Optimal Energy Estimation in Path-Integral Monte Carlo Simulations

TL;DR

This paper analyzes and compares energy estimators in path-integral Monte Carlo simulations, demonstrating how combining estimators and using refined update schemes can reduce statistical errors effectively.

Contribution

It provides a detailed analysis of energy estimators' variance and autocorrelation, and introduces an optimal combination method to improve energy estimation accuracy.

Findings

Combining estimators reduces statistical error without extra cost.

Refined update schemes like multigrid improve estimator performance.

Autocorrelation analysis guides optimal estimator combination.

Abstract

We investigate the properties of two standard energy estimators used in path-integral Monte Carlo simulations. By disentangling the variance of the estimators and their autocorrelation times we analyse the dependence of the performance on the update algorithm and present a detailed comparison of refined update schemes such as multigrid and staging techniques. We show that a proper combination of the two estimators leads to a further reduction of the statistical error of the estimated energy with respect to the better of the two without extra cost.