Study of a generalized Metropolis decision rule in auxiliary field quantum Monte Carlo

TL;DR

This paper introduces a generalized Metropolis decision rule with a tunable parameter in auxiliary field quantum Monte Carlo, aiming to improve simulation efficiency by optimizing acceptance rates and autocorrelation times.

Contribution

It proposes a new flexible acceptance criterion in quantum Monte Carlo, enabling better control over simulation parameters and potentially enhancing computational efficiency.

Findings

Tuning the acceptance rate affects autocorrelation times.

The generalized rule can improve simulation efficiency.

Results demonstrated on the 2D Hubbard model.

Abstract

We consider a generalization of the standard Metropolis algorithm acceptance/rejection decision rule and numerically explore its properties using auxiliary field quantum Monte Carlo. The generalization involves a free parameter which, given a criterion for proposing attempted moves, can be used to tune the average acceptance rate in a particular way. Such tuning can also potentially change Monte Carlo autocorrelation times, and the combination of the changing acceptance rate and autocorrelation times raises the possibility of more efficient simulations. We explore these issues using primarily massively parallel quantum Monte Carlo runs of the ``test case'' two-dimensional Hubbard model, and discuss results and applications.