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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 extractedusing an unfolding procedure for the Dirac eigenvalues obtained in the CLmethod. For large quark mass, we find that the NNS distribution obeys theGinibre ensemble as expected. For small quark mass, the NNS distributionfollows the Wigner surmise for correct convergence case, while it follows theGinibre ensemble for wrong convergence case. The Wigner surmise is physicallyreasonable from the chemical potential independence of the ChRMT. The Ginibreensemble is known to be favored in a phase quenched QCD at finite chemicalpotential. Our result suggests a possibility that the originally universalbehavior of the NNS distribution is preserved even in the CL method for correctconvergence case.

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