Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914271293603840 |
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| author | Zhang, Wenxue Moeed, Muhammad Shaeer Bright, Andrew Serwatka, Tobias De Oliveira, Estevao Roy, Pierre-Nicholas |
| author_facet | Zhang, Wenxue Moeed, Muhammad Shaeer Bright, Andrew Serwatka, Tobias De Oliveira, Estevao Roy, Pierre-Nicholas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain Zhang, Wenxue Moeed, Muhammad Shaeer Bright, Andrew Serwatka, Tobias De Oliveira, Estevao Roy, Pierre-Nicholas Chemical Physics Mesoscale and Nanoscale Physics Statistical Mechanics Atomic and Molecular Clusters Quantum Physics 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. |
| title | Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain |
| topic | Chemical Physics Mesoscale and Nanoscale Physics Statistical Mechanics Atomic and Molecular Clusters Quantum Physics |
| url | https://arxiv.org/abs/2410.13633 |