The chiral transition as an Anderson transition

TL;DR

This paper investigates the transition in spectral statistics of the QCD Dirac operator at finite temperature, revealing a change from localized Poisson to delocalized random matrix behavior across the critical temperature.

Contribution

It demonstrates the spectral transition in QCD-like theories at finite temperature, linking localization phenomena to the chiral phase transition.

Findings

Spectral statistics change from Poisson to random matrix at T_c

Localized modes dominate below T_c

Delocalized modes appear above T_c

Abstract

At low temperature the low-lying QCD Dirac spectrum obeys random matrix statistics. Recently we found that above $T_{c}$ the lowest part of the spectrum consists of localized modes that obey Poisson statistics. An interesting implication of this is that as the system crosses $T_{c}$ from above, the spectral statistics at $\lambda=0$ changes from Poisson to random matrix. Here we study this transition and its possible implications for the finite temperature transition of QCD-like theories.