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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 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 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
charge density wave in a broad doping regime,
including commensurate ones. We find that in the large limit, intersite
Coulomb repulsion strongly suppresses the single-particle weight of the
metallic state.Comment: 10 pages, 11 figures, submitted to PR
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