Fokker-Planck equation governing the distribution of walkers in AFQMC
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914108884910080 |
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| author | Li, Alfred Mahajan, Ankit Sharma, Sandeep |
| author_facet | Li, Alfred Mahajan, Ankit Sharma, Sandeep |
| contents | Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. In this paper, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wavefunction actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wavefunction in constrained path AFQMC, contrary to the common assumption, the wavefunction sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fokker-Planck equation governing the distribution of walkers in AFQMC Li, Alfred Mahajan, Ankit Sharma, Sandeep Chemical Physics Strongly Correlated Electrons Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. In this paper, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wavefunction actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wavefunction in constrained path AFQMC, contrary to the common assumption, the wavefunction sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this paper. |
| title | Fokker-Planck equation governing the distribution of walkers in AFQMC |
| topic | Chemical Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2510.19914 |