2005/08/31 by Lode Pollet, Kris Van Houcke, Stefan Rombouts +1 · 1 citation
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Degrees of freedom (physics and chemistry) #Hybrid Monte Carlo #Markov chain Monte Carlo #Mathematics #Monte Carlo algorithm #Monte Carlo method #Monte Carlo molecular modeling #Physics #Physics of Superconductivity and Magnetism #Quantum Monte Carlo #Quantum many-body systems #Quantum mechanics #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.jcp.2007.03.013
published as J Comp Phys, 225/2 pp. 2249-2266 (2007) · replaced with published version
openalex publication_date 2007/03/29 · arxiv created 2007/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 have a non-zero winding number. 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.