  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.
