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.