Multigrid Method versus Staging Algorithm for PIMC Simulations

TL;DR

This paper compares the efficiency of multigrid and staging algorithms in path integral Monte Carlo simulations, showing both outperform local updates and analyzing their optimal conditions and relative advantages.

Contribution

It provides a comparative analysis of two non-local update algorithms for PIMC, highlighting their performance improvements and operational conditions.

Findings

Both algorithms reduce autocorrelation times compared to local updates.

Staging algorithm performs optimally under specific conditions.

Multigrid method also effectively mitigates slowing down in simulations.

Abstract

We present a comparison of the performance of two non-local update algorithms for path integral Monte Carlo (PIMC) simulations, the multigrid Monte Carlo method and the staging algorithm. Looking at autocorrelation times for the internal energy we show that both refined algorithms beat the slowing down which is encountered for standard local update schemes in the continuum limit. We investigate the conditions under which the staging algorithm performs optimally and give a brief discussion of the mutual merits of the two algorithms.