Anderson localization in sigma models

TL;DR

This paper investigates Anderson localization in sigma models, comparing spectral properties of fermions in different dimensions, revealing the presence or absence of an Anderson transition.

Contribution

It demonstrates the dimensional dependence of Anderson transition in sigma models, extending understanding from QCD-like theories to nonlinear sigma models.

Findings

In 2D, all fermion modes are localized, no Anderson transition occurs.

In 3D, an Anderson transition is observed, indicating delocalization of fermion modes.

The study introduces a level spacing ratio distribution as a new spectral observable.

Abstract

In QCD above the chiral restoration temperature there exists an Anderson transition in the fermion spectrum from localized to delocalized modes. We investigate whether the same holds for nonlinear sigma models which share properties like dynamical mass generation and asymptotic freedom with QCD. In particular we study the spectra of fermions coupled to (quenched) CP(N-1) configurations at high temperatures. We compare results in two and three space-time dimensions: in two dimensions the Anderson transition is absent, since all fermion modes are localized, while in three dimensions it is present. Our measurements include a more recent observable characterizing level spacings: the distribution of ratios of consecutive level spacings.