Universal Fluctuations in Spectra of the Lattice Dirac Operator

Recently, Kalkreuter obtained the complete Dirac spectrum for an SU(2) lattice gauge theory. We performed a statistical analysis of his data and found that the eigenvalue correlations can be described by the Gaussian symplectic ensemble. Long range fluctuations are strongly suppressed: The variance of a sequence of levels containing n eigenvalues on average is given by (1/2π²)(lnn+const). Our findings are in agreement with the antiunitary symmetry of the lattice Dirac operator for Nc0ex0ex=0ex0ex2 with staggered fermions. For Nc0ex0ex=0ex0ex3 we predict that the eigenvalue correlations are given by the Gaussian unitary ensemble.