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

Abstract

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 ${\text{LaAlO}}_{3}$ and ${\text{SrTiO}}_{3}$, where half-electron per unit cell is transferred to the ${\text{TiO}}_{2}$ 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 ${\text{LaAlO}}_{3}{\text{-SrTiO}}_{3}$ interface.