Population size bias in Diffusion Monte Carlo

TL;DR

This paper investigates how the required population size in Diffusion Monte Carlo scales with system size, revealing significant biases that affect energy estimates and comparing DMC with PIGS methods.

Contribution

It demonstrates the population bias in DMC increases with system size and compares its scaling to PIGS, highlighting the latter's advantages for large systems.

Findings

Population size bias in DMC grows with system size.

DMC and PIGS yield different energy estimates for small clusters.

PIGS scales more favorably than DMC for large systems.

Abstract

The size of the population of random walkers required to obtain converged estimates in DMC increases dramatically with system size. We illustrate this by comparing ground state energies of small clusters of parahydrogen (up to 48 molecules) computed by Diffusion Monte Carlo (DMC) and Path Integral Ground State (PIGS) techniques. We contend that the bias associated to a finite population of walkers is the most likely cause of quantitative numerical discrepancies between PIGS and DMC energy estimates reported in the literature, for this few-body Bose system. We discuss the viability of DMC as a general-purpose ground state technique, and argue that PIGS, and even finite temperature methods, enjoy more favorable scaling, and are therefore a superior option for systems of large size.