Kitaev Honeycomb Model

Kitaev's exactly solvable honeycomb spin model (2003) hosts two phases: a gapped toric-code-like phase with Abelian anyons (visons), and a gapless/gapped phase with non-Abelian Majorana fermions. Each hexagonal plaquette carries a Z₂ flux — a conserved vison number.

J_x 0.50

J_y 0.50

J_z 1.00

Phase

A (Toric)

Vison gap Δ_v

—

Majorana gap Δ_m

—

H = −J_x Σ_x σᵢˣσⱼˣ − J_y Σ_y σᵢʸσⱼʸ − J_z Σ_z σᵢᶻσⱼᶻ ; exact ground state via Majorana decomposition