Abstract
From the complete extended Hubbard-Holstein Hamiltonian we obtain a polaronic effective Hamiltonian by successive application of generalized displacement and squeezing transformations, with wavevector dependent characteristic parameters which make possible a phonon-induced long range interaction between charges, whose sign can change with the distance. As an application we consider the four-site chain, in which the bare electronic interactions are 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 optimization of the displacement and squeezing parameters. We consider the behaviour of the static spin and charge correlation functions for the half-filled case, upon varying the shape of the Wannier functions for given electron-phonon coupling. Special attention is devoted to the influence of the phonon coupling on the presence of competing or coexisting charge- and spin-ordered states.
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