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

TL;DR

This paper demonstrates that the entanglement spectrum of (2+1)D topological states with chiral edge states is equivalent to the thermal spectrum of the edge conformal field theory, linking entanglement and physical edge states.

Contribution

It provides a theoretical proof that the entanglement spectrum corresponds to the edge state spectrum using boundary conformal field theory and quantum quench techniques.

Findings

Entanglement spectrum matches the edge state spectrum.

Edge states can be viewed as a thermal state of the boundary CFT.

Supports Li and Haldane's observation on entanglement and edge spectra.

Abstract

We consider (2+1)-dimensional topological quantum states which possess edge states 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 states the reduced density matrix of a finite spatial region of the gapped topological state is a thermal density matrix of the chiral edge state CFT which would appear at the spatial boundary of that region. We obtain this result by applying a physical instantaneous cut to the gapped system, and by viewing the cutting process as a sudden "quantum quench" into a CFT, using the tools of boundary conformal field theory. We thus provide a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state.