Topological Entanglement Entropy

Kitaev toric code — anyons, ground state degeneracy, and γ = log 2

Toric Code

Mode

Topological Quantities

γ = ln 2
S_topo
S_area
GSD4
Anyons0
Excit. gap

Hamiltonian:

H = −J_e Σ_v A_v − J_m Σ_p B_p

Vertex: A_v = ⊗_{i∈v} σ_i^x

Plaquette: B_p = ⊗_{i∈p} σ_i^z

Entanglement entropy:

S(R) = α|∂R| − γ + ...

γ = ln D = ln 2

e-anyon: A_v = −1 (red vertices)
m-anyon: B_p = −1 (blue plaquettes)
Anyons come in pairs (strings)