Localized eigenmodes of the overlap operator and their impact on the eigenvalue distribution

TL;DR

This paper investigates how localized eigenmodes of the overlap operator influence the eigenvalue distribution in lattice QCD, highlighting their impact on chiral symmetry and lattice artifacts.

Contribution

It identifies the presence of localized eigenmodes in the overlap operator and explores how parameter adjustments can mitigate their effects on physical observables.

Findings

Localized eigenmodes are prevalent in the overlap operator, especially in mixed action simulations.

Adjusting the clover term and overlap projection parameters reduces lattice artifacts caused by these modes.

Localized modes can significantly affect chiral symmetry-sensitive quantities.

Abstract

In a system where chiral symmetry is spontaneously broken, the low energy eigenmodes of the continuum Dirac operator are extended. On the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes that affect physical quantities sensitive to chiral symmetry. While the infrared eigenmodes of the Wilson Dirac operator are usually extended even on coarse lattices, the chiral overlap operator has many localized eigenmodes in the physical region, especially in mixed action simulations. Depending on their density, these modes can introduce strong lattice artifacts. The effect can be controlled by changing the parameters of the overlap operator, in particular the clover improvement term and the center of the overlap projection.