Improving the locality of the overlap Dirac operator via approximate solutions of the Ginsparg-Wilson relation

TL;DR

This paper develops an optimized free field hypercubic Dirac operator that better satisfies the Ginsparg-Wilson relation, leading to a more local overlap Dirac operator with improved locality bounds, especially in near-trivial gauge backgrounds.

Contribution

It introduces an approximate solution to the Ginsparg-Wilson relation that enhances the locality properties of the overlap Dirac operator.

Findings

Stronger analytic locality bounds achieved.

Improved locality persists in gauge backgrounds close to trivial.

Enhanced operator construction for lattice QCD simulations.

Abstract

We determine the free field hypercubic Dirac operator which is optimally close to satisfying the Ginsparg-Wilson relation. Inserting this operator into the overlap formula, we show that the analytic locality bound on the resulting overlap Dirac operator is substantially stronger than in the standard case. This improvement generally persists in gauge backgrounds when the plaquette variables are all close to unity.