Numerical reinvestigation of the Aoki phase withNf=2Wilson fermions at zero temperature

Abstract

We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose an explicitly symmetry-breaking source term $h\overline{\ensuremath{\psi}}i{\ensuremath{\gamma}}_{5}{\ensuremath{\tau}}^{3}\ensuremath{\psi}$ was added to the fermion action. The order parameter $〈\overline{\ensuremath{\psi}}i{\ensuremath{\gamma}}_{5}{\ensuremath{\tau}}^{3}\ensuremath{\psi}〉$ was computed with the hybrid Monte Carlo algorithm at several values of $(\ensuremath{\beta},\ensuremath{\kappa},h)$ on lattices of sizes ${4}^{4}$ to ${12}^{4}$ and extrapolated to $h=0.$ The existence of a parity-flavor breaking phase can be confirmed at $\ensuremath{\beta}=4.0$ and 4.3, while we do not find parity-flavor breaking at $\ensuremath{\beta}=4.6$ and 5.0.