Polyakov loops and spectral properties of the staggered Dirac operator

Abstract

We study the spectrum of the staggered Dirac operator in SU(2) gauge fields close to the free limit, for both the fundamental and the adjoint representation. Numerically we find a characteristic cluster structure with spacings of adjacent levels separating into three scales. We derive an analytical formula which explains the emergence of these different spectral scales. The behavior on the two coarser scales is determined by the lattice geometry and the Polyakov loops, respectively. Furthermore, we analyze the spectral statistics on all three scales, comparing to predictions from random matrix theory.

11 pages, 25 figures; v2: minor changes, as published in Phys. Rev. D

References in corpus (28)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Random Matrix Theory and Chiral Symmetry in QCD
• Microscopic universality in the spectrum of the lattice Dirac operator
• Staggered eigenvalue mimicry
• Quark spectra, topology and random matrix theory
• Lattice QCD in the epsilon-regime and random matrix theory
• Distribution of the k-th smallest Dirac operator eigenvalue
• Universal fluctuations in spectra of the lattice Dirac operator
• Dual quark condensate and dressed Polyakov loops
• Linking confinement to spectral properties of the Dirac operator
• Smallest Dirac Eigenvalue Distribution from Random Matrix Theory
• The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
• Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry
• Universal scaling of the valence quark mass dependence of the chiral condensate
• Spectral sum rules and Selberg's integral
• Spectral sums of the Dirac-Wilson Operator and their relation to the Polyakov loop
• The Low-Lying Dirac Spectrum of Staggered Quarks
• Microscopic Spectral Density of the Dirac Operator in Quenched QCD
• Complete spectra of the Dirac operator and their relation to confinement
• Microscopic universality with dynamical fermions
• Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
• Small eigenvalues of the staggered Dirac operator in the adjoint representation and Random Matrix Theory
• Semiclassical limits for the QCD Dirac operator
• U(1) staggered Dirac operator and random matrix
• Random Matrix Theory and the Spectra of Overlap Fermions

Cited by in corpus (13)

• Thermodynamics of the QCD plasma and the large-N limit
• Anderson Localization in Quark-Gluon Plasma
• Radius of convergence in lattice QCD at finite ${\mu }_B$ with rooted staggered fermions
• Strong dynamics with matter in multiple representations: SU(4) gauge theory with fundamental and sextet fermions
• Continuum Goldstone spectrum of two-color QCD at finite density with staggered quarks
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Numerical properties of staggered quarks with a taste-dependent mass term
• Dirac Spectra of 2-dimensional QCD-like theories
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Shift of Symmetries of Naive Fermions in QCD-like Lattice Theories
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• Topological zero modes at nonzero chemical potential
• Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential