusion_rule(::NotAbelianStyle, c1::C, c2::C) where {C<:AbstractCategory}
-  degen, labels = label_fusion_rule(C, category_label(c1), category_label(c2))
-  return gradedrange(labelled.(degen, C.(labels)))
+  degen, sectors = label_fusion_rule(C, category_label(c1), category_label(c2))
+  return gradedrange(labelled.(degen, sectors))
 end
 
 # abelian case: return Category
 function fusion_rule(::AbelianStyle, c1::C, c2::C) where {C<:AbstractCategory}
-  return C(label_fusion_rule(C, category_label(c1), category_label(c2)))
+  _, sectors = label_fusion_rule(C, category_label(c1), category_label(c2))
+  return only(sectors)
 end
 
 function label_fusion_rule(category_type::Type{<:AbstractCategory}, ::Any, ::Any)

NDTensors/src/lib/Sectors/src/category_definitions/fib.jl

@@ -30,7 +30,11 @@ trivial(::Type{Fib}) = Fib(0)
 quantum_dimension(::NotAbelianStyle, f::Fib) = istrivial(f) ? 1.0 : ((1 + √5) / 2)
 
 # Fusion rules identical to su2₃
-label_fusion_rule(::Type{Fib}, l1, l2) = label_fusion_rule(su2{3}, l1, l2)
+function label_fusion_rule(::Type{Fib}, l1, l2)
+  degen, suk_sectors = label_fusion_rule(su2{3}, l1, l2)
+  sectors = Fib.(category_label.(suk_sectors))
+  return degen, sectors
+end
 
 label_to_str(f::Fib) = istrivial(f) ? "1" : "τ"
 

NDTensors/src/lib/Sectors/src/category_definitions/ising.jl

@@ -30,7 +30,11 @@ trivial(::Type{Ising}) = Ising(0)
 quantum_dimension(::NotAbelianStyle, i::Ising) = (category_label(i) == 1//2) ? √2 : 1.0
 
 # Fusion rules identical to su2₂
-label_fusion_rule(::Type{Ising}, l1, l2) = label_fusion_rule(su2{2}, l1, l2)
+function label_fusion_rule(::Type{Ising}, l1, l2)
+  degen, suk_sectors = label_fusion_rule(su2{2}, l1, l2)
+  sectors = Ising.(category_label.(suk_sectors))
+  return degen, sectors
+end
 
 # TODO: Use `Val` dispatch here?
 label_to_str(i::Ising) = ("1", "σ", "ψ")[twice(category_label(i)) + 1]

NDTensors/src/lib/Sectors/src/category_definitions/o2.jl

@@ -71,5 +71,5 @@ function label_fusion_rule(::Type{O2}, l1, l2)
       end
     end
   end
-  return degens, labels
+  return degens, O2.(labels)
 end

NDTensors/src/lib/Sectors/src/category_definitions/su.jl

@@ -92,9 +92,9 @@ quantum_dimension(s::SU{2}) = category_label(s)[1] + 1
 GradedAxes.dual(s::SU{2}) = s
 
 function label_fusion_rule(::Type{<:SU{2}}, s1, s2)
-  labels = collect((i,) for i in (abs(s1[1] - s2[1])):2:(s1[1] + s2[1]))
-  degen = ones(Int, length(labels))
-  return degen, labels
+  irreps = collect(SU{2}((i,)) for i in (abs(s1[1] - s2[1])):2:(s1[1] + s2[1]))
+  degen = ones(Int, length(irreps))
+  return degen, irreps
 end
 
 # define angular momentum-like interface using half-integers
@@ -123,7 +123,7 @@ function label_fusion_rule(::Type{<:SU{3}}, left, right)
   end
 
   if right[1] == 0  # avoid issues with singlet
-    return [1], [left]
+    return [1], [SU{3}(left)]
   end
 
   left_row1 = left[1]
@@ -172,6 +172,6 @@ function label_fusion_rule(::Type{<:SU{3}}, left, right)
 
   unique_labels = sort(unique(irreps))
   degen = [count(==(irr), irreps) for irr in unique_labels]
-
-  return degen, unique_labels
+  sectors = SU{3}.(unique_labels)
+  return degen, sectors
 end

NDTensors/src/lib/Sectors/src/category_definitions/su2k.jl

@@ -22,5 +22,6 @@ trivial(::Type{su2{k}}) where {k} = su2{k}(0)
 function label_fusion_rule(::Type{su2{k}}, j1, j2) where {k}
   labels = collect(abs(j1 - j2):min(k - j1 - j2, j1 + j2))
   degen = ones(Int, length(labels))
-  return degen, labels
+  sectors = su2{k}.(labels)
+  return degen, sectors
 end

NDTensors/src/lib/Sectors/src/category_definitions/u1.jl

@@ -19,7 +19,7 @@ category_label(u::U1) = u.n
 trivial(::Type{U1}) = trivial(U1{Int})
 trivial(::Type{U1{T}}) where {T} = U1(T(0))
 
-label_fusion_rule(::Type{<:U1}, n1, n2) = n1 + n2
+label_fusion_rule(T::Type{<:U1}, n1, n2) = [1], [T(n1 + n2)]
 
 # hide label type in printing
 function Base.show(io::IO, u::U1)

NDTensors/src/lib/Sectors/src/category_definitions/zn.jl

@@ -19,7 +19,8 @@ modulus(c::Z) = modulus(typeof(c))
 trivial(category_type::Type{<:Z}) = category_type(0)
 
 function label_fusion_rule(category_type::Type{<:Z}, n1, n2)
-  return (n1 + n2) % modulus(category_type)
+  irrep = category_type((n1 + n2) % modulus(category_type))
+  return [1], [irrep]
 end
 
 GradedAxes.dual(c::Z) = typeof(c)(mod(-category_label(c), modulus(c)))