Slave spins away from half filling: Cluster mean-field theory of the Hubbard and extended Hubbard models

A slave-spin representation of fermion operators has recently been proposed for the half-filled single and multiband Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. We solve the resulting spin problem using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength U is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical U for the Mott transition as a function of a frustrating nearest-neighbor interaction on lattices relevant for various correlated systems, namely, the cobaltates, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In addition to a uniform metallic state, we find a root(3) x root(3) charge density wave in a broad doping regime, including commensurate ones. We find that in the large U limit, intersite Coulomb repulsion V strongly suppresses the single-particle weight of the metallic state.