Eigenvalue Density of the Non-Hermitian Wilson Dirac Operator
Mario Kieburg, Jacobus JM Verbaarschot, Savvas Zafeiropoulos
PHYSICAL REVIEW LETTERS | AMER PHYSICAL SOC | Published : 2012
We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the ϵ domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and negative chiralities as well as an explicit analytical expression for the number of additional real modes.
Awarded by U.S. DOE
We thank Gernot Akemann and Kim Splittorff for helpful comments. M. K. is financially supported by the Alexander-von-Humboldt Foundation. J. V. and S. Z. are supported by U.S. DOE Grant No. DE-FG-88ER40388.