Journal
PHYSICAL REVIEW LETTERS
Volume 108, Issue 19, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.108.196402
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Funding
- NSF [DMR-0706140, PHY05-51164]
- JSPS
- Alfred P. Sloan Foundation
- Grants-in-Aid for Scientific Research [23740298] Funding Source: KAKEN
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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.
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