Anderson localization in sigma models

Falk Bruckmann,Jacob Wellnhofer,M Della Morte,P Fritzsch,C Pena Ruano,E Gámiz Sánchez

doi:10.1051/epjconf/201817507005

Falk Bruckmann, Jacob Wellnhofer + Show 4 more

Open Access

https://doi.org/10.1051/epjconf/201817507005

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Journal: EPJ Web of Conferences	Publication Date: Jan 1, 2018
Citations: 7	License type: CC BY 4.0

Affiliation: University of Regensburg

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.

Highlights

Anderson localization has been studied for a number of years in the context of QCD
We investigate whether the same holds for nonlinear sigma models which share properties like dynamical mass generation and asymptotic freedom with QCD
In the confined phase the QCD Dirac operator has no gap in the spectrum; its statistics is well described by the Gaussian unitary ensemble (GUE) of random matrix theory

Summary

Introduction

Anderson localization has been studied for a number of years in the context of QCD. In the confined phase the QCD Dirac operator has no gap in the spectrum; its statistics is well described by the Gaussian unitary ensemble (GUE) of random matrix theory. In QCD above the chiral restoration temperature there exists an Anderson transition in the fermion spectrum from localized to delocalized modes. At the same time the statistics of the low end of the spectrum becomes Poissonian, that is, the eigenmodes become localized [1,2,3,4,5], the same is true for the quenched case [1, 6]. For eigenvalues corresponding to localized modes the level spacing is Poissonian, P(s) = e−s.

Results

Conclusion