Entanglement Gap and a New Principle of Adiabatic Continuity

R. Thomale, A. Sterdyniak, N. Regnault, and B. Andrei Bernevig
Phys. Rev. Lett. 104, 180502 – Published 3 May 2010

Abstract

We give a complete definition of the entanglement gap separating low-energy, topological levels from high-energy, generic ones, in the "entanglement spectrum" of fractional quantum Hall (FQH) states. This is accomplished by removing the magnetic length inherent in the FQH problem—a procedure which we call taking the conformal limit. The counting of the low-lying entanglement levels starts off as the counting of modes of the edge theory of the FQH state, but quickly develops finite-size effects which we find to serve as a fingerprint of the FQH state. As the sphere manifold where the FQH resides grows, the level spacing of the states at the same angular momentum goes to zero, suggestive of the presence of relativistic gapless edge states. By using the adiabatic continuity of the low-entanglement energy levels, we investigate whether two states are topologically connected.

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  • Received 12 November 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.180502

©2010 American Physical Society

Authors & Affiliations

R. Thomale1, A. Sterdyniak2, N. Regnault2, and B. Andrei Bernevig1

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 2Laboratoire Pierre Aigrain, ENS and CNRS, 24 rue Lhomond, 75005 Paris, France

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Vol. 104, Iss. 18 — 7 May 2010

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