Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature

Abstract

We investigate the Anderson transition found in the spectrum of the Dirac operator of Quantum Chromodynamics (QCD) at high temperature, studying the properties of the critical quark eigenfunctions. Applying multifractal finite-size scaling we determine the critical point and the critical exponent of the transition, finding agreement with previous results, and with available results for the unitary Anderson model. We estimate several multifractal exponents, finding also in this case agreement with a recent determination for the unitary Anderson model. Our results confirm the presence of a true Anderson localization-delocalization transition in the spectrum of the quark Dirac operator at high-temperature, and further support that it belongs to the 3D unitary Anderson model class.

10 pages, 6 figures

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Cited by in corpus (21)

• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Anderson Metal-to-Critical Transition in QCD
• Reconfinement, localization and thermal monopoles in $SU(3)$ trace-deformed Yang-Mills theory
• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit
• Spectrum of the Laplace-Beltrami Operator and the Phase Structure of Causal Dynamical Triangulation
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• Super-Universality in Anderson Localization
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Mobility Edge in the Anderson model on partially disordered random regular graphs
• Localised Dirac eigenmodes, chiral symmetry breaking, and Goldstone's theorem at finite temperature
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• Localization and delocalization of fermions in a background of correlated spins
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• Borel-Padé re-summation of the $\beta$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes
• Metal or Insulator? Dirac operator spectrum in holographic QCD
• Topological Dimensions from Disorder and Quantum Mechanics?
• Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature