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Real-space entanglement spectrum of quantum Hall states

A. Sterdyniak, A. Chandran, N. Regnault, B. A. Bernevig, and Parsa Bonderson
Phys. Rev. B 85, 125308 – Published 16 March 2012

Abstract

We investigate the entanglement spectra arising from sharp real-space partitions of the system for quantum Hall states. These partitions differ from the previously utilized orbital and particle partitions and reveal complementary aspects of the physics of these topologically ordered systems. We show, by constructing one to one maps to the particle partition entanglement spectra, that the counting of the real-space entanglement spectra levels for different particle number sectors versus their angular momentum along the spatial partition boundary is equal to the counting of states for the system with a number of (unpinned) bulk quasiholes excitations corresponding to the same particle and flux numbers. This proves that, for an ideal model state described by a conformal field theory, the real-space entanglement spectra level counting is bounded by the counting of the conformal field theory edge modes. This bound is known to be saturated in the thermodynamic limit (and at finite sizes for certain states). Numerically analyzing several ideal model states, we find that the real-space entanglement spectra indeed display the edge modes dispersion relations expected from their corresponding conformal field theories. We also numerically find that the real-space entanglement spectra of Coulomb interaction ground states exhibit a series of branches, which we relate to the model state and (above an entanglement gap) to its quasiparticle-quasihole excitations. We also numerically compute the entanglement entropy for the ν=1 integer quantum Hall state with real-space partitions and compare against the analytic prediction. We find that the entanglement entropy indeed scales linearly with the boundary length for large enough systems, but that the attainable system sizes are still too small to provide a reliable extraction of the subleading topological entanglement entropy term.

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  • Received 11 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.125308

©2012 American Physical Society

Authors & Affiliations

A. Sterdyniak1, A. Chandran2, N. Regnault1, B. A. Bernevig2, and Parsa Bonderson3

  • 1Laboratoire Pierre Aigrain, ENS and CNRS, 24 rue Lhomond, 75005 Paris, France
  • 2Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 3Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA

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Issue

Vol. 85, Iss. 12 — 15 March 2012

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