The Kitaev honeycomb model (Kitaev, 2006) is an exactly solvable quantum spin model with bond-directional interactions:
The model maps exactly to free Majorana fermions in a static Z₂ gauge field. Each hexagonal plaquette has a conserved flux Wₚ = ±1. In the ground state, all Wₚ = +1 (vison-free sector). The three phases are: A-phase (gapped, when one coupling dominates) and B-phase (gapless, Dirac spectrum, when all J are comparable). Visons (Wₚ = −1) are gapped flux excitations that can carry non-Abelian statistics in the B-phase with a magnetic field — making them candidates for topological qubits. α-RuCl₃ and Na₂IrO₃ are candidate materials. Clicking a hexagon toggles its vison state.