Universal Fluctuations in Spectra of the Lattice Dirac Operator
Abstract
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 Nc = 2 with staggered fermions. For Nc = 3 we predict that the eigenvalue correlations are given by the Gaussian unitary ensemble.
- Publication:
-
Physical Review Letters
- Pub Date:
- May 1995
- DOI:
- 10.1103/PhysRevLett.74.3920
- arXiv:
- arXiv:hep-lat/9501025
- Bibcode:
- 1995PhRvL..74.3920H
- Keywords:
-
- High Energy Physics - Lattice;
- Condensed Matter
- E-Print:
- 8 pages + 3 figures (will be faxed on request)