Dirac eigenmodes at the QCD Anderson transition

TL;DR

This paper investigates the spatial structure of Dirac eigenmodes in high-temperature QCD, confirming their multifractal nature at the Anderson transition point, which parallels properties observed in the Anderson model.

Contribution

It provides the first verification of scale invariance and multifractal structure of Dirac eigenmodes at the QCD Anderson transition point.

Findings

Eigenmodes exhibit scale invariance at the critical point

Dirac eigenmodes are multifractal at the transition

Spectral statistics align with Anderson model predictions

Abstract

Recently we found an Anderson-type localization-delocalization transition in the QCD Dirac spectrum at high temperature. Using spectral statistics we obtained a critical exponent compatible with that of the corresponding Anderson model. Here we study the spatial structure of the eigenmodes both in the localized and the transition region. Based on previous studies in the Anderson model, at the critical point, the eigenmodes are expected to have a scale invariant multifractal structure. We verify the scale invariance of Dirac eigenmodes at the critical point.