### Session L29: Quantum Entanglement

2:30 PM–5:30 PM, Tuesday, March 22, 2011
Room: C148

Chair: Lana Sheridan, National University of Singapore

Abstract ID: BAPS.2011.MAR.L29.8

### Abstract: L29.00008 : General relation between energy spectrum and entanglement spectrum

3:54 PM–4:06 PM

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#### Authors:

Xiaoliang Qi
(Stanford University)

Hosho Katsura
(Gakushuin Univeristy, Tokyo, Japan)

Andreas Ludwig
(University of California, Santa Barbara)

We demonstrate that the bipartite density matrix, arising from a spatial bipartitioning of a gapped topological state which possesses gapless edge modes in the form of a conformal field theory (CFT ) (when terminated against a topologically trivial state/vacuum), such as e.g. a general quantum Hall state, is the density matrix of a the chiral edge state CFT at a finite temperature. We obtain this result by applying a physical instantaneous cut of 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. In particular, we obtain a general relation between the Hamiltonian spectrum of gapless theories and the entanglement spectrum of the gapped theory obtained from coupling two gapless theories.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.L29.8