Entanglement spectroscopy using quantum Monte Carlo

Chia-Min Chung, Lars Bonnes, Pochung Chen, and Andreas M. Läuchli
Phys. Rev. B 89, 195147 – Published 30 May 2014

Abstract

We present a numerical scheme to reconstruct a subset of the entanglement spectrum of quantum many body systems using quantum Monte Carlo. The approach builds on the replica trick to evaluate particle number resolved traces of the first n of powers of a reduced density matrix. From this information we reconstruct n entanglement spectrum levels using a polynomial root solver. We illustrate the power and limitations of the method by an application to the extended Bose-Hubbard model in one dimension where we are able to resolve the quasidegeneracy of the entanglement spectrum in the Haldane-insulator phase. In general, the method is able to reconstruct the largest few eigenvalues in each symmetry sector and typically performs better when the eigenvalues are not too different.

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  • Received 31 May 2013
  • Revised 21 May 2014

DOI:https://doi.org/10.1103/PhysRevB.89.195147

©2014 American Physical Society

Authors & Affiliations

Chia-Min Chung1,2,*, Lars Bonnes1,†, Pochung Chen2,3, and Andreas M. Läuchli1

  • 1Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
  • 2Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
  • 3Frontier Research Center on Fundamental and Applied Sciences of Matters, National Tsing Hua University, Hsinchu 30013, Taiwan

  • *chiaminchung@gmail.com
  • lars.bonnes@uibk.ac.at

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Vol. 89, Iss. 19 — 15 May 2014

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