Chiral transition, eigenmode localisation and Anderson-like models

TL;DR

This paper explores how chiral symmetry restoration and eigenmode localisation in finite-temperature QCD are connected to confinement properties, using lattice simulations and an Anderson-like toy model to illustrate their interplay.

Contribution

It introduces a simplified Anderson-like model capturing key QCD features, demonstrating the link between confinement and both chiral symmetry and eigenmode localisation.

Findings

The toy model reproduces qualitative aspects of chiral symmetry breaking.

Confinement transition triggers both chiral symmetry restoration and localisation.

Eigenmode localisation correlates with Polyakov line order and confining properties.

Abstract

We discuss chiral symmetry restoration and eigenmode localisation in finite-temperature QCD by looking at the lattice Dirac operator as a random Hamiltonian. We argue that the features of QCD relevant to both phenomena are the presence of order in the Polyakov line configuration, and the correlations that this induces between spatial links across time slices. This ties the fate of chiral symmetry and of localisation of the lowest Dirac eigenmodes to the confining properties of the theory. We then show numerical results obtained in a QCD-inspired Anderson-like toy model, derived by radically simplifying the QCD dynamics while keeping the important features mentioned above. The toy model reproduces all the important qualitative aspects of chiral symmetry breaking and localisation in QCD, thus supporting the central role played by the confinement/deconfinement transition in triggering both phenomena.