Energy estimators for random series path-integral methods

TL;DR

This paper analyzes and compares different energy estimators in random series path integral methods, demonstrating their finite variances, implementation simplicity, and the importance of estimator agreement for validation, with applications to molecular hydrogen clusters.

Contribution

It provides a comprehensive analysis of energy estimators in path integral methods, highlighting their properties and validation techniques, and applies them to molecular hydrogen clusters.

Findings

Both T-method and H-method estimators have finite variances.

Agreement between estimators serves as a validation check.

Applied estimators to hydrogen clusters with consistent results.

Abstract

We perform a thorough analysis on the choice of estimators for random series path integral methods. In particular, we show that both the thermodynamic (T-method) and the direct (H-method) energy estimators have finite variances and are straightforward to implement. It is demonstrated that the agreement between the T-method and the H-method estimators provides an important consistency check on the quality of the path integral simulations. We illustrate the behavior of the various estimators by computing the total, kinetic, and potential energies of a molecular hydrogen cluster using three different path integral techniques. Statistical tests are employed to validate the sampling strategy adopted as well as to measure the performance of the parallel random number generator utilized in the Monte Carlo simulation. Some issues raised by previous simulations of the hydrogen cluster are clarified.