Quantum Spin Liquid — Z₂ Gauge Theory

The Kitaev honeycomb model and toric code realize Z₂ gauge theories. The ground state is a quantum spin liquid with no broken symmetry. Excitations are fractionalized: e (electric) and m (magnetic) anyons, also called spinons and visons. The Z₂ flux (vison) is a π-flux through a plaquette, detectable by the ground-state expectation value W_p = ∏_{i∈p} σ^z_i = ±1. A vison-spinon composite is a fermion — all from a bosonic spin model!