Kitaev Honeycomb Model: Anyons & Topological Phase
Exactly solvable spin-1/2 model • Abelian & non-Abelian anyons • Z₂ gauge field
Coupling Constants
Jₓ (x-links)
0.5
Jᵧ (y-links)
0.5
Jᵤ (z-links)
0.5
Magnetic field h
0.0
Phase: A (Gapped, Abelian anyons)
H = −Jₓ Σ σˣσˣ − Jᵧ Σ σʸσʸ
− Jᵤ Σ σᶻσᶻ − h Σ σᶻ
Phase A: |Jₓ|,|Jᵧ|,|Jᵤ| satisfy
triangle inequality → gapped
Phase B: gapless → non-Abelian
with h≠0
Create Flux Pair (visons)
Annihilate Visons
A sublattice
B sublattice
Vison (flux)
Kitaev (2003): spin-1/2 on honeycomb lattice is exactly solvable via Majorana fermions. Phase B + time-reversal breaking h supports non-Abelian anyons useful for fault-tolerant quantum computing.