Generalized Suzuki-Chin Factorization in Bosonic Path Integral Molecular Dynamics

TL;DR

This paper demonstrates that the generalized Suzuki-Chin factorization improves convergence in bosonic path integral molecular dynamics simulations, effectively speeding up calculations without significant additional computational cost.

Contribution

The study extends the GSF decomposition to bosonic PIMD, showing it enhances convergence and can be integrated with quadratic scaling methods without modifications.

Findings

GSF improves convergence speed by a factor of 2-4 across temperatures.

GSF can be applied as a re-weighting factor without altering sampling.

The method is effective for both bosonic and fermionic expectation values.

Abstract

Modern implementations of path integral molecular dynamics (PIMD) simulations of distinguishable particles frequently make use of high order factorization schemes for the Boltzmann operator to expedite convergence of equilibrium averages. Among these methods is the generalized Suzuki-Chin factorization (GSF), which is accurate up to fourth order in the imaginary-time step. In this work, we show that the GSF decomposition of the Boltzmann operator is applicable to bosonic PIMD, and results in an improved convergence of estimators. In particular, we show that the recently developed quadratic scaling bosonic PIMD need not change when using the GSF. The GSF scheme is implemented as a re-weighting factor for observables, without affecting the sampling generated by the standard, second-order, primitive factorization. We study the effect of this factorization for bosons in a harmonic trap and a sinusoidal potential. We also assess the effectiveness of GSF in calculating fermionic expectation values for harmonically-trapped atoms. In all these cases, we find that the GSF speeds up convergence with the Trotter number by a factor of $\sim 2-4$ across a wide temperature range, at only a modest computational cost.