  We study the phase diagram of the extended Hubbard model on the kagome
lattice at 1/3 filling. By combining a configuration interaction approach to an
unrestricted Hartree-Fock, we construct an effective hamiltonian which takes
the correlations back on top of the mean-field solution. We obtain a rich phase
diagram with, in particular, the presence of two original phases. The first one
consists of polarized droplets of metal standing on the hexagons of the
lattice, and an enlarged kagome charge order, inversely polarized, on the
remaining sites. The second, obeying a local ice-rule type constraint on the
triangles of the kagome lattice, is driven by an antiferromagnetically coupling
of spins and is constituted of disconnected 6-spin singlet rings. The nature
and stability of these phases at large interactions is studied via variational
wave functions and perturbation theory.
