TOPOLOGICAL ORDER
Toric Code · Anyons · Ground State Degeneracy
MODEL
Toric Code (Kitaev 2003)
Z₂ Gauge Theory
Fibonacci Anyons
LATTICE
4×4
6×6
8×8
Create Anyon Pair
Move Anyon
Reset
OBSERVABLES
Genus g
1 (torus)
GSD
4 = 2^(2g)
Anyons present
0
Wilson loop Z₁
+1
Wilson loop Z₂
+1
PHYSICS
H = -J_e Σ_v A_v - J_m Σ_p B_p
Toric code on torus has GSD=4 states, locally indistinguishable. Anyons (e-particles and m-vortices) are created in pairs. Braiding e around m gives phase -1 (mutual statistics). Cannot be deconfined by local perturbations — topological protection.