[WIP] TensorKitSectors

Project.toml

@@ -10,6 +10,7 @@ FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 HalfIntegers = "f0d1745a-41c9-11e9-1dd9-e5d34d218721"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SplitApplyCombine = "03a91e81-4c3e-53e1-a0a4-9c0c8f19dd66"
+TensorKitSectors = "13a9c161-d5da-41f0-bcbd-e1a08ae0647f"
 TensorProducts = "decf83d6-1968-43f4-96dc-fdb3fe15fc6d"
 
 [compat]
@@ -19,5 +20,6 @@ FillArrays = "1.13.0"
 HalfIntegers = "1.6.0"
 Random = "1.10.0"
 SplitApplyCombine = "1.2.3"
+TensorKitSectors = "0.1.4"
 TensorProducts = "0.1.3"
 julia = "1.10"

src/lib/SymmetrySectors/SymmetrySectors.jl

@@ -1,17 +1,20 @@
 module SymmetrySectors
 
+using TensorKitSectors: TensorKitSectors
+
 export U1, Z, dual
 
 include("symmetry_style.jl")
 include("abstractsector.jl")
-include("sector_definitions/fib.jl")
-include("sector_definitions/ising.jl")
-include("sector_definitions/o2.jl")
+include("sector_definitions/tensorkitsector.jl")
+# include("sector_definitions/fib.jl")
+# include("sector_definitions/ising.jl")
+# include("sector_definitions/o2.jl")
 include("sector_definitions/trivial.jl")
 include("sector_definitions/su.jl")
 include("sector_definitions/su2k.jl")
-include("sector_definitions/u1.jl")
-include("sector_definitions/zn.jl")
+# include("sector_definitions/u1.jl")
+# include("sector_definitions/zn.jl")
 include("namedtuple_operations.jl")
 include("sector_product.jl")
 

src/lib/SymmetrySectors/sector_definitions/su.jl

@@ -96,7 +96,7 @@ function label_fusion_rule(::Type{<:SU{2}}, s1, s2)
 end
 
 # define angular momentum-like interface using half-integers
-SU2(h::Number) = SU{2}((twice(HalfInteger(h)),))
+# SU2(h::Number) = SU{2}((twice(HalfInteger(h)),))
 
 # display SU2 using half-integers
 function Base.show(io::IO, s::SU{2})

src/lib/SymmetrySectors/sector_definitions/tensorkitsector.jl

@@ -0,0 +1,98 @@
+# Generic wrapper
+# ---------------
+struct TensorKitSector{I<:TensorKitSectors.Sector} <: AbstractSector
+  sector::I
+end
+
+function SymmetryStyle(::Type{TensorKitSector{I}}) where {I}
+  if TensorKitSectors.FusionStyle(I) == TensorKitSectors.UniqueFusion()
+    return AbelianStyle()
+  else
+    return NotAbelianStyle()
+  end
+end
+
+trivial(::Type{TensorKitSector{I}}) where {I} = TensorKitSector(one(I))
+GradedUnitRanges.dual(s::TensorKitSector) = TensorKitSector(TensorKitSectors.dual(s.sector))
+
+quantum_dimension(x::TensorKitSector) = TensorKitSectors.dim(x.sector)
+
+function nsymbol(s1::I, s2::I, s3::I) where {I<:TensorKitSector}
+  return TensorKitSectors.Nsymbol(s1.sector, s2.sector, s3.sector)
+end
+
+function fusion_rule(::AbelianStyle, c1::I, c2::I) where {I<:TensorKitSector}
+  return TensorKitSector(only(TensorKitSectors.otimes(c1.sector, c2.sector)))
+end
+function fusion_rule(::NotAbelianStyle, c1::I, c2::I) where {I<:TensorKitSector}
+  return gradedrange([
+    TensorKitSector(c) => nsymbol(c1, c2, TensorKitSector(c)) for
+    c in TensorKitSectors.otimes(c1.sector, c2.sector)
+  ])
+end
+
+Base.:(==)(s1::TensorKitSector, s2::TensorKitSector) = s1.sector == s2.sector
+Base.isless(s1::TensorKitSector, s2::TensorKitSector) = isless(s1.sector, s2.sector)
+
+# Specific implementations
+# ------------------------
+const U1 = TensorKitSector{TensorKitSectors.U1Irrep}
+sector_label(s::U1) = s.sector.charge
+Base.isless(s1::U1, s2::U1) = s1.sector.charge < s2.sector.charge
+
+const Z{N} = TensorKitSector{TensorKitSectors.ZNIrrep{N}}
+sector_label(s::Z) = s.sector.n
+
+const O2 = TensorKitSector{TensorKitSectors.CU1Irrep}
+sector_label(s::O2) = s.sector.s == 1 ? Half(-1) : Half(s.sector.j)
+function O2(s::Int)
+  return s == -1 ? O2(TensorKitSectors.CU1Irrep(0, 1)) : O2(TensorKitSectors.CU1Irrep(s))
+end
+
+const SU2 = TensorKitSector{TensorKitSectors.SU2Irrep}
+sector_label(s::SU2) = s.sector.j
+
+const Fib = TensorKitSector{TensorKitSectors.FibonacciAnyon}
+Fib(s::AbstractString) = Fib(
+  if s == "1"
+    :I
+  elseif s == "τ"
+    :τ
+  else
+    error()
+  end,
+)
+
+const Ising = TensorKitSector{TensorKitSectors.IsingAnyon}
+function sector_label(s::Ising)
+  label = s.sector.s
+  return if label === :I
+    Half(0)
+  elseif label === :σ
+    Half(1//2)
+  else
+    Half(1)
+  end
+end
+Ising(s::AbstractString) = Ising(
+  if s == "1"
+    :I
+  elseif s == "σ"
+    :σ
+  elseif s == "ψ"
+    :ψ
+  else
+    error()
+  end,
+)
+Ising(s::Number) = Ising(
+  if s == 0
+    :I
+  elseif s == 1//2
+    :σ
+  elseif s == 1
+    :ψ
+  else
+    error()
+  end,
+)

test/test_symmetrysectors_fusion_rules.jl

@@ -74,7 +74,8 @@ using TestExtras: @constinferred
     @test space_isequal((@constinferred s12 ⊗ s0o), gradedrange([s12 => 1]))
     @test space_isequal((@constinferred s12 ⊗ s1), gradedrange([s12 => 1, O2(3//2) => 1]))
     @test space_isequal(
-      (@constinferred s12 ⊗ s12), gradedrange([s0o => 1, s0e => 1, s1 => 1])
+      (@constinferred s12 ⊗ s12),
+      gradedrange([s0e => 1, s0o => 1, s1 => 1]),
     )
 
     @test (@constinferred quantum_dimension(s0o ⊗ s1)) == 2