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How does Gauge Cooling Stabilize Complex Langevin?

How does Gauge Cooling Stabilize Complex Langevin?
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Year:    2020

Author:    Zhenning Cai, Yana Di, Xiaoyu Dong

Communications in Computational Physics, Vol. 27 (2020), Iss. 5 : pp. 1344–1377

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Communications in Computational Physics, Vol. 27 (2020), Iss. 5 : pp. 1344–1377

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:    Complex Langevin method gauge cooling Polyakov loop.

Author Details

Zhenning Cai

Yana Di

Xiaoyu Dong

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