Effective models for the single impurity Anderson and Kondo model from continuous unitary transformations

Abstract

The method of continuous unitary transformations (CUTs) is applied to the Anderson impurity and the Kondo model aiming at the systematic derivation of convergent e ective models. If CUTs are applied in a conventional way, diverging di erential equations occur. Similar to poor mans scaling the energy scale, below which the couplings diverge, corresponds to the Kondo temperature TK. We present a way to apply CUTs to the Kondo and to the Anderson impurity model so that no divergences occur but a converged e ective low-energy model is derived with small nite parameters at arbitrarily small energies. The ground state corresponds to a bound singlet with a binding energy given by the Kondo temperature TK.