Anderson localization in QCD-like theories

TL;DR

This paper reviews the evidence for Anderson localization phenomena in the Dirac spectrum of QCD-like theories, highlighting the transition's universality class and potential physical implications at high temperatures.

Contribution

It establishes the Anderson transition in QCD-like theories' Dirac spectrum as belonging to the same universality class as electronic Anderson models, linking lattice results to condensed matter physics.

Findings

Localized modes are observed at the low end of the spectrum in SU(2) and Nf=2+1 QCD.

The transition shares the same universality class as the Anderson transition in electronic systems.

The transition may have implications for high-temperature QCD phases.

Abstract

We review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low-end of the spectrum have been found in SU(2) Yang-Mills theory with overlap and staggered valence fermions as well as in Nf=2+1 QCD with staggered quarks. We draw an analogy between the transition from localized to delocalized modes in the Dirac spectrum and the Anderson transition in electronic systems. The QCD transition turns out to be in the same universality class as the transition in the corresponding Anderson model. We also speculate on the possible physical relevance of this transition to QCD at high temperature and the possible finite temperature phase transition in QCD-like models with different fermion contents.