Staggered eigenvalue mimicry

TL;DR

This paper demonstrates that UV-filtered staggered Dirac operators can closely mimic overlap operators in the infrared spectrum, showing near-degeneracy and topological sensitivity, supporting their use in lattice QCD simulations.

Contribution

It provides evidence that filtered staggered fermions can approximate overlap fermions, suggesting an approximate index theorem and validating the square-rooting procedure for dynamical fermion simulations.

Findings

Filtered staggered spectra show 4-fold near-degeneracy.

Clear separation between zero and non-zero modes observed.

Supports the use of square-rooted staggered determinants for N_f=2 simulations.

Abstract

We study the infrared part of the spectrum for UV-filtered staggered Dirac operators and compare them to the overlap counterpart. With sufficient filtering and at small enough lattice spacing the staggered spectra manage to ``mimic'' the overlap version. They show a 4-fold near-degeneracy, and a clear separation between would-be zero modes and non-zero modes. This suggests an approximate index theorem for filtered staggered fermions and a correct sensitivity to the topology of QCD. Moreover, it supports square-rooting the staggered determinant to obtain dynamical ensembles with $N_f=2$.