Entanglement Spectrum

Li-Haldane (2008): the entanglement spectrum (ES) of a topological state encodes its edge physics. For the Laughlin ν=1/3 FQH state, ES eigenvalues mirror the chiral boson edge spectrum — more than entanglement entropy, the full spectrum reveals the topological order.

Parameters

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Li-Haldane Conjecture

Entanglement Hamiltonian: Given ground state |Ψ⟩, partition system A∪B. Reduced density matrix ρ_A = Tr_B|Ψ⟩⟨Ψ| = e^{-H_E}/Z. The entanglement spectrum {ξᵢ} are eigenvalues of H_E.

Li-Haldane (2008): For Laughlin ν=1/p states, the counting of ES levels at each angular momentum sector matches the counting of edge modes — a chiral boson with central charge c=1.

Universal counting: ES multiplet structure at momentum k: p(k) partitions = 1,1,2,3,5,7,11,... This is the edge state counting — topology encoded in the bulk ground state.