Scaling law for topologically ordered systems at finite temperature

S. Iblisdir, D. Pérez-García, M. Aguado, and J. Pachos
Phys. Rev. B 79, 134303 – Published 16 April 2009

Abstract

Understanding the behavior of topologically ordered lattice systems at finite temperature is a way of assessing their potential as fault-tolerant quantum memories. We compute the natural extension of the topological entanglement entropy for T>0, namely, the subleading correction Itopo to the area law for mutual information. Its dependence on T can be written, for Abelian Kitaev models, in terms of information-theoretical functions and readily identifiable scaling behavior, from which the interplay between volume, temperature, and topological order, can be read. These arguments are extended to non-Abelian quantum double models, and numerical results are given for the D(S3) model, showing qualitative agreement with the Abelian case.

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  • Received 20 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.134303

©2009 American Physical Society

Authors & Affiliations

S. Iblisdir1, D. Pérez-García2, M. Aguado3, and J. Pachos4

  • 1Departament d’Estructura i Constituents de la Materia, Universitat Barcelona, 08028 Barcelona, Spain
  • 2Departamento de Análisis Matemático, Universitad Complutense de Madrid, 28040 Madrid, Spain
  • 3Max Planck Institutesse für Quantenoptik, Max-Kopfermann-Str., Garching D-85748, Germany
  • 4School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom

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Issue

Vol. 79, Iss. 13 — 1 April 2009

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