ES of FQH ground state mirrors the conformal edge spectrum — topological order encoded in entanglement
The Li-Haldane conjecture (2008): the entanglement spectrum {ξ_i} of a FQH ground state, obtained from the reduced density matrix ρ_A = Tr_B|Ψ⟩⟨Ψ| = e^{-H_E}, has the same counting structure as the physical edge excitation spectrum. For the ν=1/m Laughlin state, the ES counting at angular momentum L_z is given by the number of partitions of L_z into distinct parts ≤ m — matching the U(1)_m Kac-Moody CFT spectrum. This reveals that topological order is encoded in quantum entanglement.