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

TL;DR

This paper proposes a mechanism for localization of low-lying Dirac eigenmodes in high-temperature QCD based on spatial fluctuations of Polyakov lines, supported by an Anderson-like model with Ising spins.

Contribution

It introduces a novel Anderson-like model with Ising spins to explain localization phenomena in high-temperature QCD, linking Polyakov line fluctuations to eigenmode localization.

Findings

Localized modes appear in the ordered phase of the Ising model

The model qualitatively explains the temperature and lattice spacing dependence of localization

Supports the proposed mechanism for localization 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.