Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain
Abstract
In this work, we propose a Path Integral Monte Carlo (PIMC) approach based on discretized continuous degrees of freedom and rejection-free Gibbs sampling. The ground state properties of a chain of planar rotors with dipole-dipole interactions are used to illustrate the approach. Energetic and structural properties are computed and compared to exact diagonalization and Numerical Matrix Multiplication for to assess the systematic Trotter factorization error convergence. For larger chains with up to N = 100 rotors, Density Matrix Renormalization Group (DMRG) calculations are used as a benchmark. We show that using Gibbs sampling is advantageous compared to traditional Metroplolis-Hastings rejection importance sampling. Indeed, Gibbs sampling leads to lower variance and correlation in the computed observables.
Cite
@article{arxiv.2410.13633,
title = {Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain},
author = {Wenxue Zhang and Muhammad Shaeer Moeed and Andrew Bright and Tobias Serwatka and Estevao De Oliveira and Pierre-Nicholas Roy},
journal= {arXiv preprint arXiv:2410.13633},
year = {2026}
}