Ground states of the Falicov-Kimball model with correlated hopping

Two-dimensional spinless Falicov-Kimball model (FKM) with correlated hopping is studied perturbatively in the limit of large on-site Coulomb interaction U. In the half filled case (i.e., ρ_i+ρ_e=1, where ρ_i,ρ_e are densities of ions and electrons, respectively) the effective Hamiltonian in spin variables is derived up to terms proportional to U^-3. Unlike the simplest FKM case, it contains odd parity terms (resulting from the correlated hopping) in addition to even parity ones. The ground-state phase diagram of the effective Hamiltonian is examined in the (a/t,h) plane, where a/t is a parameter characterizing strength of the correlated hopping and h is a difference of chemical potentials of two sorts of particles present in the system. It appears to be asymmetric with respect to the change h→-h and an additional ordered phase is found for a certain interval of a/t.