基于Schwinger-Dyson方程的Diagrammatic Monte-Carlo算法的Metropolis修正
Metropolis updates for Diagrammatic Monte-Carlo algorithms from Schwinger-Dyson equations
摘要：
基于量子场论中的Schwinger-Dyson方程，我们描述了一种构造Metropolis更新的Diagrammatic Monte-Carlo（DiagMC）算法的一般方法。这种方法绕过了显式的对偶变换，枚举或分类图，并可用于具有未知或复杂对偶表示的格点量子场论（如非阿贝尔格点规范理论）。以这种方式构造的DiagMC算法仍然会受到符号问题的困扰，然而，符号问题与传统蒙特卡罗模拟中的符号问题完全不同，并且其起源于具有正和负权重的图之间的取消。为了测试所提出的方法，我们应用DiagMC计算的前7个订单的1/N扩展的四次矩阵模型，并找到良好的协议与解析结果，除了附近的临界耦合的临界减速集。
英文摘要：
We describe a general recipe for constructing Metropolis updates for Diagrammatic Monte-Carlo (DiagMC) algorithms, based on the Schwinger-Dyson equations in quantum field theory. This approach bypasses explicit duality transformations, enumeration or classification of diagrams and can be used for lattice quantum field theories with unknown or complicated dual representations (such as non-Abelian lattice gauge theories). DiagMC algorithms constructed in this way can still be plagued by the sign problem, which is, however, completely different from the sign problem in conventional Monte-Carlo simulations and has its origin in cancellations between diagrams with positive and negative weights. To test the presented approach, we apply DiagMC to calculate the first 7 orders of 1/N expansion in the quartic matrix model and find good agreement with analytic results, with the exception of the close vicinity of the critical coupling where the critical slowing down sets in.
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