Fermion Parity: FermionParity
FermionParity is the two-sector fermionic category $SVect$ for even and odd parity. Odd sectors pick up a minus sign when exchanged with another odd sector.
Sector type
TensorKitSectors.FermionParity — Type
struct FermionParity <: Sector
FermionParity(isodd::Bool)Represents sectors with fermion parity. The fermion parity is a $ℤ₂$ quantum number that yields an additional sign when two odd fermions are exchanged, corresponding to a BraidingStyle that is Fermionic().
Fields
isodd::Bool: indicates whether the fermion parity is odd (true) or even (false).
See also: FermionNumber, FermionSpin
The labels are FermionParity(false) for even parity and FermionParity(true) for odd parity. They are displayed as FermionParity(0) and FermionParity(1). The unit is even parity, and every sector is self-dual.
Fusion Rules
Fusion is addition modulo two:
\[p ⊗ q = p ⊕ q.\]
The category has FusionStyle(FermionParity) = UniqueFusion().
Topological Data
All quantum dimensions are 1, and Fsymbol is trivial on allowed channels.
The braiding style is Fermionic(). The Rsymbol is -1 only when both input sectors are odd:
\[R^{11}_0 = -1.\]
The twists are
\[θ_0 = 1,\qquad θ_1 = -1.\]
fusiontensor is defined for array construction, but it emits a warning because plain arrays with FermionParity labels cannot preserve all fermionic signs.