How does Gauge Cooling Stabilize Complex Langevin?

Authors

  • Zhenning Cai Department of Mathematics, National University of Singapore, Level 4, Block S17, 10 Lower Kent Ridge Road, Singapore 119076.
  • Yana Di Division of Science and Technology, BNU-HKBU United International College, Zhuhai 519087, China.
  • Xiaoyu Dong LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.

DOI:

https://doi.org/10.4208/cicp.OA-2019-0126

Keywords:

Complex Langevin method, gauge cooling, Polyakov loop.

Abstract

We study the mechanism of the gauge cooling technique to stabilize the complex Langevin method in the one-dimensional periodic setting. In this case, we find the exact solutions for the gauge transform which minimizes the Frobenius norm of link variables. Thereby, we derive the underlying stochastic differential equations by continuing the numerical method with gauge cooling, and thus provide a number of insights on the effects of gauge cooling. A specific case study is carried out for the Polyakov loop model in SU(2) theory, in which we show that the gauge cooling may help form a localized distribution to guarantee there is no excursion too far away from the real axis. 

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Published

2020-05-06

Issue

Vol. 27 No. 5 (2020)

Section

Articles