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.

arXiv comment10 pages, 6 figures

References in corpus (38)

• Anderson Transitions
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The QCD equation of state with dynamical quarks
• Localization of ultrasound in a three-dimensional elastic network
• Three-dimensional localization of ultracold atoms in an optical disordered potential
• Random Matrix Theory and Chiral Symmetry in QCD
• The equation of state in lattice QCD: with physical quark masses towards the continuum limit
• Spontaneous Flavor and Parity Breaking with Wilson Fermions
• Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1-xMnxAs
• Fractal superconductivity near localization threshold
• Multifractal finite-size-scaling and universality at the Anderson transition
• Exact relations between multifractal exponents at the Anderson transition
• The Anderson transition: time reversal symmetry and universality
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Observation of multifractality in Anderson localization of ultrasound
• Enhancement of superconductivity by Anderson localization
• Two-eigenfunction correlation in a multifractal metal and insulator
• Localization in Lattice QCD
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Anderson Localization in Quark-Gluon Plasma
• Universality and the QCD Anderson Transition
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
• Anderson localization through Polyakov loops: lattice evidence and Random matrix model
• Poisson to Random Matrix Transition in the QCD Dirac Spectrum
• Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD
• Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum
• Kondo-Anderson Transitions
• Finite Size Scaling Analysis of the Anderson Transition
• Chiral Random Matrix Model for Critical Statistics
• On the phase structure of QCD with Wilson fermions
• Spectral Statistics in Chiral-Orthogonal Disordered Systems
• An Ising-Anderson model of localisation in high-temperature QCD
• Anderson localization in QCD-like theories
• Influence of boundary conditions on level statistics and eigenstates at the metal insulator transition
• Quantum percolation transition in 3d: density of states, finite size scaling and multifractality
• The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator

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• 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
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• 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