Test for a universal behavior of Dirac eigenvalues in the complex Langevin method

Understand

We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at non-zero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues.

• The NNS distribution is extracted using an unfolding procedure for the Dirac eigenvalues obtained in the CL method.
• For large quark mass, we find that the NNS distribution obeys the Ginibre ensemble as expected.
• For small quark mass, the NNS distribution follows the Wigner surmise for correct convergence case, while it follows the Ginibre ensemble for wrong convergence case.