Staggered fermions, zero modes, and flavor-singlet mesons
  We examine the taste structure of eigenvectors of the staggered-fermion Dirac operator. We derive a set of conditions on the eigenvectors of modes with small eigenvalues (near-zero modes), such that staggered fermions reproduce the 't Hooft vertex in the continuum limit. We also show that, assuming these conditions, the correlators of flavor-singlet mesons are free of contributions singular in $1/m$, where $m$ is the quark mass. This conclusion holds also when a single flavor of sea quark is represented by the fourth root of the staggered-fermion determinant. We then test numerically, using the HISQ action, whether these conditions hold on realistic lattice gauge fields. We find that the needed structure does indeed emerge. 
Gordon C. Donald, Christine T. H. Davies, Eduardo Follana and Andreas   S. Kronfeld
hep-lat