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

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