Combining harmonic sampling with the worm algorithm to improve the efficiency of path integral Monte Carlo.

Abstract

We propose an improved Path Integral Monte Carlo (PIMC) algorithm called harmonic PIMC (H-PIMC) and its generalization, mixed PIMC (M-PIMC). PIMC is a powerful tool for studying quantum condensed phases. However, it often suffers from a low acceptance ratio for solids and dense confined liquids. We develop two sampling schemes especially suited for such problems by dividing the potential into its harmonic and anharmonic contributions. In H-PIMC we generate the imaginary time paths for the harmonic part of the potential exactly and accept or reject it based on the anharmonic part. In M-PIMC we restrict the harmonic sampling to the vicinity of local minimum and use standard PIMC otherwise, in order to optimize efficiency. We benchmark H-PIMC on systems with increasing anharmonicity, improving the acceptance ratio and lowering the autocorrelation time. For weakly to moderately anharmonic systems, at βℏω=16, H-PIMC improves the acceptance ratio by a factor of 6-16 and reduces the autocorrelation time by a factor of 7-30. We also find that the method requires a smaller number of imaginary time slices for convergence, which leads to another two- to threefold acceleration. For strongly anharmonic systems, M-PIMC converges with a similar number of imaginary time slices as standard PIMC but allows the optimization of the autocorrelation time. We extend M-PIMC to periodic systems and apply it to a sinusoidal potential. Finally, we combine H- and M-PIMC with the worm algorithm, allowing us to obtain similar efficiency gains for systems of indistinguishable particles.