Atomic forces by quantum Monte Carlo: application to phonon dispersion calculation

TL;DR

This paper demonstrates the first successful use of quantum Monte Carlo methods to calculate phonon dispersion in diamond, achieving high accuracy and efficiency improvements over traditional density functional theory.

Contribution

It introduces a novel application of ab initio QMC to phonon calculations, significantly reducing statistical errors and enabling more accurate phonon predictions in correlated materials.

Findings

QMC-phonon dispersion closely matches experimental data

Statistical error in force evaluation reduced by two orders of magnitude

QMC calculations are up to 10,000 times more efficient than previous methods

Abstract

We report the first successful application of the {\it ab initio} quantum Monte Carlo (QMC) framework to a phonon dispersion calculation. A full phonon dispersion of diamond is successfully calculated at the variational Monte Carlo (VMC) level, based on the frozen-phonon technique. The VMC-phonon dispersion is in good agreement with the experimental results, giving renormalized harmonic optical frequencies very close to the experimental values, by significantly improving upon density functional theory (DFT) in the generalized gradient approximation. Key to success for the QMC approach is the statistical error reduction in atomic force evaluation. We show that this can be achieved by using well conditioned atomic basis sets, by explicitly removing the basis-set redundancy, which reduces the statistical error of forces by up to two orders of magnitude. This leads to affordable and accurate QMC-phonons calculations, up to $10^{4}$ times more efficient than previous attempts, and paves the way to new applications, particularly in correlated materials, where phonons have been poorly reproduced so far.