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,
Germany
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
Abstract
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.
PACS
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
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