title: General relationship between the entanglement spectrum and the edge state spectrum of topological quantum states.
abstract: We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional conformal field theory, 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 conformal field theory 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 conformal field theory, 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.
authors.affiliation: Department of Physics, Stanford University, Stanford, California 94305, USA.
authors.forename: Xiao-Liang
authors.initials: XL
authors.lastname: Qi
authors.forename: Hosho
authors.initials: H
authors.lastname: Katsura
authors.forename: Andreas W W
authors.initials: AW
authors.lastname: Ludwig