Topological charge using cooling and the gradient flow

Abstract

The equivalence of cooling to the gradient flow when the cooling step nc and the continuous flow step of gradient flow τ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate nc and τ and show that the results for the topological charge become equivalent when rescaling τ≃nc/(3-15c1), where c1 is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved, and the Iwasaki gauge actions to configurations produced with Nf=2+1+1 twisted mass fermions. We compute the topological charge, its distribution, and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling τ≃nc/(3-15c1) leads to equivalent results. © 2015 American Physical Society.