Some remarks on Lefschetz thimbles and complex Langevin dynamics
Some remarks on Lefschetz thimbles and complex Langevin dynamics
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关于 Lefschetz 顶针和复杂 Langevin 动力学的一些评论
DOI：
10.1007/jhep10(2014)159
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发表时间：
2014
影响因子：
5.4
通讯作者：
D. Sexty
中科院分区：
文献类型：
--
作者：
G. Aarts;L. Bongiovanni;E. Seiler;D. Sexty
Lefschetz顶针和复杂朗之万动力学都提供了一种方法来解决在配分函数中具有复权重的理论中普遍存在的数值符号问题，例如由于非零化学势。这里我们收集了四次模型的一些结果，以及U(1)和SU(2)模型在行列式存在时的一些结果，由于奇异漂移，这些模型具有一些以前没有讨论过的特征。我们找到了经典逃逸与稳定顶针之间关系的证据，并给出了一个退化不动点的例子。我们通常发现，在复杂的朗之万动力学中采样的分布与顶针(S)有关，但有一些重要的警告，例如由于朗之万动力学中存在不稳定的不动点。
Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, eg due to nonzero chemical potential. Here we collect some findings for the quartic model, and for U (1) and SU (2) models in the presence of a determinant, which have some features not discussed before, due to a singular drift. We find evidence for a relation between classical runaways and stable thimbles, and give an example of a degenerate fixed point. We typically find that the distributions sampled in complex Langevin dynamics are related to the thimble (s), but with some important caveats, for instance due to the presence of unstable fixed points in the Langevin dynamics.