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

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

Keitaro Nagata
(
- KEK, Tsukuba
)
,
Jun Nishimura
(
- KEK, Tsukuba and
- Tsukuba, Graduate U. Adv. Studies
)
,
Shinji Shimasaki
(
- KEK, Tsukuba and
- Keio U.
)

Apr 26, 2016

20 pages

Published in:

JHEP 07 (2016) 073

Published: Jul 14, 2016

e-Print:

1604.07717 [hep-lat]

DOI:

10.1007/JHEP07(2016)073

Report number:

KEK-TH-1854,
KEK-CP-322

View in:

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Abstract: (arXiv)

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.

Note:

20 pages, 4 figures. One reference is added in version 2

Phase Diagram of QCD
Lattice QCD
Langevin equation: complex
matrix model: random
matrix model: chiral
quantum chromodynamics: density
density: finite
operator: Dirac
energy levels
transformation: gauge

References(40)

Figures(9)

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