Entanglement Spectrum — Topological Phase

The entanglement spectrum (ES) of the reduced density matrix ρ_A = Tr_B|ψ⟩⟨ψ| is defined via ρ_A = e^{−H_E}, where H_E = −ln ρ_A has eigenvalues ξ_i (entanglement energies). In topological phases, the ES has protected in-gap modes — a direct reflection of edge states by the bulk-boundary correspondence. For the SSH chain with |t/t'|<1 and the Kitaev chain in topological phase, a characteristic crossing at ξ=0 (ξ=ln 2) appears, counting edge modes.