Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential

We consider the phase diagram of twisted mass Wilson fermions of two-flavor QCD in the parameter space of the quark mass, the isospin chemical potential, the twist angle and the lattice spacing. This work extends earlier studies in the continuum and those at zero chemical potential. We evaluate the phase diagram as well as the spectrum of the (pseudo-)Goldstone bosons using the chiral Lagrangian for twisted mass Wilson fermions at non-zero isospin chemical potential. The phases are obtained from a mean field analysis. At zero twist angle we find that already an infinitesimal isospin chemical potential destroys the Aoki phase. The reason is that in this phase we have massless Goldstone bosons with a non-zero isospin charge. At finite twist angle only two different phases are present, one phase which is continuously connected to the Bose condensed phase at non-zero chemical potential and another phase which is continuously connected to the normal phase. For either zero or maximal twist the phase diagram is more complicated as the saddle point equations allow for more solutions.