Comparing lattice Dirac operators in smooth instanton backgrounds

TL;DR

This paper compares various lattice Dirac operators in smooth instanton backgrounds, analyzing their eigenvalue flows and ability to reproduce continuum zero modes, highlighting the advantages of chirally improved operators.

Contribution

It provides a comparative analysis of Wilson, chirally improved, and overlap Dirac operators in instanton backgrounds, revealing the improved performance of chirally improved operators.

Findings

Overlap fermions with Wilson input struggle with zero modes for small instantons.

Chirally improved operators better reproduce continuum zero modes.

Eigenvalue flow analysis shows differences among operators.

Abstract

We compare the behavior of different lattice Dirac operators in gauge backgrounds which are lattice discretizations of a classical instanton. In particular we analyze the standard Wilson operator, a chirally improved Dirac operator and the overlap operators constructed from these two operators. We discuss the flow of real eigenvalues as a function of the instanton size. An analysis of the eigenvectors shows that overlap fermions with the Wilson operator as input operator have difficulties with reproducing the continuum zero mode already for moderately small instantons. This problem is greatly reduced when using the chirally improved operator for the overlap projection.