Systematic lowering of the scaling of Monte Carlo calculations by partitioning and subsampling

Antoine Bienvenu, Jonas Feldt, Julien Toulouse, and Roland Assaraf
Phys. Rev. E 106, 025301 – Published 1 August 2022

Abstract

We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or fragments, and subsampling each fragment (i.e., performing side walks) while freezing the environment. No bias is introduced and a zero-variance principle holds in the limit of separability, i.e., when the fragments are independent. In practice, the usual bottleneck of Monte Carlo calculations—the scaling of the statistical fluctuations as a function of the number of particles N—is relieved for extensive observables. We illustrate the method in variational Monte Carlo on the two-dimensional Hubbard model and on metallic hydrogen chains using Jastrow-Slater wave functions. A factor O(N) is gained in numerical efficiency.

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  • Received 9 February 2022
  • Accepted 5 July 2022

DOI:https://doi.org/10.1103/PhysRevE.106.025301

©2022 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Antoine Bienvenu1, Jonas Feldt1, Julien Toulouse1,2, and Roland Assaraf1,*

  • 1Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
  • 2Institut Universitaire de France, F-75005 Paris, France

  • *assaraf@lct.jussieu.fr

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Vol. 106, Iss. 2 — August 2022

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