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 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 ≤ 3 to assess the systematic Trotter factorization error convergence. For larger chains with up to N = 100 rotors, Density Matrix Renormalization Group calculations are used as a benchmark. We show that using Gibbs sampling is advantageous compared to traditional Metropolis–Hastings rejection importance sampling. Indeed, Gibbs sampling leads to lower variance and correlation in the computed observables.