Localization in lattice QCD (with emphasis on practical implications)

TL;DR

This paper explores the phase diagram of lattice QCD, linking Anderson localization phenomena to the Aoki phase, and discusses the implications for domain-wall and overlap fermions in maintaining locality and chirality.

Contribution

It provides a unified microscopic picture of the QCD phase diagram, connecting localization properties with spontaneous symmetry breaking and analyzing the validity of fermion formulations.

Findings

The Aoki phase corresponds to zero mobility edge of the Wilson operator.

Locality and chirality are maintained only outside the Aoki phase.

Implications for the validity of domain-wall and overlap fermions in different phases.

Abstract

When Anderson localization takes place in a quenched disordered system, a continuous symmetry can be broken spontaneously without accompanying Goldstone bosons. Elaborating on this observation we propose a unified, microscopic physical picture of the phase diagram of both quenched and unquenched QCD with two flavors of Wilson fermions. The phase with Goldstone bosons -- by definition the Aoki phase -- is always identified as the region where the mobility edge of the (hermitian) Wilson operator is zero. We then discuss the implications for domain-wall and overlap fermions. We conclude that both formulations are valid only well outside the Aoki phase of the associated Wilson-operator kernel, because this is where locality and chirality can be both maintained.