Locality with staggered fermions

TL;DR

This paper investigates the non-locality issues of using the square root of the staggered fermion determinant in lattice QCD simulations, highlighting potential violations of fundamental field theory properties.

Contribution

It provides analytical and numerical evidence that the square root of the staggered fermion operator is non-local in the continuum limit, raising concerns about the validity of this approach.

Findings

The square root operator has the correct determinant weight.

The operator is non-local in the continuum limit.

Using the square root trick may violate causality and unitarity.

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. A definition of such a theory necessitates an underlying local fermion operator with the same determinant and the corresponding Green's functions to establish causality and unitarity. We illustrate this point by studying analytically and numerically the square root of the staggered fermion operator. 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.