Atomic forces by quantum Monte Carlo: Application to phonon dispersion calculations

We report a successful application of the 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, and improving upon previous density functional theory estimates. Key to success for the QMC approach is the statistical error reduction in the atomic force evaluation. We show that this can be achieved by using well conditioned atomic basis sets and by explicitly removing the basis-set redundancy, which reduces the statistical error of forces by up to two orders of magnitude by combining it with the so-called space-warp transformation algorithm. This leads to affordable and accurate QMC-phonons calculations, which are up to 10(4) times more efficient than a bare force treatment, and paves the way to new applications, particularly in correlated materials, where phonons have been poorly reproduced so far.