Slave spin cluster mean field theory away from half-filling: Application   to the Hubbard and the extended Hubbard Model
  A new slave-spin representation of fermion operators has recently been proposed for the half-filled Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. The resulting spin problem can be solved 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 second-neighbor interaction on lattices relevant for various correlated systems, namely the cobaltites, 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 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, intersite Coulomb repulsion $V$ strongly suppresses the single-particle weight of the metallic state. 
S. R. Hassan and L. de' Medici