Reduction of Autocorrelation Times in Lattice Path Integral Quantum Monte Carlo via Direct Sampling of the Truncated Exponential Distribution

TL;DR

This paper introduces a direct sampling method for truncated exponential distributions that accelerates Path Integral Monte Carlo simulations of Bose-Hubbard models by reducing autocorrelation times and improving acceptance ratios.

Contribution

The paper presents a novel direct sampling technique for truncated exponential distributions, enhancing efficiency in PIMC simulations of lattice quantum systems.

Findings

Faster convergence to the target distribution compared to rejection sampling

Improved acceptance ratios in Monte Carlo simulations

Reduced autocorrelation times leading to faster simulations

Abstract

In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the probability distribution from which random variates are sampled, simulations can be made more efficient, by virtue of an autocorrelation time reduction. In this paper, we illustrate how to directly sample random variates from a two dimensional truncated exponential distribution. We show that our direct sampling approach converges faster to the target distribution compared to rejection sampling. The direct sampling of one and two dimensional truncated exponential distributions is then applied to a recent Path Integral Monte Carlo (PIMC) algorithm for the simulation of Bose-Hubbard lattice models at zero temperature. The new sampling method results in improved acceptance ratios and reduced autocorrelation times of estimators, providing an effective speed up of the simulation.