Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions

ORAL

Abstract

High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic Monte Carlo simulations. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as 1/N in sample number N; parametrically faster than 1/N1/2 in Monte Carlo simulations. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.
Finally, I will also present a recent extension of the technique to compute whole time-dependent Green functions via a kernel approach.

*The Flatiron Institute is a division of the Simons Foundation. X. W. and M. M. acknowledge funding from the French-Japanese ANR QCONTROL, E. U. FET UltraFastNano, and FLAG-ERA Gransport.

Presenters

  • Corentin Bertrand

    • Simons Foundation
    • Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA

Authors

  • Marjan Maček

    • Université Grenoble Alpes, CEA, IRIG-PHELIQS, 38000 Grenoble, France
  • Philipp Dumitrescu

    • Center for Computational Quantum Physics, Flatiron Institute
    • Simons Foundation
    • Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA
  • Corentin Bertrand

    • Simons Foundation
    • Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA
  • Bill Triggs

    • Laboratoire Jean Kuntzmann
    • Laboratoire Jean Kuntzmann, Université Grenoble Alpes, CNRS, 38401 Grenoble, France
  • Olivier Parcollet

    • Center for Computational Quantum Physics, Flatiron Institute
    • Center of Computational Quantum Physics, Flatiron Institute, New York City, USA
    • Center for Computational Quantum Physics, Flatiron institute
    • Simons Foundation
    • Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA
  • Xavier Waintal

    • Univ. Grenoble Alpes, CEA, IRIG-PHELIQS, 38000 Grenoble, France
    • Université Grenoble Alpes
    • CEA Grenoble
    • Université Grenoble Alpes, CEA, IRIG-PHELIQS, 38000 Grenoble, France