Statistical properties at the spectrum edge of the
QCD Dirac operator
Jian-Zhong Ma1 - Thomas Guhr1 - Tilo Wettig2
1 Max-Planck-Institut für Kernphysik, Postfach 103980, D-69029 Heidelberg,
2 Institut für Theoretische Physik, Technische Universität München, D-85747 Garching, Germany
Received: 6 November 1997 / Revised version: 19 January 1998 Communicated by F. Lenz
The statistical properties of the spectrum of the staggered Dirac operator in an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and at the spectrum edge. Two commonly used statistics, the number variance and the spectral rigidity, are investigated. While the spectral fluctuations at the edge are suppressed to the same extent as in the bulk, the spectra are more rigid at the edge. To study this effect, we introduce a microscopic unfolding procedure to separate the variation of the microscopic spectral density from the fluctuations. For the unfolded data, the number variance shows oscillations of the same kind as before unfolding, and the average spectral rigidity becomes larger than the one in the bulk. In addition, the short-range statistics at the origin is studied. The lattice data are compared to predictions of chiral random-matrix theory, and agreement with the chiral Gaussian Symplectic Ensemble is found.
11.15.Ha Lattice gauge theory - 05.45.+b Theory and models of chaotic systems - 11.30.Rd Chiral symmetries - 12.38.Gc Lattice QCD calculations