Filtered overlap: speedup, locality, kernel non-normality and Z_A~1

TL;DR

This paper demonstrates that UV filtering of the Wilson kernel in the overlap operator improves localization, reduces kernel non-normality, and brings the axial-vector renormalization constant closer to 1, resulting in significant computational speed-ups.

Contribution

The study introduces UV filtering to the Wilson kernel in the overlap operator, enhancing localization and renormalization properties while achieving a 2-4 times speed-up.

Findings

Improved localization on coarse lattices

Axial-vector renormalization constant Z_A closer to 1

Speed-up factor of 2-4 for certain applications

Abstract

We investigate the overlap operator with a UV filtered Wilson kernel. The filtering leads to a better localization of the operator even on coarse lattices and with the untuned choice $\rho=1$. Furthermore, the axial-vector renormalization constant $Z_A$ is much closer to 1, reducing the mismatch with perturbation theory. We show that all these features persist over a wide range of couplings and that the details of filtering prove immaterial. We investigate the properties of the kernel spectrum and find that the kernel non-normality is reduced. As a side effect we observe that for certain applications of the filtered overlap a speed-up factor of 2-4 can be achieved.