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

Abstract

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.

11 pages, 23 plots in 11 figures; some comments and references added, some axis labels corrected; journal version

References in corpus (11)

• Anderson Transitions
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Dual quark condensate and dressed Polyakov loops
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Anderson Localization in Quark-Gluon Plasma
• The topological structure of SU(2) gluodynamics at T > 0 : an analysis using the Symanzik action and Neuberger overlap fermions
• The dyonic picture of topological objects in the deconfined phase
• Eigenvalues and Eigenvectors of the Staggered Dirac Operator at Finite Temperature
• Localization properties of fermions and bosons
• Chiral symmetry restoration at finite temperature in the planar limit
• More about chiral symmetry restoration at finite temperature in the planar limit

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• Poisson to Random Matrix Transition in the QCD Dirac Spectrum
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• The Chiral Symmetry Breaking/Restoration in Dyonic Vacuum
• An Ising-Anderson model of localisation in high-temperature QCD
• Topology across the finite temperature transition studied by overimproved cooling in gluodynamics and QCD
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• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors
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