An Ising-Anderson model of localisation in high-temperature QCD

Abstract

We discuss a possible mechanism leading to localisation of the low-lying Dirac eigenmodes in high-temperature lattice QCD, based on the spatial fluctuations of the local Polyakov lines in the partially ordered configurations above $T_c$. This mechanism provides a qualitative explanation of the dependence of localisation on the temperature and on the lattice spacing, and also of the phase diagram of QCD with an imaginary chemical potential. To test the viability of this mechanism we propose a three-dimensional effective, Anderson-like model, mimicking the effect of the Polyakov lines on the quarks. The diagonal, on-site disorder is governed by a three-dimensional Ising-like spin model with continuous spins. Our numerical results show that localised modes are indeed present in the ordered phase of the Ising model, thus supporting the proposed mechanism for localisation in QCD.

arXiv comment20 pages, 5 figures

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• Reconfinement, localization and thermal monopoles in $SU(3)$ trace-deformed Yang-Mills theory
• An Anderson-like model of the QCD chiral transition
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• Localization and chiral properties near the ordering transition of an Anderson-like toy model for QCD
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Localised Dirac eigenmodes, chiral symmetry breaking, and Goldstone's theorem at finite temperature
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• Chiral transition, eigenmode localisation and Anderson-like models
• Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature