Controlling complex Langevin simulations of lattice models by boundary term analysis
Controlling complex Langevin simulations of lattice models by boundary term analysis
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DOI：
10.1103/physrevd.101.014501
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发表时间：
2019-10
影响因子：
5
通讯作者：
M. Scherzer;E. Seiler;D. Sexty;I. Stamatescu
中科院分区：
文献类型：
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作者：
M. Scherzer;E. Seiler;D. Sexty;I. Stamatescu
众所周知，复朗之万 (CL) 方法有时无法收敛或收敛到错误的极限，这一事实的一个原因很久以前就已被确定：接近无穷大或接近漂移极点的概率密度衰减不充分，导致边界项破坏了正确性的形式论证。为了更深入地理解这种现象，在之前的论文中，我们在一个简单的模型中彻底研究了此类边界项的出现，其中分析结果可以与数值进行比较。在这里，我们继续对更多物理上有趣的模型进行这种类型的分析，重点关注无穷远的边界。我们从阿贝尔和非阿贝尔单斑块模型开始，然后进行 Polyakov 链模型，最后进行高密度 QCD (HDQCD) 和 3D XY 模型。我们证明使用边界项直接估计 CL 方法的系统误差原则上是可能的。
One reason for the well known fact that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, in a previous paper we have studied the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. Here we continue this type of analysis for more physically interesting models, focusing on the boundaries at infinity. We start with abelian and non-abelian one-plaquette models, then we proceed to a Polyakov chain model and finally to high density QCD (HDQCD) and the 3D XY model. We show that the direct estimation of the systematic error of the CL method using boundary terms is in principle possible.