Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD

TL;DR

This paper investigates how Anderson localization influences the chiral phase transition in QCD using an Instanton Liquid Model, revealing localization phenomena similar to disordered conductors and identifying a temperature-dependent mobility edge.

Contribution

It demonstrates that Anderson localization is a key mechanism in the chiral phase transition within the ILM framework, with detailed analysis of eigenmode localization and spectral properties.

Findings

Eigenvectors become more localized with increasing temperature.

A mobility edge separates localized and delocalized eigenstates, shifting with temperature.

Localization transition exhibits features of a 3D Anderson transition.

Abstract

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an Instanton Liquid Model (ILM) at temperatures around the chiral phase transition. Generically we find the Dirac eigenvectors become more localized as the temperature is increased. At the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a transition to localization similar to the one observed in a disordered conductor. This suggests that Anderson localization is the fundamental mechanism driving the chiral phase transition. We also find an additional temperature dependent mobility edge (separating delocalized from localized eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues as the temperature is increased. In both regions, the origin and the bulk, the transition to localization exhibits features of a 3D Anderson transition including multifractal eigenstates and spectral properties that are well described by critical statistics. Similar results are obtained in both the quenched and the unquenched case though the critical temperature in the unquenched case is lower. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.