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

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Abstract
We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at nonzero 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 the correct convergence case, while it follows the Ginibre ensemble for the wrong convergence case. The Wigner surmise is physically reasonable from the chemical potential independence of the ChRMT. The Ginibre ensemble is known to be favored in a phase-quenched QCD at finite chemical potential. Our result suggests a possibility that the originally universal behavior of the NNS distribution is preserved even in the CL method for the correct convergence case.
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Funding Information
  • Japan Society for the Promotion of Science (25-2059, 26-1717, 26800154)
  • Ministry of Education, Culture, Sports, Science, and Technology
  • Osaka University
  • Kyoto University (SR16000)
  • JICFuS

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