Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918437269274624 |
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| author | Bonanno, Claudio Bulgarelli, Andrea Cellini, Elia Nada, Alessandro Panfalone, Dario Vadacchino, Davide Verzichelli, Lorenzo |
| author_facet | Bonanno, Claudio Bulgarelli, Andrea Cellini, Elia Nada, Alessandro Panfalone, Dario Vadacchino, Davide Verzichelli, Lorenzo |
| contents | We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge employing open boundary conditions, while removing exactly their unphysical effects using a non-equilibrium Monte Carlo approach in which periodic boundary conditions are gradually switched on. We perform a detailed analysis of the computational costs of this strategy in the case of the four-dimensional $\mathrm{SU}(3)$ Yang-Mills theory. After achieving full control of the scaling, we outline a clear strategy to sample topology efficiently in the continuum limit, which we check at lattice spacings as small as $0.045$ fm. We also generalize this approach by designing a customized Stochastic Normalizing Flow for evolutions in the boundary conditions, obtaining superior performances with respect to the purely stochastic non-equilibrium approach, and paving the way for more efficient future flow-based solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_25704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory Bonanno, Claudio Bulgarelli, Andrea Cellini, Elia Nada, Alessandro Panfalone, Dario Vadacchino, Davide Verzichelli, Lorenzo High Energy Physics - Lattice Statistical Mechanics Machine Learning High Energy Physics - Phenomenology We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge employing open boundary conditions, while removing exactly their unphysical effects using a non-equilibrium Monte Carlo approach in which periodic boundary conditions are gradually switched on. We perform a detailed analysis of the computational costs of this strategy in the case of the four-dimensional $\mathrm{SU}(3)$ Yang-Mills theory. After achieving full control of the scaling, we outline a clear strategy to sample topology efficiently in the continuum limit, which we check at lattice spacings as small as $0.045$ fm. We also generalize this approach by designing a customized Stochastic Normalizing Flow for evolutions in the boundary conditions, obtaining superior performances with respect to the purely stochastic non-equilibrium approach, and paving the way for more efficient future flow-based solutions. |
| title | Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory |
| topic | High Energy Physics - Lattice Statistical Mechanics Machine Learning High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2510.25704 |