Phase diagram of the extended Hubbard chain with charge-dipole interactions

We consider a modified extended Hubbard model (EHM) which, in addition to t he on-site repulsion U and nearest-neighbor repulsion V includes polarizati on effects in second-order perturbation theory. The model is equivalent to an EHM with renormalized U plus a next-nearest-neighbor repulsion term. Usi ng a method based on topological quantum numbers (charge and spin Berry pha ses), we generalize to finite hopping t the quantum phase diagram in one di mension constructed by van den Brink et al. [Phys. Rev. Lett. 75, 4658 (199 5)]. At hopping t = 0 there are two charge density-wave phases, one spin de nsity-wave phase, and one intermediate phase with charge and spin ordering, depending on the parameter values. At t not equal 0 the nature of each pha se is confirmed by studying correlation functions. However, in addition to the strong-coupling phases, a small region with bond ordering appears. The region occupied by the intermediate phase first increases and then decrease s with increasing t, until it finally disappears for t of the order but lar ger than U. For small t, the topological transitions agree with the results of second-order perturbation theory.