Theory of the Anderson Impurity Model: The Schrieffer-Wolff Transformation Reexamined

We test the method of infinitesimal unitary transformations recently introduced by Wegner on the Anderson single impurity model. It is demonstrated that infinitesimal unitary transformations in contrast to the Schrieffer-Wolff transformation allow the construction of an effective Kondo Hamiltonian consistent with the established results in this well understood model. The main reason for this is the intrinsic energy scale separation of Wegner's approach with respect to arbitrary energy differences coupled by matrix elements. This allows the construction of an effective Hamiltonian without facing a vanishing energy denominator problem. Similar energy denominator problems are troublesome in many models. Infinitesimal unitary transformations have the potential to provide a general framework for the systematic derivation of effective Hamiltonians without such problems.