  We study the complete extended Hubbard-Holstein Hamiltonian on a four-site
chain with equally spaced sites, with spacing-dependent electronic interaction
parameters evaluated in terms of Wannier functions built from Gaussian atomic
orbitals. By successive application of generalized displacement and squeezing
transformations, an effective polaronic Hamiltonian is obtained, containing a
purely phonon-induced, long-range intersite charge interaction. The phase
diagrams for N=1,2,3,4 electrons have been determined by variational
minimization of the sum of the electronic and the phononic energy, paying
special attention to the effects of the above mentioned phonon-induced
long-range interaction. To characterize the physics of each ground state, we
have evaluated how variations of the site spacing affect the behavior of
several correlation functions of experimental interest, with the aim of
representing lattice deformation effects, either spontaneous or induced by
external pressure.
