Stability of correlated electronic systems under the influence of the electron - phonon interaction

We have used an exact diagonalization technique to study the stability of the t − J-Holstein and Hubbard-Holstein models under the influence of the electron-phonon interaction. Previous results have been obtained using frozen-phonon technique or introducing only a few dynamical phonon modes due to the large Hilbert space. To check these results we have done exact diagonalization in a small cluster (four sites) including all the phonon modes allowed by symmetry. We compare our results with those obtained by using the adiabatic approximation.