Spin and charge correlations in the extended Hubbard-Holstein model

From the complete extended Hubbard-Holstein Hamiltonian we obtain a polaron ic effective Hamiltonian by successive application of generalized displacem ent and squeezing transformations, with wavevector dependent characteristic parameters which make possible a phonon-induced long range interaction bet ween charges, whose sign can change with the distance. As an application we consider the four-site chain, in which the bare electronic interactions ar e evaluated by model Wannier functions of gaussian shape. The ground states for different ranges of interactions are obtained by exact diagonalization of the effective Hamiltonian, followed by simultaneous and independent opt imization of the displacement and squeezing parameters. We consider the beh aviour of the static spin and charge correlation functions for the half-fil led case, upon varying the shape of the Wannier functions for given electro n-phonon coupling. Special attention is devoted to the influence of the pho non coupling on the presence of competing or coexisting charge- and spin-or dered states.