Scaling flow-based approaches for topology sampling in $mathrm{SU}(3)$ gauge theory

2025-10-29

AI Summary

Topological freezing in four-dimensional SU(3) lattice gauge theory severely impedes reliable sampling of the topological charge near the continuum limit. To address this, we propose a novel non-equilibrium Monte Carlo sampling method: it initiates simulations with open boundary conditions and progressively switches to periodic boundaries, while employing a custom-designed stochastic normalizing flow to optimize the boundary evolution. This approach dramatically suppresses topological charge autocorrelations, enabling efficient and controllable sampling of topological sectors. We validate the method on fine lattices with spacing down to 0.045 fm, confirming good scaling behavior and demonstrating a substantial improvement in sampling efficiency over conventional stochastic methods. Our work establishes a scalable new paradigm for overcoming the topological freezing bottleneck and advancing flow-based lattice algorithms.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Mitigating topological freezing in lattice gauge theories near continuum limit
• Reducing topological charge autocorrelation using open boundary conditions
• Developing efficient topology sampling strategies for SU(3) Yang-Mills theory

Innovation

• Out-of-equilibrium simulations mitigate topological freezing
• Open boundary conditions reduce topological charge autocorrelation
• Customized Stochastic Normalizing Flow enhances boundary evolution performance