Locality and topology with fat link overlap actions

TL;DR

This paper investigates the locality and topological features of fat link clover overlap actions, demonstrating improved properties over Wilson overlap and potential for accurate topological charge representation in lattice QCD.

Contribution

It introduces and analyzes fat link clover overlap actions, showing their enhanced locality and topological accuracy compared to Wilson overlap.

Findings

Fat link overlap actions improve locality properties.

FCO remains local in the continuum limit regardless of gauge coupling.

FCO accurately reproduces instanton zero modes and satisfies the index theorem.

Abstract

We study the locality and topological properties of fat link clover overlap (FCO) actions. We find that a small amount of fattening (2-4 steps of APE or 1 step of HYP) already results in greatly improved properties compared to the Wilson overlap (WO). We present a detailed study of the localisation of the FCO and its connection to the density of low modes of $A^\dagger A$. In contrast to the Wilson overlap, on quenched gauge backgrounds we do not find any dependence of the localization of the FCO on the gauge coupling. This suggests that the FCO remains local in the continuum limit. The FCO also faithfully reproduces the zero mode wave functions of typical lattice instantons, not like the Wilson overlap. After a general discussion of different lattice definitions of the topological charge we also show that the FCO together with the Boulder charge are likely to satisfy the index theorem in the continuum limit. Finally, we present a high statistics computation of the quenched topological susceptibility with the FCO action.