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

摘要

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