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Coarse-grained belief propagation for simulation of interacting quantum systems at all temperatures

Bilgin, Ersen and Poulin, David (2010) Coarse-grained belief propagation for simulation of interacting quantum systems at all temperatures. Physical Review B, 81 (5). Art. No. 054106. ISSN 1098-0121.

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We continue our numerical study of quantum belief propagation initiated in [Phys. Rev. A 77, 052318 (2008)]. We demonstrate how the method can be expressed in terms of an effective thermal potential that materializes when the system presents quantum correlations, but is insensitive to classical correlations. The thermal potential provides an efficient means to assess the precision of belief propagation on graphs with no loops. We illustrate these concepts using the one-dimensional quantum Ising model and compare our results with exact solutions. We also use the method to study the transverse field quantum Ising spin glass for which we obtain a phase diagram that is largely in agreement with the one obtained in [Phys. Rev. B 78, 134424 (2008).] using a different approach. Finally, we introduce the coarse-grained belief propagation (CGBP) algorithm to improve belief propagation at low temperatures. This method combines the reliability of belief propagation at high temperatures with the ability of entanglement renormalization to efficiently describe low-energy subspaces of quantum systems with local interactions. With CGBP, thermodynamic properties of quantum systems can be calculated with a high degree of accuracy at all temperatures.

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Additional Information:© 2010 The American Physical Society. Received 26 October 2009; revised 6 January 2010; published 9 February 2010. Computational resources were provided by the Réseau québécois de calcul de haute performance RQCHP. D.P. receives financial support from Canada’s NSERC and le Fonds québécois de la recherche sur la nature et les technologies. E.B. is supported by DoE under Grant No. DE-FG03- 92-ER40701 and NSF under Grant No. PHY-0803371.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council (Canada)UNSPECIFIED
Fonds québécois de la recherche sur la nature et les technologiesUNSPECIFIED
U. S. Department of EnergyDE-FG03- 92-ER40701
Issue or Number:5
Classification Code:PACS: 05.30.-d, 02.70.-c, 05.50.+q, 75.50.Lk
Record Number:CaltechAUTHORS:20100331-105550083
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17829
Deposited By: Ruth Sustaita
Deposited On:07 Apr 2010 17:28
Last Modified:03 Oct 2019 01:34

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