Sector Types
This page provides an overview of the concrete sector types implemented in TensorKitSectors.jl.
Summary Table
| Sector Type | Group/Category | Fusion Style | Braiding | Infinite? | Common Use Cases |
|---|---|---|---|---|---|
Trivial | Trivial group | Unique | Bosonic | No | No symmetry |
ZNIrrep | ℤₙ (cyclic) | Unique | Bosonic | No | Clock models, discrete symmetries |
U1Irrep | U(1) | Unique | Bosonic | Yes | Particle number, charge conservation |
SU2Irrep | SU(2) | Simple | Bosonic | Yes | Spin systems, angular momentum |
CU1Irrep | U(1) ⋊ ℤ₂ | Simple | Bosonic | Yes | Particle-hole symmetry, O(2) |
DNIrrep | Dₙ (dihedral) | Simple | Bosonic | No | Molecular/crystal symmetries |
A4Irrep | A₄ (alternating) | Generic | Bosonic | No | Tetrahedral symmetry |
FibonacciAnyon | Fibonacci category | Simple | Anyonic | No | Topological quantum computing |
IsingAnyon | Ising category | Simple | Anyonic | No | Majorana fermions, ν=5/2 QHE |
FermionParity | fℤ₂ | Unique | Fermionic | No | Fermion parity conservation |
FermionNumber | fU₁ | Unique | Fermionic | Yes | Fermion number conservation |
FermionSpin | fSU₂ | Simple | Fermionic | Yes | Fermions with spin symmetry |
ProductSector | Product categories | Varies | Varies | Varies | Multiple simultaneous symmetries |
TimeReversed | Inverted braiding | Varies | Varies | Varies | ?? |