Low fermionic eigenmode dominance in QCD on the lattice

Abstract

We demonstrate the utility of a spectral approximation to fermion loop operators using low-lying eigenmodes of the Hermitian Dirac-Wilson matrix, $Q={\ensuremath{\gamma}}_{5}M.$ The investigation is based on a total of 400 full QCD vacuum configurations, with two degenerate flavors of dynamical Wilson fermions at $\ensuremath{\beta}=5.6,$ at two different sea quark masses. The spectral approach is highly competitive for accessing both topological charge and disconnected diagrams, on large lattices and small quark masses. We propose suitable partial summation techniques that provide sufficient saturation for estimating $\mathrm{Tr}{Q}^{\ensuremath{-}1},$ which is related to the topological charge. In the effective mass plot of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ meson we achieved a consistent early plateau formation, by ground state projecting the connected piece of its propagator.