Boosting the accuracy and speed of quantum Monte Carlo: size-consistency and time-step

TL;DR

This paper introduces a new Green function modification for diffusion Monte Carlo that restores size-consistency at large time-steps, significantly reducing errors and enabling faster, more accurate simulations of complex molecular and crystal systems.

Contribution

The authors propose a simple Green function modification that improves size-consistency and reduces time-step errors in DMC simulations, leading to substantial speedups.

Findings

Restores size-consistency at large time-steps in DMC.

Reduces time-step errors significantly.

Achieves up to two orders of magnitude speedup.

Abstract

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard to provide high quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation relies on modifications of the Green function to avoid singularities near the nodal surface of the trial wavefunction. We show that these modifications affect the DMC energies in a way that is not size-consistent, resulting in large time-step errors. Building on the modifications of Umrigar {\em et al.} and of DePasquale {\em et al.} we propose a simple Green function modification that restores size-consistency to large values of time-step; substantially reducing the time-step errors. The new algorithm also yields remarkable speedups of up to two orders of magnitude in the calculation of molecule-molecule binding energies and crystal cohesive energies, thus extending the horizons of what is possible with DMC.