Coupling Constants
Phase:
B (Gapless)
Flux Sector
x-bond (σxσx)
y-bond (σyσy)
z-bond (σzσz)
Vison (flux)
In each plaquette, Z₂ flux Wp = ∏σ = ±1. Visons are static Z₂ gauge excitations; Majorana fermions hop in the background flux. In phase B+κ, non-Abelian anyons appear at vison cores.
Phase Diagram
Phase A (gapped): one coupling dominates (|Jα| > |Jβ|+|Jγ|). Abelian anyons. Z₂ topological order.
Phase B (gapless): triangle inequality satisfied. Dirac-like Majorana fermions. With κ≠0 → gapped non-Abelian phase (Ising universality).
Gap: Δ ∝ κ·|Jx Jy Jz|/J²
Phase B (gapless): triangle inequality satisfied. Dirac-like Majorana fermions. With κ≠0 → gapped non-Abelian phase (Ising universality).
Gap: Δ ∝ κ·|Jx Jy Jz|/J²