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Universal fluctuations in spectra of the lattice Dirac operator

Jan, 1995

11 pages

Published in:

Phys.Rev.Lett. 74 (1995) 3920-3923

e-Print:

hep-lat/9501025 [hep-lat]

DOI:

10.1103/PhysRevLett.74.3920

Report number:

SUNY-NTG-95-3

View in:

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Abstract: (arXiv)

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.

Note:

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

gauge field theory: SU(2)
lattice field theory
operator: Dirac
spectrum: fluctuation
fluctuation: spectrum
correlation
statistical analysis
numerical calculations: Monte Carlo

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Figures(0)

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