Staggered eigenvalue mimicry

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 nonzero 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 $N_f=2$.