Edge-mode combinations in the entanglement spectra of non-Abelian fractional quantum Hall states on the torus

Zhao Liu, Emil J. Bergholtz, Heng Fan, and Andreas M. Läuchli
Phys. Rev. B 85, 045119 – Published 19 January 2012

Abstract

We present a detailed analysis of bipartite entanglement in the non-Abelian Moore-Read fractional quantum Hall state of bosons and fermions on the torus. In particular, we show that the entanglement spectra can be decomposed into intricate combinations of different sectors of the conformal field theory describing the edge physics, and that the edge level counting and tower structure can be microscopically understood by considering the vicinity of the thin-torus limit. We also find that the boundary entropy density of the Moore-Read state is markedly higher than in the Laughlin states investigated so far. Despite the torus geometry being somewhat more involved than in the sphere geometry, our analysis and insights may prove useful when adopting entanglement probes to other systems that are more easily studied with periodic boundary conditions, such as fractional Chern insulators and lattice problems in general.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
1 More
  • Received 9 September 2011

DOI:https://doi.org/10.1103/PhysRevB.85.045119

©2012 American Physical Society

Authors & Affiliations

Zhao Liu1,2, Emil J. Bergholtz3,4, Heng Fan2, and Andreas M. Läuchli3,5

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann Straße 1, D-85748 Garching, Germany
  • 2Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 3Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany
  • 4Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
  • 5Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 85, Iss. 4 — 15 January 2012

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×