The Anderson transition in QCD with $N_f=2+1+1$ twisted mass quarks: overlap analysis

Chiral Random Matrix Theory has proven to describe the spectral properties of low temperature QCD very well. However, at temperatures above the chiral symmetry restoring transition it can not provide a global description. The level-spacing distribution in the lower part of the spectrum of the Dirac operator is Poisson-like. There the eigenmodes are localized in space-time and separated from the rest of the spectrum by a so-called mobility edge. In analogy to Anderson localization in condensed-matter systems with random disorder this has been called the QCD-Anderson transition. Here, we study the localization features of the low-lying eigenmodes of the massless overlap operator on configurations generated with $N_f=2+1+1$ twisted mass Wilson sea quarks and present results concerning the temperature dependence of the mobility edge and the mechanism of the quark-mode localization. We have used various methods to fix the spectral position of the delocalization transition and verify that the mobility edge extrapolates to zero at a temperature within the chiral transition region.