Combining Harmonic Sampling with the Worm Algorithm to Improve the Efficiency of Path Integral Monte Carlo Article Swipe

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Sourav Karmakar , S. Paul , Adrian Del Maestro , Barak Hirshberg ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2511.04597

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, to optimize efficiency. We benchmark H-PIMC on systems with increasing anharmonicity, improving the acceptance ratio and lowering the auto-correlation time. For weakly to moderately anharmonic systems, at $β\hbar ω=16$, 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 four-fold 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 auto-correlation 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.

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Type: preprint
Landing Page: http://arxiv.org/abs/2511.04597
PDF: https://arxiv.org/pdf/2511.04597
OA Status: green
OpenAlex ID: https://openalex.org/W4416026977

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DOI: https://doi.org/10.48550/arxiv.2511.04597

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Title: Combining Harmonic Sampling with the Worm Algorithm to Improve the Efficiency of Path Integral Monte Carlo

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Type: preprint

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Publication year: 2025

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Publication date: 2025-11-06

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Authors: Sourav Karmakar, S. Paul, Adrian Del Maestro, Barak Hirshberg

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Landing page: https://arxiv.org/abs/2511.04597

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