Eigenvalues and Eigenvectors of the Staggered Dirac Operator at Finite Temperature

Abstract

We examine the eigenvalues and eigenvectors of the staggered Dirac operator on thermal ensembles created in QCD with two flavours of staggered quarks. We see that across the phase transition a gap opens in the spectrum. For finite volume lattices in the low-temperature phase the eigenvectors are extended, but generic field configurations in the high temperature phase give rise to localized eigenstates. We examine measures of the stability of such localization and find that at finite volumes localization occurs through Mott's mechanism of the formation of mobility edges. However, the band gap between the localized and extended states seem to scale to zero in the limit of large volume.

References in corpus (16)

• 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
• The critical end point of QCD
• Smallest Dirac Eigenvalue Distribution from Random Matrix Theory
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory
• The Low-Lying Dirac Spectrum of Staggered Quarks
• Eigenvalue spectrum of massless Dirac operators on the lattice
• Eigenvalue Distributions of the QCD Dirac Operator
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• Quenched QCD at finite temperature with chiral Fermions
• The Analysis of Space-Time Structure in QCD Vacuum I: Localization vs Global Behavior in Local Observables and Dirac Eigenmodes
• Applications of the Eigenmodes of the Staggered Dirac Operator
• Dirac eigenvalues and eigenvectors at finite temperature
• Probing the QCD vacuum with overlap fermions

Cited by in corpus (14)

• Inverse magnetic catalysis and the Polyakov loop
• The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions
• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• Anderson Localization in Quark-Gluon Plasma
• Anderson localization through Polyakov loops: lattice evidence and Random matrix model
• Poisson to Random Matrix Transition in the QCD Dirac Spectrum
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Hadronic Screening in Improved Taste
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• A short introduction to heavy-ion physics
• Statistical tweaks and flow scale from masses