Impurity Spin Susceptibility of the Anderson model: A Perturbative Approach

We have investigated the temperature dependence of the impurity spin susceptibility for a single-impurity Anderson model. Our analysis is based on a perturbative approach to the Anderson Hamiltonian in which the expansion parameter is proportional to U, the on-site Coulomb repulsion energy. We find that the perturbative expansion correctly reproduces the results obtained with the renormalization-group approach. Our work shows that, in most relevant cases, if the conduction-electron density of states is not taken to be a simple constant for all energies, the impurity spin-spin response function and the impurity spin susceptibility differ substantially. In fact, in calculating the latter, particular care must be exercised in order to properly include the effects induced on the conduction electrons by the presence of the impurity. For all practical purposes, this amounts to a breakdown of what is commonly referred to as the Clogston-Anderson compensation theorem. A condition allowing one to establish in most cases the relevance of these corrections is discussed.