The locality problem for two tastes of staggered fermions

TL;DR

This paper investigates whether the square root of the staggered fermion operator can define a local two-taste fermion theory, finding it non-local in the continuum limit and raising concerns about the validity of the square root trick.

Contribution

The study provides analytical and numerical evidence that the square root of the staggered fermion operator is non-local, highlighting potential issues in lattice QCD simulations.

Findings

The operator has the correct weight but is non-local in the continuum limit.

The work warns against blindly using the square root trick in simulations.

The existence of a local operator reproducing the square root remains unresolved.

Abstract

We address the locality problem arising in simulations, which take the square root of the staggered fermion determinant as a Boltzmann weight to reduce the number of dynamical quark tastes from four to two. We study analytically and numerically the square root of the staggered fermion operator as a candidate to define a two taste theory from first principles. Although it has the correct weight, this operator is non-local in the continuum limit. Our work serves as a warning that fundamental properties of field theories might be violated when employing blindly the square root trick. The question, whether a local operator reproducing the square root of the staggered fermion determinant exists, is left open.