A lattice mean-field study of the phase diagram of interacting parity-breaking Weyl semimetals

We perform a mean-field study of the phase diagram of interacting Weyl semimetals with broken parity, that is, with different densities of right- and left-handed quasiparticles. As a simple model system, we consider the Wilson-Dirac Hamiltonian with the chiral chemical potential and on-site repulsive interactions. We find that the chiral chemical potential somewhat shrinks the region of the pion condensation (Aoki phase) in the parameter space of the bare mass and the interaction strength, so that the condensation thresholds are at smaller interaction strengths. The renormalized chiral chemical potential monotonously grows with interaction strength everywhere in the phase diagram, and only the growth rate is discontinuous across the phase transition lines. These findings are in full agreement with previous results obtained by one of the authors for the continuum Dirac Hamiltonian, except for the fact that for our lattice model with explicitly broken chiral symmetry the boundaries of the Aoki phase remain sharp second-order phase transitions even at nonzero chiral chemical potential and there are no signatures of Cooper-type instabilities in the weakly interacting regime.