Universal fluctuations in spectra of the lattice Dirac operator

Details Universal fluctuations in spectra of the lattice Dirac operator Universal fluctuations in spectra of the lattice Dirac operator

1995-01-21

arxiv.org/abs/hep-lat/9501025v1

Phys.Rev.Lett.74:3920-3923,1995

Physics

High Energy Physics

High Energy Physics - Lattice

8 pages + 3 figures (will be faxed on request)

Scientific paper

10.1103/PhysRevLett.74.3920

Recently, Kalkreuter obtained the complete Dirac spectrum for an $SU(2)$ lattice gauge theory with dynamical staggered fermions on a $12^4$ lattice for $\beta =1.8$ and $\beta=2.8$. We performed a statistical analysis of his data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble. In particular, long range fluctuations are strongly suppressed: the variance of a sequence of levels containing $n$ eigenvalues on average is given by $\Sigma_2(n) \sim\frac 1{2\pi^2}(\log n + {\rm const.})$ instead of $\Sigma_2(n) = n$ for a random sequence of levels. Our findings are in agreement with the anti-unitary symmetry of the lattice Dirac operator for $N_c=2$ with staggered fermions which differs from the continuuum theory. For $N_c = 3$ we predict that the eigenvalue correlations are given by the Gaussian Unitary Ensemble.

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