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We consider (2+1)-dimensional topological quantum states which possess edgestates described by a chiral (1+1)-dimensional Conformal Field Theory (CFT),such as e.g. a general quantum Hall state. We demonstrate that for such statesthe reduced density matrix of a finite spatial region of the gapped topologicalstate is a thermal density matrix of the chiral edge state CFT which wouldappear at the spatial boundary of that region. We obtain this result byapplying a physical instantaneous cut to the gapped system, and by viewing thecutting process as a sudden "quantum quench" into a CFT, using the tools ofboundary conformal field theory. We thus provide a demonstration of theobservation made by Li and Haldane about the relationship between theentanglement spectrum and the spectrum of a physical edge state.

General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States