The Aoki phase revisited

TL;DR

This paper investigates the vacuum structure of the Aoki phase in lattice QCD with Wilson fermions through numerical simulations, revealing complex behavior and potential non-zero values of certain observables, but facing statistical challenges at larger volumes.

Contribution

It provides a detailed numerical study of the Aoki phase's vacuum structure using the p.d.f. framework without external sources, highlighting new insights into observable behaviors.

Findings

Observable $iar ext{psi} ext{gamma}_5 ext{psi}$ can be non-zero.

Rich vacuum structure suggested by simulations.

Large statistical errors at higher volumes.

Abstract

In order to elucidate the vacuum structure of the Aoki phase, we carried out a numerical investigation of QCD with two flavours of Wilson fermions, within the p.d.f. framework and in the absence of external sources. The simulations performed at V = 44 suggest a rich vacuum structure, where the observable $i\bar\psi\gamma_5\psi$ is allowed to take non-zero values of the same order of magnitude than the order parameter of the Aoki phase $i\bar\psi\gamma_5\tau_3\psi$. However, the simulation at higher volumes V = 6^4 suffers from large statistical errors.