Topological Index Theorem on the Lattice through the Spectral Flow of Staggered Fermions

TL;DR

This paper numerically verifies the spectral flow method for defining topological charge in lattice QCD using staggered fermions, showing consistency with traditional measures and improvements with finer lattices.

Contribution

It provides numerical evidence supporting the spectral flow approach for topological charge on the lattice, demonstrating its effectiveness and dependence on lattice spacing.

Findings

Clear separation of spectral crossings near and far from zero.

Topological charge from crossings agrees with near-zero mode definition in most cases.

Crossings move closer to zero as lattice spacing decreases.

Abstract

We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic (quenched) gauge configurations. We obtain clear numerical evidence that the definition works as expected: there is a clear separation between crossings near and far away from the origin, and the topological charge defined through the crossings near the origin agrees, for most configurations, with the one defined through the near-zero modes of large taste-singlet chirality of the staggered Dirac operator. The crossings are much closer to the origin if we improve the Dirac operator used in the definition, and they move towards the origin as we decrease the lattice spacing.