Numerical estimation of critical parameters using the bond entropy

Rafael A. Molina and Peter Schmitteckert
Phys. Rev. B 75, 235104 – Published 6 June 2007

Abstract

Using a model of spinless fermions in a lattice with nearest-neighbor and next-nearest-neighbor interactions, we show that the entropy of the reduced two-site density matrix (the bond entropy) can be used as an extremely accurate and easy to calculate numerical indicator for the critical parameters of the quantum phase transition when the basic ordering pattern has a two-site periodicity. The actual behavior of the bond entropy depends on the particular characteristics of the transition under study. For the Kosterlitz-Thouless-type phase transition from a Luttinger liquid phase to a charge-density wave state, the bond entropy has a local maximum, while in the transition from the Luttinger liquid to the phase separated state, the derivative of the bond entropy has a divergence due to the cancellation of the third eigenvalue of the two-site reduced density matrix.

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  • Received 3 January 2007

DOI:https://doi.org/10.1103/PhysRevB.75.235104

©2007 American Physical Society

Authors & Affiliations

Rafael A. Molina1 and Peter Schmitteckert2

  • 1Instituto de Estructura de la Materia-CSIC, Serrano 123, 28006 Madrid, Spain
  • 2Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany

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Issue

Vol. 75, Iss. 23 — 15 June 2007

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