Kitaev
Honeycomb
Spin Liquid
J
x
coupling
1.00
J
y
coupling
1.00
J
z
coupling
1.00
Magnetic field h
0.00
Phase: B (gapless)
x-bonds (J_x σˣσˣ)
y-bonds (J_y σʸσʸ)
z-bonds (J_z σᶻσᶻ)
Majorana flux (W_p)
Toggle Vison
Clear Flux
Kitaev (2003):
Exactly solvable spin-1/2 model on honeycomb lattice. H = −Σ J_α σ_iᵅ σ_jᵅ for α-bonds.
Maps to free Majorana fermions in a static Z₂ gauge field.
Phase A
(gapped): one |J_α| > sum of others.
Phase B
(gapless): |J_α| ≤ |J_β| + |J_γ|.
Magnetic field opens gap in B phase →
non-Abelian anyons
(Ising model). Plaquette operators W_p = ±1 are conserved Z₂ fluxes.