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Strongly Correlated Systems pp 153–184Cite as

Loop Algorithm

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Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 176))

Abstract

The loop algorithm for the world-line quantum Monte Carlo method on quantum lattice models is presented. After introducing the path integral representation that maps a quantum model to a classical one, we describe the continuous imaginary time limit, cluster algorithm, and the rejection free scheme, which are the major improvements on the quantum Monte Carlo technique during the last decades. By means of the loop algorithm, one can simulate various unfrustrated quantum lattice models of millions of sites at extremely low temperatures with absolute accuracy, being free from the critical and fine-mesh slowing down and the Suzuki-Trotter discretization error. We also discuss some technical aspects of the algorithm such as effective implementation and parallelization.

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Authors and Affiliations

  1. Institute for Solid State Physics, University of Tokyo, 7-1-26-R501 Port Island South, Kobe, 650-0047, Japan

    Synge Todo

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  1. Synge Todo
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Correspondence to Synge Todo .

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Editors and Affiliations

  1. Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, Fisciano (SA), 84084, Italy

    Adolfo Avella

  2. Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, Fisciano (SA), 84084, Italy

    Ferdinando Mancini

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Todo, S. (2013). Loop Algorithm. In: Avella, A., Mancini, F. (eds) Strongly Correlated Systems. Springer Series in Solid-State Sciences, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35106-8_6

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  • DOI: https://doi.org/10.1007/978-3-642-35106-8_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35105-1

  • Online ISBN: 978-3-642-35106-8

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