Comparative studies of the deformation techniques for the singular-drift problem in the complex Langevin method

Abstract

In application of the complex Langevin method to QCD at high density and low temperature, the singular-drift problem occurs due to the appearance of near-zero eigenvalues of the Dirac operator. In order to avoid this problem, we proposed to deform the Dirac operator in such a way that the near-zero eigenvalues do not appear and to extrapolate the deformation parameter to zero from the available data points. Here we test three different types of deformation in a simple large-$N$ matrix model, which undergoes an SSB due to the phase of the fermion determinant, and compare them to see the consistency with one another.