A renormalisation group approach to the mixed valence problem

The Anderson model of a magnetic impurity in a non-magnetic metallic host is investigated for cases in which the intra-atomic coulomb repulsion U is infinite. Using the (suitably defined) continuous group of renormalisation transformations the original Hamiltonian is transformed into a family of effective Hamiltonians by reducing the band edge cutoff D. Comparing problems which differ by an infinitesimal change in D leads directly to differential scaling equations for the energy of the localised level ( epsilon ) and the hybridisation interaction ( nu 1 ). Extrapolating this trend beyond the limit where perturbation theory is expected to be reliable eventually leads to a ground manifold of base states in which the localised level is unoccupied and the impurity behaves as if it is non-magnetic giving rise to ordinary potential scattering. Similar scaling equations are derived for a periodic array of atoms with mixed valence, but there are extra terms in the effective Hamiltonian reflecting the interactions between localised electrons via conduction electrons.