Kitaev Honeycomb Model: Z₂ Flux Sectors

Click bonds to flip them — visons (Z₂ fluxes) appear in adjacent plaquettes

x-bond (Jx) y-bond (Jy) z-bond (Jz) W=-1 flux (vison) W=+1 (vacuum)
Flipped bonds: 0
Visons (W=-1): 0
Ground sector: Yes
The Kitaev honeycomb model has exact Z₂ gauge symmetry. Each plaquette has a conserved flux Wp = ±1. Flipping a bond creates or annihilates visons in the two adjacent plaquettes. Visons are Abelian anyons — braiding a fermion around a vison gives a phase of −1. In the B-phase (all J equal), Majorana fermions become gapless; adding a magnetic field opens a gap and makes the anyons non-Abelian (Ising anyons).