Scaling tests with dynamical overlap and rooted staggered fermions

TL;DR

This paper compares the scaling behavior of overlap and rooted staggered fermions in the 1-flavor Schwinger model, revealing differences in chiral and continuum limits and suggesting universality in certain observables.

Contribution

It provides a detailed scaling analysis of overlap and rooted staggered fermions, highlighting their differences and similarities in the Schwinger model.

Findings

Chiral and continuum limits do not commute for rooted staggered fermions.

Universal continuum limit observed for topological susceptibility and related quantities.

The ratio of overlap to rooted staggered determinants remains constant up to O(a^2) effects.

Abstract

We present a scaling analysis in the 1-flavor Schwinger model with the full overlap and the rooted staggered determinant. In the latter case the chiral and continuum limit of the scalar condensate do not commute, while for overlap fermions they do. For the topological susceptibility a universal continuum limit is suggested, as is for the partition function and the Leutwyler-Smilga sum rule. In the heavy-quark force no difference is visible even at finite coupling. Finally, a direct comparison between the complete overlap and the rooted staggered determinant yields evidence that their ratio is constant up to $O(a^2)$ effects.