Valence-bond entanglement entropy of frustrated spin chains

Fabien Alet, Ian P. McCulloch, Sylvain Capponi, and Matthieu Mambrini
Phys. Rev. B 82, 094452 – Published 29 September 2010

Abstract

We extend the definition of the recently introduced valence-bond entanglement entropy to arbitrary SU(2) wave functions of S=1/2 spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional J1J2 spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a “good” bipartition should be chosen, for instance, according to the Marshall sign.

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  • Received 10 May 2010

DOI:https://doi.org/10.1103/PhysRevB.82.094452

©2010 American Physical Society

Authors & Affiliations

Fabien Alet1,2, Ian P. McCulloch3, Sylvain Capponi1,2, and Matthieu Mambrini1,2

  • 1Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse–UPS, F-31062 Toulouse, France
  • 2LPT (IRSAMC), CNRS, F-31062 Toulouse, France
  • 3School of Physical Sciences, The University of Queensland, Brisbane, Queensland 4072, Australia

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Issue

Vol. 82, Iss. 9 — 1 September 2010

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