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 $N\le 3$ 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.

References in corpus (5)

• The density-matrix renormalization group in the age of matrix product states
• The ITensor Software Library for Tensor Network Calculations
• A quantum phase transition in the one-dimensional water chain
• Quantum criticality in chains of planar rotors with dipolar interactions
• Effect of neighbouring molecules on ground-state properties of many-body polar linear rotor systems

Cited by in corpus (3)

• Pair Approximating the Action For Molecular Rotations in Path Integral Monte Carlo
• Path Integral Monte Carlo in the Angular Momentum Basis for a Chain of Planar Rotors
• Qubit encodings for lattices of dipolar planar rotors