Pair Approximating the Action For Molecular Rotations in Path Integral Monte Carlo

TL;DR

This paper introduces a pair-DVR approach for molecular rotations in path integral Monte Carlo, improving convergence and accuracy for systems with pair-wise interactions by leveraging the pair propagator and PIGS framework.

Contribution

The work develops a novel pair-DVR method integrated with PIGS to enhance path sampling accuracy for molecular rotations with pair interactions.

Findings

Pair-DVR converges faster than primitive methods.

Accurate energetic and structural properties obtained.

Method performs well near criticality.

Abstract

Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair Discrete Variable Representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed Helium, is naturally well-suited for systems interacting with a pair-wise potential. Consequently, paths sampled using the pair action tend to be closer to the exact paths (compared to primitive Trotter paths) for such systems leading to convergence with less imaginary time steps. Therefore, our approach relies on using the pair factorization approach in conjunction with a discretized Path Integral Ground State (PIGS) paradigm to study a chain of planar rotors interacting with a pair-wise dipole interaction. We first use the Wigner-Kirkwood density expansion to analyze the asymptotics of the pair propagator in imaginary time. Then, we exhibit the utility of the pair factorization scheme via convergence studies comparing the pair and primitive propagators. Finally, we compute energetic and structural properties of this system including the correlation function and Binder ratio as functions of the coupling strength to examine the behaviour of the pair-DVR method near criticality. Density Matrix Renormalization Group results are used for benchmarking throughout.