Statistical properties at the spectrum edge of the QCD Dirac operator

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.

12 pages, 22 figures, minor typos corrected, version to appear in Euro. Phys. J. A

Cited by in corpus (20)

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• From chiral Random Matrix Theory to chiral Perturbation Theory
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• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• The supersymmetric technique for random-matrix ensembles with zero eigenvalues
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Eigenvalue spectrum of massless Dirac operators on the lattice
• Microscopic universality with dynamical fermions
• Crossover to Non-universal Microscopic Spectral Fluctuations in Lattice Gauge Theory
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• Power-law deformation of Wishart-Laguerre ensembles of random matrices
• Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data
• Spectral correlations of the massive QCD Dirac operator at finite temperature
• Staggered chiral random matrix theory
• Random Matrix Theory and QCD at nonzero chemical potential
• Universal and non-universal behavior in Dirac spectra
• Spectra of massive QCD Dirac Operators from Random Matrix Theory: all three chiral symmetry breaking patterns
• Randomness on the Lattice
• Comparing lattice Dirac operators with Random Matrix Theory