How to identify zero modes for improved staggered fermions

TL;DR

This paper investigates the eigenvalue spectrum of the staggered Dirac operator, identifying zero modes and non-zero modes, and verifies a chiral Ward identity to improve the detection of zero modes in staggered fermions.

Contribution

It introduces a modified Lanczos algorithm and a numerical check of the chiral Ward identity to reliably identify zero modes in improved staggered fermions.

Findings

Successful identification of zero modes using the modified Lanczos algorithm

Verification of the chiral Ward identity numerically

First step towards a more reliable zero mode detection method

Abstract

We present results of the eigenvalue spectrum for the staggered Dir\"ac operator obtained using a modified Lanczos algorithm. We identify zero modes and non-zero modes. We derive the chiral Ward identity derived from the conserved $U(1)_A$ symmetry, and check it numerically. This is the first step toward construction of an improved method to identify zero modes reliably with staggered fermions.