Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations

Stephen Inglis and Roger G. Melko
Phys. Rev. E 87, 013306 – Published 22 January 2013

Abstract

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

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  • Received 31 July 2012

DOI:https://doi.org/10.1103/PhysRevE.87.013306

Published by the American Physical Society

Authors & Affiliations

Stephen Inglis*

  • Department of Physics and Astronomy, University of Waterloo, 200 University Avenue, Ontario, Canada, N2L 3G1

Roger G. Melko

  • Department of Physics and Astronomy, University of Waterloo, 200 University Avenue, Ontario, Canada, N2L 3G1 and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada, N2L 2Y5

  • *dartonias@gmail.com

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Vol. 87, Iss. 1 — January 2013

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