Extended framework for the hybrid Monte Carlo in lattice gauge theory
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916900571709440 |
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| author | Christ, Norman H. Jin, Lu-Chang Lehner, Christoph Lundstrum, Erik Matsumoto, Nobuyuki |
| author_facet | Christ, Norman H. Jin, Lu-Chang Lehner, Christoph Lundstrum, Erik Matsumoto, Nobuyuki |
| contents | We develop an extended framework for the hybrid Monte Carlo (HMC) algorithm in lattice gauge theory by embedding the $SU(N)$ group into the space of general complex matrices,$M_N(\mathbb{C})$. Auxiliary directions will be completely factorized in the path integral, and the embedding does not alter the expectation values of the original theory. We perform the molecular dynamics updates by using the matrix elements of $W \in M_N(\mathbb{C})$ as the dynamical variables without group theoretic constraints. The framework enables us to introduce non-separable Hamiltonians for the HMC in lattice gauge theory exactly, whose immediate application includes the Riemannian manifold HMC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extended framework for the hybrid Monte Carlo in lattice gauge theory Christ, Norman H. Jin, Lu-Chang Lehner, Christoph Lundstrum, Erik Matsumoto, Nobuyuki High Energy Physics - Lattice We develop an extended framework for the hybrid Monte Carlo (HMC) algorithm in lattice gauge theory by embedding the $SU(N)$ group into the space of general complex matrices,$M_N(\mathbb{C})$. Auxiliary directions will be completely factorized in the path integral, and the embedding does not alter the expectation values of the original theory. We perform the molecular dynamics updates by using the matrix elements of $W \in M_N(\mathbb{C})$ as the dynamical variables without group theoretic constraints. The framework enables us to introduce non-separable Hamiltonians for the HMC in lattice gauge theory exactly, whose immediate application includes the Riemannian manifold HMC. |
| title | Extended framework for the hybrid Monte Carlo in lattice gauge theory |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2412.19904 |