Electron correlations and quantum lattice vibrations in strongly coupled electron-phonon systems: A variational slave boson approach

We investigate the ground-state properties of the two-dimensional Hubbard model with an additional Holstein-type electron-phonon coupling on a square lattice. The effects of quantum lattice vibrations on the strongly correlated electronic system are treated by means of a variational squeezed-polaron wave function proposed by Zheng, where the possibility of static (frozen) phonon-staggered ordering is taken into account. Adapting the Kotliar-Ruckenstein slave boson approach to the effective electronic Hamiltonian, which is obtained in the vacuum state of the transformed phonon subsystem, our theory is evaluated within a two-sublattice saddle-point approximation at arbitrary band-filling over a wide range of electron-electron and electron-phonon interaction strengths. We determine the order parameters for long-range charge and/or spin ordered states from the self-consistency conditions for the auxilary boson fields, including an optimization procedure with respect to the variational displacement, polaron and squeezing parameters. In order to characterize the crossover from the adiabatic (=0) to the nonadiabatic (=) regime, the frequency dependencies of these quantities are studied in detail. In the predominant charge (spin) ordered phases the static Peierls dimerization (magnetic order) is strongly reduced with increasing . As the central result we present the slave boson ground-state phase diagram of the Holstein-Hubbard model for finite phonon frequencies.