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arXiv · 2410.13633

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

Wenxue Zhang·Muhammad Shaeer Moeed·Andrew Bright·Tobias Serwatka·Estevao De Oliveira·Pierre-Nicholas Roy
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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.

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Wenxue Zhang, Muhammad Shaeer Moeed, Andrew Bright, Tobias Serwatka, Estevao De Oliveira, Pierre-Nicholas Roy. 2024-10-17. Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain. https://doi.org/10.1063/5.0244162

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