Polaron formation in a model Hamiltonian with covalent electron-phonon interactions

We have performed an exact diagonalization of a many body Hamiltonian that includes electron correlations and electron-phonon interactions. Electronic and phononic parameters entering in the Hamiltonian were chosen for the cluster O(4)-Cu-O(4) cluster in YBa2Cu3O7. Electronic and phononic degrees of freedom are coupled through the bare electron hopping, as in the Su-Schieffer-Heeger (SSH) Hamiltonian [W. P. Su et al., Phys. Rev. Lent. 42, 1698 (1979); A. J. Heeger, Rev. Mod. Phys. 60, 781 (1988)]. Fixing all parameters entering in the model Hamiltonian, the electron-phonon coupling was varied in order to reproduce structural short-range distortions found in the z-axis direction for YBa2-Cu3O7. Although the inferred structural distortions are reproduced, we find that this type of coupling, unlike the electron-phonon coupling introduced in Peierls-Hubbard models, does not lead to excitations with polaronic energies and negative isotopic shifts typical of polaronic excitations.