Sector Types

This page provides an overview of the concrete sector types implemented in TensorKitSectors.jl.

Summary Table

Sector TypeGroup/CategoryFusion StyleBraidingInfinite?Common Use Cases
TrivialTrivial groupUniqueBosonicNoNo symmetry
ZNIrrepℤₙ (cyclic)UniqueBosonicNoClock models, discrete symmetries
U1IrrepU(1)UniqueBosonicYesParticle number, charge conservation
SU2IrrepSU(2)SimpleBosonicYesSpin systems, angular momentum
CU1IrrepU(1) ⋊ ℤ₂SimpleBosonicYesParticle-hole symmetry, O(2)
DNIrrepDₙ (dihedral)SimpleBosonicNoMolecular/crystal symmetries
A4IrrepA₄ (alternating)GenericBosonicNoTetrahedral symmetry
FibonacciAnyonFibonacci categorySimpleAnyonicNoTopological quantum computing
IsingAnyonIsing categorySimpleAnyonicNoMajorana fermions, ν=5/2 QHE
FermionParityfℤ₂UniqueFermionicNoFermion parity conservation
FermionNumberfU₁UniqueFermionicYesFermion number conservation
FermionSpinfSU₂SimpleFermionicYesFermions with spin symmetry
ProductSectorProduct categoriesVariesVariesVariesMultiple simultaneous symmetries
TimeReversedInverted braidingVariesVariesVaries??