Ground States of the Falicov-Kimball Model Extended by Nonlocal Coulomb Interactions

The small-cluster exact-diagonalizations are used to study the ground states of the Falicov-Kimball model extended by nonlocal Coulomb interactions (the nearest-neighbour interaction $U_{nn}$ and the correlated hopping t'). It is shown that the ground-state phase diagrams found for the conventional Falicov-Kimball model are strongly changed when the nonlocal interactions are added. This is illustrated for two selected values of the on-site Coulomb interaction (U) that represent typical behaviours of the model in the intermediate and strong coupling limit. A number of remarkable results are found. (i) The phase separation takes place for a wide range of $U_{nn}$ and t' in both interaction limits. (ii) New types of inhomogeneous charge ordering are observed for nonzero $U_{nn}$ and t'. (iii) Depending on the values of $U_{nn}$ and t', the model is able to describe both the continuous as well as discontinuous changes of the f-electron occupation number.