Numerical Renormalization Group 1 II Application to Impurity Models 8 II . 1 Impurity Models with Non - Fermi Liquid Behaviour 8 II . 2 The Soft - Gap Anderson

The numerical renormalization group method (NRG) has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG has since then been applied to the calculation of static and dynamic properties of a variety of impurity models, in particular in the very low temperature regime. These investigations lead to a deeper understanding of the physics of magnetic impurities in a free conduction band, modeled by the single impurity Anderson or Kondo model. The properties of the nonFermi liquid ground state in the two-channel Kondo model and related models have also been studied in detail. Furthermore, the NRG has given insight into the e ect of correlations within the conduction band on the Kondo physics. In addition to the investigation of pure impurity models, the method has been recently applied to lattice models within the dynamical mean eld theory. In this context, the Mott metal-insulator transition in the Hubbard model has been investigated. For this problem, the ability of the NRG method to resolve arbitrarily low energy scales allows to study in detail the vanishing of the quasiparticle peak at the Mott transition. Further applications of the NRG include the appearance of a charge ordered state in the extended Hubbard model and the formation of the heavy fermion liquid in the periodic Anderson model. Table of