Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain

TL;DR

This paper introduces a novel Path Integral Monte Carlo method using Gibbs sampling for simulating a chain of dipolar planar rotors, demonstrating improved efficiency and accuracy over traditional sampling techniques.

Contribution

The work develops a PIMC approach with Gibbs sampling for discretized continuous variables, validated on dipolar rotor chains, and compares favorably to existing methods like DMRG and exact diagonalization.

Findings

Gibbs sampling reduces variance and correlation in Monte Carlo simulations.

The method accurately computes energetic and structural properties for chains up to 100 rotors.

Systematic Trotter error convergence is demonstrated and benchmarked against established techniques.

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 $N \leq 3$ 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.