The flavour projection of staggered fermions and the quarter-root trick

TL;DR

This paper demonstrates that the flavour projection of staggered fermions can be understood as a projection across four parallel lattices, and relates this to the quarter-root trick used in lattice QCD simulations.

Contribution

It provides a new interpretation of the flavour projection as a lattice projection and clarifies its compatibility with the quarter-root trick.

Findings

Flavour projection can be represented as a projection between four parallel lattices.

The staggered Dirac operator respects the flavour projection.

The path integral form aligns with the quarter-root trick before projection.

Abstract

It is shown that the flavour projection of staggered fermions can be written as a projection between the fields on four separate, but parallel, lattices, where the fields on each are modified forms of the standard staggered fermion field. Because the staggered Dirac operator acts equally on each lattice, it respects this flavour projection. We show that the system can be gauged in the usual fashion and that this does not interfere with flavour projection. We also consider the path integral, showing that, prior to flavour projection, it evaluates to the same form on each lattice and that this form is equal to that used in the quarter-root trick. The flavour projection leaves a path integral for a single flavour of field on each lattice.