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 Hubb ard model with an additional Holstein-type electron-phonon coupling on a square lattice. The effects of quantum lattice vibrations on the st rongly correlated electronic system are treated by means of a variatio nal squeezed-polaron wave function proposed by Zheng, where the possib ility of static (frozen) phonon-staggered ordering is taken into accou nt. Adapting the Kotliar-Ruckenstein slave boson approach to the effec tive 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 stre ngths. We determine the order parameters for long-range charge and/or spin ordered states from the self-consistency conditions for the auxil ary boson fields, including an optimization procedure with respect to the variational displacement, polaron and squeezing parameters. In ord er to characterize the crossover from the adiabatic (omega = 0) to the nonadiabatic (omega = infinity) regime, the frequency dependencies of these quantities are studied in detail. In the predominant charge (sp in) ordered phases the static Peierls dimerization (magnetic order) is strongly reduced with increasing omega. As the central result we pres ent the slave boson ground-state phase diagram of the Holstein-Hubbard model for finite phonon frequencies.