Lefschetz顶针的模拟测量理论

J. Pawlowski, M. Scherzer, C. Schmidt, Felix Ziegler, F. Ziesch'e
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引用次数: 3

摘要

Lefschetz顶针最近被提出作为蒙特卡罗模拟中复杂动作问题(符号问题)的一种可能的解决方案。本文讨论了具有复耦合的纯阿贝尔规范理论,并应用了广义Lefschetz顶针的概念。我们提出将切向流形的并集理论模拟为顶针。我们构造了一个局部的metropolis型算法,该算法被约束于一个特定的切流形。我们还讨论了如何从这个结果出发,通过重新加权的方法来考虑连续次超前切向流形。在1+1维的$U(1)$规范理论上证明了该算法,并研究了剩余符号问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Simulating gauge theories on Lefschetz Thimbles
Lefschetz thimbles have been proposed recently as a possible solution to the complex action problem (sign problem) in Monte Carlo simulations. Here we discuss pure abelian gauge theory with a complex coupling $\beta$ and apply the concept of Generalized Lefschetz thimbles. We propose to simulate the theory on the union of the tangential manifolds to the thimbles. We construct a local Metropolis-type algorithm, that is constrained to a specific tangential manifold. We also discuss how, starting from this result, successive subleading tangential manifolds can be taken into account via a reweighting approach. We demonstrate the algorithm on $U(1)$ gauge theory in 1+1 dimensions and investigate the residual sign problem.
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