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A new slave-spin representation of fermion operators has recently beenproposed for the half-filled Hubbard model. We show that with the addition of agauge variable, the formalism can be extended to finite doping. The resultingspin problem can be solved using the cluster mean-field approximation. Thisapproximation takes short-range correlations into account by exactdiagonalization on the cluster, whereas long-range correlations beyond the sizeof clusters are treated at the mean-field level. In the limit where the clusterhas only one site and the interaction strength $U$ is infinite, this approachreduces to the Gutzwiller approximation. There are some qualitative differenceswhen the size of the cluster is finite. We first compute the critical $U$ forthe Mott transition as a function of a frustrating second-neighbor interactionon lattices relevant for various correlated systems, namely the cobaltites, thelayered organic superconductors and the high-temperature superconductors. Forthe triangular lattice, we also study the extended Hubbard model withnearest-neighbor repulsion. In additionto a uniform metallic state, we find a$\sqrt(3) \times \sqrt(3)$ charge density wave in a broad doping regime,including commensurate ones. We find that in the large $U$ limit, intersiteCoulomb repulsion $V$ strongly suppresses the single-particle weight of themetallic state.

Slave spin cluster mean field theory away from half-filling: Application to the Hubbard and the extended Hubbard Model