As lattice gauge theories with non-trivial topological features are driven towards the continuum limit, standard Markov Chain Monte Carlo simulations suffer for topological freezing, i.e., a dramatic growth of autocorrelations in topological observables. A widely used strategy is the adoption of Open Boundary Conditions (OBC), which restores ergodic sampling of topology but at the price of breaking translation invariance and introducing unphysical boundary artifacts. In this contribution we summarize a scalable, exact flow-based strategy to remove them by transporting configurations from a prior with a OBC defect to a fully periodic ensemble, and apply it to 4d SU(3) Yang--Mills theory. The method is based on a Stochastic Normalizing Flow (SNF) that alternates non-equilibrium Monte Carlo updates with localized, gauge-equivariant defect coupling layers implemented via masked parametric stout smearing. Training is performed by minimizing the average dissipated work, equivalent to a Kullback--Leibler divergence between forward and reverse non-equilibrium path measures, to achieve more reversible trajectories and improved efficiency. We discuss the scaling with the number of degrees of freedom affected by the defect and show that defect SNFs achieve better performances than purely stochastic non-equilibrium methods at comparable cost. Finally, we validate the approach by reproducing reference results for the topological susceptibility.

翻译：随着具有非平凡拓扑特征的格点规范理论趋近于连续极限，标准的马尔可夫链蒙特卡洛模拟会受到拓扑冻结的影响，即拓扑可观测量自相关的急剧增长。一种广泛采用的策略是采用开放边界条件，这能恢复拓扑的遍历采样，但代价是破坏了平移不变性并引入了非物理的边界伪影。在本研究中，我们总结了一种可扩展的、精确的基于流的方法，通过将具有开放边界条件缺陷的构型传输到完全周期性的系综中来消除这些伪影，并将其应用于四维SU(3)杨-米尔斯理论。该方法基于随机归一化流，该流交替使用非平衡蒙特卡洛更新与通过掩码参数化stout涂抹实现的局域化、规范等变的缺陷耦合层。训练通过最小化平均耗散功来完成，这等价于前向与反向非平衡路径测度之间的Kullback-Leibler散度，以实现更高的可逆性和改进的效率。我们讨论了受缺陷影响的自由度数量带来的标度问题，并表明在可比成本下，缺陷随机归一化流比纯随机的非平衡方法获得了更好的性能。最后，我们通过复现拓扑磁化率的参考结果验证了该方法的有效性。