Topology and Staggered Fermion Action Improvement

TL;DR

This paper investigates how improvements to staggered fermion actions affect their sensitivity to gauge field topology, showing that better actions enhance zero mode identification and align non-chiral mode distributions with Random Matrix Theory.

Contribution

It demonstrates that improved staggered fermion actions improve the detection of topological zero modes and match theoretical predictions more closely.

Findings

Improved actions increase separation between zero and non-chiral modes.

Zero modes can be identified more unambiguously with better actions.

Non-chiral mode distributions agree with Random Matrix Theory predictions.

Abstract

It is conventional wisdom that staggered fermions do not feel gauge field topology. However, the response of staggered fermion eigenmodes to the topology of the gauge field can depend quite sensitively on the way in which the staggered fermion action is improved. We study this issue using a variety of improved staggered quark actions. We observe that the separation between the ``would be'' zero modes and the non-chiral modes increases with the level of improvement. This enables the ``zero modes'' to be identified unambiguously. The distribution of the remaining non-chiral modes is compared with the predictions of Random Matrix Theory. Satisfactory agreement is obtained.