Spinless model of mixed valence: exact results and perturbation theory

The author studies a model of spinless electrons in f and d states on a lattice, with d-d hopping, one-electron f-d hybridisation between adjacent sites and intrasite f-d interactions (energies t, V and U respectively). In the limit t=0, the model is shown to be equivalent to a Hubbard model in a staggered magnetic field. In the limit U= infinity , a canonical transformation reduces it to a system of two species of fermions with unequal band masses and hard-core interactions. In the case of one electron per site the author treats t and V in second-order perturbation theory and derives an effective pseudospin Hamiltonian that has Dzyaloshinskii-Moriya interactions in addition to anisotropic Heisenberg coupling. These equivalences, exact and perturbative, are used to study the ground state and low lying excitations. With one electron per site and large U there is a charge-ordered phase provided the f-d energy separation is not too large. There are two phase transitions as the separation is varied from - infinity to infinity . Suggestions in the literature that there is a single phase transition if V=0 are shown to be incorrect, even if U is not that large