Engineering local optimality in quantum Monte Carlo algorithms

  • Authors:

  • Lode Pollet;Kris Van Houcke;Stefan M. A. Rombouts

  • Affiliations:

  • Theoretische Physik, ETH Zürich, CH - 8093 Zürich, Switzerland;Vakgroep subatomaire en stralingsfysica, Proeftuinstraat 86, Universiteit Gent, Belgium;Vakgroep subatomaire en stralingsfysica, Proeftuinstraat 86, Universiteit Gent, Belgium

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

Quantified Score

Hi-index 31.45

Visualization

Abstract

Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic models. Both algorithms work in the grand-canonical ensemble and can have a winding number larger than zero. However, they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm. We let us guide by the rigorous statements on the globally optimal form of Markov chain Monte Carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm. We provide numerical examples for the soft-core Bose-Hubbard model and various spin-S models.