Locality and thermalization in closed quantum systems

J. Sirker, N. P. Konstantinidis, F. Andraschko, and N. Sedlmayr
Phys. Rev. A 89, 042104 – Published 9 April 2014

Abstract

We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization process. We also show that this approach is useful to investigate thermalization based on a finite-size scaling of numerical data. The condition follows from an exact representation of the observable as the sum of a projection onto the local conserved charges of the system and a projection onto the nonlocal ones. We show that thermalization requires that the time average of the latter part vanishes in the thermodynamic limit while time and statistical averages for the first part are identical. As an example, we use this thermalization condition to analyze exact diagonalization data for a one-dimensional spin model. We find that local correlators do thermalize in the thermodynamic limit, although we find no indications that the eigenstate thermalization hypothesis applies.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 12 March 2013
  • Revised 2 September 2013

DOI:https://doi.org/10.1103/PhysRevA.89.042104

©2014 American Physical Society

Authors & Affiliations

J. Sirker1,2,*, N. P. Konstantinidis1, F. Andraschko1,2, and N. Sedlmayr1,†

  • 1Department of Physics and Research Center OPTIMAS, Technical University Kaiserslautern, D-67663 Kaiserslautern, Germany
  • 2Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

  • *jsirker@physik.uni-kl.de
  • Current address: Institute de Physique Théorique, CEA/Saclay, Orme des Merisiers, 91190 Gif-sur-Yvette Cedex, France.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 89, Iss. 4 — April 2014

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 A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×