Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD

Nagata, Keitaro (KEK Theory Center, High Energy0 Accelerator Research Organization, 1-1 Oho, Tsukuba, 305-0801, Japan) ; Nishimura, Jun (KEK Theory Center, High Energy0 Accelerator Research Organization, 1-1 Oho, Tsukuba, 305-0801, Japan) (Department of Particle and Nuclear Physics, School of High Energy Accelerator Science, Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba, 305-0801, Japan) ; Shimasaki, Shinji (KEK Theory Center, High Energy0 Accelerator Research Organization, 1-1 Oho, Tsukuba, 305-0801, Japan) (Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa, 223-8521, Japan)

15 July 2016

Abstract: Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.


Published in: JHEP 1607 (2016) 073
Published by: Springer/SISSA
DOI: 10.1007/JHEP07(2016)073
arXiv: 1604.07717
License: CC-BY-4.0



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