Kitaev Honeycomb Model: Flux Sectors

Exactly solvable spin-1/2 model on a honeycomb lattice. Z₂ fluxes through plaquettes define vortex sectors. Click plaquettes to insert/remove π-flux vortices (non-Abelian anyons in phase B).

Couplings

Legend

No flux (W=+1)
π-flux (W=−1)
x-link (Jx)
y-link (Jy)
z-link (Jz)

Phase

About

Kitaev (2003): the honeycomb spin model maps to free Majorana fermions coupled to a Z₂ gauge field. Each hexagonal plaquette has a conserved flux W_p=±1. Phase A (gapped, abelian anyons) when one coupling dominates; Phase B (gapless, non-abelian anyons with magnetic field) when all equal.