Correlations near the atomic limit of the anderson lattice

The authors develop exact nonlinear fermionic transformations which diagonalise the spin-/ Anderson lattice in the atomic limit. The original fermions, one localised and one conduction, are transformed into two new fermions which obey perfect anti-commutation relations. They find many possible transformations of which they consider two in some detail. Firstly, they analyse a transformation which is useful in the Kondo limit. It is accurate when the two smallest energy scales in the problem are the conduction band width and the hybridisation between the localised and conduction electrons. Secondly, they analyse a transformation useful in the mixed-valence limit. Here the accurate limit is when the two smallest energies are the conduction band width and the energy separation between the two orbitals. In the second limit, when the band is less than half filled, they find an effective Hamiltonian in terms of only one relevant fermion. This Hamiltonian is fairly general in this type of problem and includes a non-linear-hopping term. The most crucial aspect is the particle-hole asymmetry with particles being much more mobile than holes. © 1988 IOP Publishing Ltd.