Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations

Matthew B. Hastings, Iván González, Ann B. Kallin, and Roger G. Melko
Phys. Rev. Lett. 104, 157201 – Published 14 April 2010

Abstract

We develop a quantum Monte Carlo procedure, in the valence bond basis, to measure the Renyi entanglement entropy of a many-body ground state as the expectation value of a unitary Swap operator acting on two copies of the system. An improved estimator involving the ratio of Swap operators for different subregions enables convergence of the entropy in a simulation time polynomial in the system size. We demonstrate convergence of the Renyi entropy to exact results for a Heisenberg chain. Finally, we calculate the scaling of the Renyi entropy in the two-dimensional Heisenberg model and confirm that the Néel ground state obeys the expected area law for systems up to linear size L=32.

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  • Received 14 January 2010

DOI:https://doi.org/10.1103/PhysRevLett.104.157201

©2010 American Physical Society

Authors & Affiliations

Matthew B. Hastings1, Iván González2, Ann B. Kallin3, and Roger G. Melko3

  • 1Microsoft Research, Station Q, CNSI Building, University of California, Santa Barbara, California, 93106, USA
  • 2Centro de Supercomputación de Galicia, Avda. de Vigo s/n, E-15705 Santiago de Compostela, Spain
  • 3Department of Physics and Astronomy, University of Waterloo, Ontario, N2L 3G1, Canada

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Issue

Vol. 104, Iss. 15 — 16 April 2010

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