Path integral Monte Carlo simulations: Study of the efficiency of energy estimators

Abstract

This article presents a study of the relative efficiency of two commonly used energy estimators for path integral Monte Carlo (MC) simulations; the Barker estimator and the virial estimator. Two different path integral MC algorithms are considered; the simple algorithm augmented with whole chain moves and the normal-mode algorithm. The behavior of the two estimators is analyzed in some model systems and the suitability of its application is discussed, considering the general characteristics of the systems to be simulated. It is concluded that there is no obvious choice when it comes to decide which estimator to use. Instead, each one may be the most appropriate depending on the specific conditions of the simulation. Identical conclusions are drawn for both algorithms considered here. For low temperature systems or with high gradient potentials, where quantum effects are more significant, the Barker estimator is to be preferred as the variance of the mean energy is smaller. On the other hand, for high temperature systems or with low gradient potentials, where quantum effects are less significant, the virial estimator has a smaller variance of the mean energy.