Is the chiral phase transition induced by a metal-insulator transition?

TL;DR

This paper explores the connection between the chiral phase transition in QCD and a metal-insulator transition, providing evidence that Anderson localization may drive chiral symmetry restoration.

Contribution

It demonstrates a localization transition in the Dirac operator modes at the chiral transition, linking quantum interference effects to chiral symmetry restoration in QCD.

Findings

Localization transition occurs at the chiral phase transition temperature.

Dirac operator eigenmodes exhibit properties similar to disordered conductors at the transition.

Results suggest Anderson localization as the mechanism for chiral symmetry restoration.

Abstract

We investigate the QCD Dirac operator with gauge configurations given by a liquid of instantons in the region of temperatures about the chiral phase transition. Both the quenched and unquenched cases are examined in detail. We present evidence of a localization transition in the low lying modes of the Dirac operator around the same temperature as the chiral phase transition. Thus both level statistics and eigenvectors of the QCD Dirac operator at the chiral phase transition have similar properties than those of a disordered conductor at the metal-insulator transition. This strongly suggests the phenomenon of Anderson localization (localization by destructive quantum interference) is the leading physical mechanism in the restoration of the chiral symmetry. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.