Surface modes and parity violation in Schwinger model on the lattice

The phase diagram of the Schwinger model on the lattice with Wilson fermions is investigated in the Hartree-Fock approximation. In case of single flavour (not directly amenable to simulations), the calculation indicates the existence of the parity violating phase at both weak and intermediate-to-strong couplings. Hartree-Fock vacuum sustains a nonzero electric field in this broken phase. The phase structure of the model with two flavours is also discussed.