Hubbard dimer in near-surface magnetic and electric field: Magneto-electro-spatial phase transitions

In the paper we present a computational study of a model involving Hubbard dimer located at the surface, with parallel or perpendicular orientation possible. The dimer is immersed in electric field and inhomogeneous magnetic field, moreover, the charge transfer between the dimer and the surface is controlled by the chemical potential. The thermodynamic description is based on exact diagonalization within grand canonical ensemble formalism and focused on determination of dimer orientation, magnetization and electric polarization. The phase diagrams for ground state and finite temperatures are constructed and discussed. The possibility of cross-overs between the parallel and the perpendicular dimer orientation under the influence of the electric or magnetic field is demonstrated. The cross-overs are accompanied by the changes in such thermodynamic quantities as magnetization and electric polarization. The calculations enable the extensive discussion of the magneto-electro-spatial phase transitions in the system.