Test for a universal behavior of Dirac eigenvalues in the complex Langevin method
Test for a universal behavior of Dirac eigenvalues in the complex Langevin method
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复朗之万方法中狄拉克特征值的普遍行为测试
DOI：
10.1103/physrevd.93.094511
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发表时间：
2016
影响因子：
5
通讯作者：
Kouji Kashiwa
中科院分区：
文献类型：
--
作者：
Terukazu Ichihara;Keitaro Nagata; Kouji Kashiwa
将复朗之万(CL)方法应用于非零化学势下的手征随机矩阵理论(ChRMT)，研究了狄拉克本征值的近邻间距(NNS)分布。对于在CL方法中获得的狄拉克特征值，使用展开过程来提取NNS分布。对于较大的夸克质量，我们发现NNS分布符合Ginibre系综。对于小夸克质量，NNS分布在正确的收敛情况下遵循Wigner猜测，而在错误的收敛情况下遵循Ginibre系综。根据ChRMT的化学势独立性，Wigner推测在物理上是合理的。在有限化学势下的相猝灭QCD中，Ginibre系综被认为是有利的。我们的结果表明，在正确收敛的情况下，即使在CL方法中，NNS分布的原始普遍行为也可能被保留。
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.