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arXiv · 1103.5437

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

Xiao-Liang Qi·Hosho Katsura·Andreas W. W. Ludwig
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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.

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Xiao-Liang Qi, Hosho Katsura, Andreas W. W. Ludwig. 2011-03-28. General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States. https://doi.org/10.1103/physrevlett.108.196402

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