Worldvolume Hybrid Monte Carlo algorithm for group manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911551702695936 |
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| author | Fukuma, Masafumi |
| author_facet | Fukuma, Masafumi |
| contents | The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the numerical sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based approaches while maintaining low computational costs. In this paper, as a general framework for applying WV-HMC to lattice gauge theories, we extend the algorithm to systems defined on compact group manifolds. The key is to introduce a symplectic structure on the tangent bundle of the worldvolume and formulate molecular dynamics upon it. The validity of the proposed algorithm is demonstrated using the one-site model with a purely imaginary coupling constant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_12002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Worldvolume Hybrid Monte Carlo algorithm for group manifolds Fukuma, Masafumi High Energy Physics - Lattice High Energy Physics - Theory The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the numerical sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based approaches while maintaining low computational costs. In this paper, as a general framework for applying WV-HMC to lattice gauge theories, we extend the algorithm to systems defined on compact group manifolds. The key is to introduce a symplectic structure on the tangent bundle of the worldvolume and formulate molecular dynamics upon it. The validity of the proposed algorithm is demonstrated using the one-site model with a purely imaginary coupling constant. |
| title | Worldvolume Hybrid Monte Carlo algorithm for group manifolds |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.12002 |