通过归一化流实现费曼图的全局采样
Global sampling of Feynman's diagrams through Normalizing Flow
AI总结：
本研究将归一化流集成到图解蒙特卡洛中，通过解耦图阶数与相互作用时间采样、迭代构建费曼图，在单格点Holstein极化子模型全耦合区间验证了其可准确复现图分布、降低样本相关性与统计误差。
摘要：
归一化流（Normalizing Flows, NF）是一类强大的生成模型，凭借其高度灵活性与表达能力，在增强蒙特卡洛算法方面的应用日益广泛。本研究探索将NF集成到图解蒙特卡洛（Diagrammatic Monte Carlo, DMC）中，提出一种旨在通过降维对费曼图复杂多维空间进行采样的架构。通过将图阶数与相互作用时间的采样解耦，该流每次聚焦于一个相互作用。这使得我们可以迭代使用同一无监督模型构建通用图，用先前采样的阶数所确定的相互作用来修饰零阶图。我们在广泛使用的单格点Holstein极化子模型的整个电子-声子耦合区间内，测试了所得的NF增强DMC。所得数据表明，该模型准确复现了图分布，降低了样本相关性，并减小了极化子结合能、相互作用格林函数等可观测量的统计误差。
英文摘要：
Normalizing Flows (NF) are powerful generative models with increasing applications in augmenting Monte Carlo algorithms due to their high flexibility and expressiveness. In this work we explore the integration of NF in Diagrammatic Monte Carlo (DMC), presenting an architecture designed to sample the intricate multidimensional space of Feynman's diagrams through dimensionality reduction. By decoupling the sampling of diagram order and interaction times, the flow focuses on one interaction at a time. This enables constructing a general diagram by employing the same unsupervised model iteratively, dressing a zero-order diagram with interactions determined by the previously sampled order. The resulting NF-augmented DMC is tested on the widely used single-site Holstein polaron model in the entire electron-phonon coupling regime. The obtained data show that the model accurately reproduces the diagram distribution reducing sample correlation and statistical error for observables such as the polaron binding energy and the interacting Green's function.
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