Locality of the fourth root of the Staggered-fermion determinant: renormalization-group approach

TL;DR

This paper demonstrates, using renormalization-group methods, that the determinant of the staggered-fermion Dirac operator can be decomposed into a product involving a local one-flavor operator, supporting the consistency of lattice QCD simulations.

Contribution

The paper proves that in the free case, the staggered-fermion determinant can be factorized into a local one-flavor operator and a local correction, with the former satisfying the Ginsparg-Wilson relation.

Findings

Decomposition exists for free staggered operator in flavor representation

The one-flavor operator satisfies the Ginsparg-Wilson relation

Results suggest possible extension to interacting theories

Abstract

Consistency of present-day lattice QCD simulations with dynamical (``sea'') staggered fermions requires that the determinant of the staggered-fermion Dirac operator, $det(D)$, be equal to $det^4(D_{rg}) det(T)$ where $D_{rg}$ is a local one-flavor lattice Dirac operator, and $T$ is a local operator containing only excitations with masses of the order of the cutoff. Using renormalization-group (RG) block transformations I show that, in the limit of infinitely many RG steps, the required decomposition exists for the free staggered operator in the ``flavor representation.'' The resulting one-flavor Dirac operator $D_{rg}$ satisfies the Ginsparg-Wilson relation in the massless case. I discuss the generalization of this result to the interacting theory.