Slave-boson phase diagram of the two-dimensional extended Hubbard model: Influence of electron-phonon coupling

Abstract

We present a detailed study of the extended Hubbard-Peierls model on a square lattice using the slave-boson method proposed by Kotliar and Ruckenstein. The emphasis is on the investigation of the ground state phase diagram. To compare the relative stability of several homogenous phases, the effective bosonized action was evaluated by means of a two-sublattice saddlepoint approximation which allows for the symmetry broken states compatible with the underlying bipartite lattice structure. Paying particular attention to the interplay of electron-electron and electron-phonon interaction, we take into account various types of magnetic ordered phases, i.e. para-, ferro-, ferri-, and antiferromagnetic states, as well as charge ordered phases, e.g. a static (π, π) Peierls distorted state. Furthermore the approach has been applied to the following special cases: the Hubbard model, the extended Hubbard model, and the Hubbard-Peierls model. A careful numerical solution of the corresponding self-consistency equations enables us to map out the ground-state phase diagrams of the various models at arbitrary band filling over the whole range of interaction strength. In the phase diagram of the Hubbard model we found a large region with ferrimagnetic order away from half-filling. The phase diagram of the halffilled band extended Hubbard model shows a first-order transition from a spin-density-wave to a charge-density-wave state which is displaced from the mean-field lineU=4V towards largerV. At large negativeU andV we obtain a domain with charge separation. The phase compares favorably with earlier quantum Monte-Carlo results. Including the local electron-phonon coupling the charge-density-wave region is considerably enlarged. Away from half-filling the phase diagram becomes more complex: besides the pure magnetic phases we obtain ferri- and paramagnetic states which show additional charge-density order. Aspects of phase separation are discussed. Finally we investigate the variation of the different gap and order parameters along characteristic lines in the parameter space and determine the renormalized quasiparticle bands.