发表机构
Berlin Institute for the Foundations of Learning and Data (BIFOLD); Technische Universität Berlin; Deutsches Elektronen-Synchrotron (DESY); Computation-Based Science and Technology Research Center, The Cyprus Institute; Bergische Universität Wuppertal; Department of Electrical Engineering (ESAT), KU Leuven; RIKEN Center for Advanced Intelligence Project (AIP)（柏林学习与数据基础研究所; 柏林工业大学; 德国电子同步加速器; 塞浦路斯研究所计算科学与技术研究中心; 伍珀塔尔山岳大学; 荷语鲁汶大学电气工程系; 理化学研究所先进智能项目中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出扇区分辨流采样混合方法，通过显式分辨拓扑扇区并利用生成模型评估配分函数，在二维U(1)晶格规范理论中克服拓扑冻结，实现无偏采样并大幅提升效率。
AI 中文摘要
拓扑涨落对于非微扰规范理论至关重要，但在趋向连续极限时变得越来越难以采样，此时马尔可夫链可能冻结在固定拓扑荷的扇区中。我们引入了一种生成式采样器，即扇区分辨采样器的混合（MSRS），它显式地分辨这些扇区，并利用了生成模型的一个关键优势——能够直接评估域限制配分函数，从而确定不连通扇区的相对权重。我们在一个参考拓扑扇区中训练生成模型，并结合一个双射拓扑移位，该移位确定性地将其样本映射到其他扇区。我们在二维紧致U(1)晶格规范理论中演示了该方法，在该理论中，它再现了拓扑荷分布，并在混合蒙特卡洛冻结且过度松弛给出不准确估计的区域内产生了无偏的磁化率。我们的方法还比现有基于流的采样器高出数个数量级。这些结果表明，显式扇区分辨为克服晶格规范理论中的拓扑障碍提供了一条有前景的途径。
英文摘要
Topological fluctuations are essential to nonperturbative gauge theories but become increasingly difficult to sample toward the continuum limit, where Markov chains can freeze in sectors of fixed topological charge. We introduce a generative sampler, a mixture of sector-resolved samplers (MSRS) that explicitly resolves these sectors and exploits a key advantage of generative models, the ability to directly evaluate the domain-restricted partition function and thereby determine the relative weights of disconnected sectors. We train a generative model in a reference topological sector combined with a bijective topological shift that deterministically maps its samples to other sectors. We demonstrate the method in two-dimensional compact U (1) lattice gauge theory, where it reproduces the topological-charge distribution and yields an unbiased susceptibility in a regime where hybrid Monte Carlo is frozen and overrelaxation gives inaccurate estimates. Our approach also outperforms existing flow-based samplers by orders of magnitude. These results demonstrate that explicit sector resolution provides a promising route to overcoming topological barriers in lattice gauge theory.
Comments9 pages, 7 figures
