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Strongly Correlated Systems pp 293–319Cite as

Fermionic and Continuous Time Quantum Monte Carlo

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

Abstract

Diagrammatic “continuous-time” algorithms for fermionic systems are algorithms that evaluate the diagrammatic perturbation series of interacting many-body systems stochastically. The algorithms involve no approximations and are numerically exact for convergent series, as they appear, for example, in the description of finite lattice problems and quantum impurity models. Among other advantages the various formulations of continuous-time algorithms are able to accurately describe systems with general, complex multi-orbital structures as they appear in the theoretical description of a wide range of transition metal and actinide compounds.

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Acknowledgments

We would like to thank our many colleagues and collaborators who have enabled extraordinary progress in the field of diagrammatic Monte Carlo methods over the last few years. In particular we would like to thank A. Lichtenstein, A. J. Millis, A. Rubtsov, and P. Werner for co-authoring Ref. [1], which we followed for large parts of this chapter. E. G. acknowledges support by NSF-DMR-1006282.

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Authors and Affiliations

  1. Department of Physics, University of Michigan, Ann Arbor, MI, 48109-1040, USA

    Emanuel Gull

  2. Institut f. Theoretische Physik, ETH, 8093, Zurich, Switzerland

    Matthias Troyer

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  1. Emanuel Gull
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  2. Matthias Troyer
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Correspondence to Emanuel Gull .

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  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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Gull, E., Troyer, M. (2013). Fermionic and Continuous Time Quantum Monte Carlo. 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_11

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