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.

20 pages, 5 figures

References in corpus (8)

• Anderson Transitions
• The QCD equation of state with dynamical quarks
• The chiral critical point of Nf=3 QCD at finite density to the order (mu/T)^4
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Anderson Localization in Quark-Gluon Plasma
• Localization properties of fermions and bosons
• Anderson transition in systems with chiral symmetry
• Axial U(1) symmetry at finite temperature with Möbius domain-wall fermions

Cited by in corpus (11)

• Deconfinement, chiral transition and localisation in a QCD-like model
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Reconfinement, localization and thermal monopoles in $SU(3)$ trace-deformed Yang-Mills theory
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• 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
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• Chiral transition, eigenmode localisation and Anderson-like models
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature
• Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition