Charge ordering and magnetism in quarter-filled Hubbard-Holstein model

We study a two-dimensional Hubbard-Holstein model with phonons treated in the adiabatic limit. A Hartree-Fock decomposition is employed for the Hubbard term. A range of electronic densities are discussed with special emphasis on the quarter filling (n=0.5). We argue that the quarter-filled system is relevant for the electronic properties observed at the interface between LaAlO₃ and SrTiO₃, where half-electron per unit cell is transferred to the TiO₂ layer as a consequence of the polar discontinuity at the interface. In addition to presenting the overall phase diagrams, we identify an interesting charge-ordered antiferromagnetic phase for n=0.5, which was also reported recently in the ab initio study of the LaAlO₃-SrTiO₃ interface.