Anderson localization through Polyakov loops: lattice evidence and Random matrix model

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.Comment: 11 pages, 23 plots in 11 figures; some comments and references added, some axis labels corrected; journal versio

Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential

We consider antisymmetric perturbations of real symmetric matrices in the context of random matrix theory and two-color quantum chromodynamics. We investigate the level spacing distributions of eigenvalues that remain real or become complex conjugate pairs under the perturbation. We work out analytical surmises from small matrices and show that they describe the level spacings of large random matrices. As expected from symmetry arguments, these level spacings also apply to the overlap Dirac operator for two-color QCD with chemical potential.Comment: 23 pages, 6 figures, 1 animation; minor corrections, references added, as published in JHE

Lattice studies of quark spectra and supersymmetric quantum mechanics

In the first part of this work, we study quark spectra at either non-zero temperature or chemical potential. In the first case, we find a possible explanation for the Anderson localization that is observed in the spectrum. We introduce a random matrix model that has the same localization and shares other important properties of the QCD Dirac operator, too. In the case of a non-vanishing chemical potential, we show that the eigenvalue spacing distributions of the Dirac operator are described by simple random matrix models. In the second part of this work, we study supersymmetry on the lattice. We summarize our progress with the blocking approach and show possible problems. Furthermore, we contruct a lattice action which is improved with respect to supersymmetry and study this action numerically