Validity of the Rooted Staggered Determinant in the continuum limit

TL;DR

This study examines whether the rooted staggered fermion approach in lattice gauge theory converges correctly to the continuum limit by comparing it with overlap fermions in the 2D Schwinger model, finding that differences vanish as lattice spacing decreases.

Contribution

The paper provides evidence that the rooted staggered determinant's differences from overlap fermions diminish at least as fast as the square of the lattice spacing, supporting the validity of the rooting procedure.

Findings

Residue scales as O(a^2), indicating irrelevance in the continuum limit.

Rooted staggered and overlap determinants become indistinguishable as a approaches zero.

Supports the theoretical justification for the rooting procedure in lattice gauge theories.

Abstract

We investigate the continuum limit of the rooted staggered determinant in the 2-dimensional Schwinger model. We match both the unrooted and rooted staggered determinant with an overlap fermion determinant of two (one) flavors and a local pure gauge effective action by fitting the coefficients of the effective action and the mass of the overlap operator. The residue of this fit measures the difference of the staggered and overlap fermion actions. We show that this residue scales at least as O(a^2), implying that any difference, be it local or non-local, between the staggered and overlap actions becomes irrelevant in the continuum limit. This observation justifies the rooting procedure.