Renormalization approach to bound states

A new semi-analytical approach to bound states based on a unitary transformation of the Hamiltonian is presented. The method is applied to study the interaction between a superconductor and a quantum spin. Known results from the t-matrix method and numerical studies are reproduced. A uniform picture of the interplay between the Yu-Shiba-Rusinov (YSR) bound states and the Kondo singlet state is presented by revealing the structure of the quasiparticles in both phases. The method can straightforwardly be extended to study the topological properties of combined bound states in chains of magnetic impurities.