Valence Bond Entanglement Entropy

Fabien Alet, Sylvain Capponi, Nicolas Laflorencie, and Matthieu Mambrini
Phys. Rev. Lett. 99, 117204 – Published 12 September 2007

Abstract

We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Néel phase.

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  • Received 16 March 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.117204

©2007 American Physical Society

Authors & Affiliations

Fabien Alet1,*, Sylvain Capponi1, Nicolas Laflorencie2,1, and Matthieu Mambrini1

  • 1Laboratoire de Physique Théorique, IRSAMC, Université Paul Sabatier, CNRS, 31062 Toulouse, France
  • 2Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

  • *alet@irsamc.ups-tlse.fr

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Vol. 99, Iss. 11 — 14 September 2007

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