解决规范场论中拓扑冻结问题，实现小格点间距下的高效采样。
Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
- 用非平衡蒙特卡洛方法逐步引入周期边界，消除物理效应偏差。
- 在0.045飞米格点间距下实现拓扑采样控制，显著降低自相关。
- 设计专用随机归一化流，性能优于纯随机方法，适合未来高效采样。
我们提出一种基于非平衡模拟的方法，以缓解接近连续极限时格点规范场论中的拓扑冻结问题。通过采用开放边界条件降低拓扑电荷的自相关性，并利用非平衡蒙特卡洛方法逐步引入周期边界条件，精确消除其非物理影响。针对四维SU(3)杨-米尔斯理论，详细分析了该策略的计算成本。在实现完全尺度控制后，提出一种在连续极限下高效采样拓扑结构的明确方案，并在最小格点间距达0.045 fm时验证了其有效性。此外，通过设计定制化的随机归一化流（Stochastic Normalizing Flow）来演化边界条件，性能优于纯随机非平衡方法，为未来更高效的基于流的方法铺平了道路。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。