Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo

TL;DR

This paper investigates advanced extrapolation techniques and improved actions in path integral Monte Carlo to enhance accuracy and efficiency in simulating quantum systems, demonstrating reduced computational costs and preserved higher-order behavior.

Contribution

It introduces and compares Richardson extrapolation and Takahashi-Imada action, showing their effectiveness in improving PIMC accuracy and efficiency without additional computational costs.

Findings

Richardson extrapolation reduces bead dependence without extra cost

Takahashi-Imada action maintains fourth-order behavior

Improved actions decrease computational time in quantum liquids

Abstract

Improvements beyond the primitive approximation in the path integral Monte Carlo method are explored both in a model problem and in real systems. Two different strategies are studied: the Richardson extrapolation on top of the path integral Monte Carlo data and the Takahashi-Imada action. The Richardson extrapolation, mainly combined with the primitive action, always reduces the number-of-beads dependence, helps in determining the approach to the dominant power law behavior, and all without additional computational cost. The Takahashi-Imada action has been tested in two hard-core interacting quantum liquids at low temperature. The results obtained show that the fourth-order behavior near the asymptote is conserved, and that the use of this improved action reduces the computing time with respect to the primitive approximation.