A Possible Aoki Phase for Staggered Fermions

TL;DR

This paper explores the possibility of an Aoki-like phase in staggered fermions, analyzing the phase diagram and mass spectrum, and concludes current simulations are outside this phase, with future simulations unlikely to enter it.

Contribution

It extends the understanding of the staggered fermion phase diagram by identifying conditions for an Aoki-like phase and analyzing its implications.

Findings

Current simulations are outside the Aoki phase.

Future improved actions are unlikely to enter the Aoki phase.

Explicit mass spectrum solutions for degenerate flavors are provided.

Abstract

The phase diagram for staggered fermions is discussed in the context of the staggered chiral Lagrangian, extending previous work on the subject. When the discretization errors are significant, there may be an Aoki-like phase for staggered fermions, where the remnant SO(4) taste symmetry is broken down to SO(3). We solve explicitly for the mass spectrum in the 3-flavor degenerate mass case and discuss qualitatively the 2+1-flavor case. From numerical results we find that current simulations are outside the staggered Aoki phase. As for near-future simulations with more improved versions of the staggered action, it seems unlikely that these will be in the Aoki phase for any realistic value of the quark mass, although the evidence is not conclusive.