2024/10/17 by Wenxue Zhang, Zhang, Wenxue, Muhammad Shaeer Moeed +7 · 2 citations
Mathematics · Physics and Astronomy · #Atomic and Molecular Clusters (physics.atm-clus) #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2410.13633
openalex publication_date 2024/10/17 · openalex created_date 2024/10/21 · openalex updated_date 2026/07/28
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 ≤ 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.