Diffusion Monte Carlo using domains in configuration space

TL;DR

This paper introduces a method to improve diffusion Monte Carlo sampling by using domain-based effective dynamics, reducing statistical fluctuations, and demonstrating its application to the Hubbard model.

Contribution

It extends previous work on effective dynamics in DMC to arbitrary domains, providing a new approach to reduce fluctuations in configuration space sampling.

Findings

Effective dynamics reduce statistical fluctuations in DMC.

Numerical application shows improved sampling in the Hubbard model.

Method can be generalized to continuous spaces.

Abstract

The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60}, 2299 (1999)}], it was shown that the probability for a walker to stay a certain amount of time in the same state obeys a Poisson law and that the on-state dynamics can be integrated out exactly, leading to an effective dynamics connecting only different states. Here, we extend this idea to the general case of a walker trapped within domains of arbitrary shape and size. The equations of the resulting effective stochastic dynamics are derived. The larger the average (trapping) time spent by the walker within the domains, the greater the reduction in statistical fluctuations. A numerical application to the Hubbard model is presented. Although this work presents the method for finite linear spaces, it can be generalized without fundamental difficulties to continuous configuration spaces.