Quantum impurity models play an important role in many areas of physics from condensed matter to AMO and quantum information. They are important models for many physical systems but also provide key insights to understanding much more complicated scenarios. In this paper we introduce a simplified method to describe the thermodynamic properties of integrable quantum impurity models. We show this method explicitly using the anisotropic Kondo and the interacting resonant level models. We derive a simplified expression for the free energy of both models in terms of a single physically transparent integral equation which is valid at all temperatures and values of the coupling constants.
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