Gauge cooling for the singular-drift problem in the complex Langevin method
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.
I will explain the idea of our method, what criteria allows us to avoid the singular drift problem. Applying the method to chiral Random Matrix Theory, I will show that the method indeed works for the chRMT, where the gauge cooling changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. This change of the eigenvalue distribution is explained by a generalized Banks-Casher relation.
I will also present a result for finite density QCD in the confinement phase.
K. Nagata, J. Nishimura, S. Shimasaki, arXiv:1604.07717, arXiv:1511.08580.