Regular and Singular Fermi Liquid fixed points in quantum impurity models

We show that thermodynamics is insufficient to probe the nature of the low energy dynamics of quantum impurity models and a more subtle analysis based on scattering theory is required. Traditionally, quantum impurity models are classified into one of two categories: Fermi liquids and non-Fermi liquids, depending on the analytic properties of the various thermodynamic quntities. We show, however, that even when a quantum impurity model is a Fermi liquid (an incoming electron at the Fermi level scatters elastically off the impurity), one may find singular thermodynamic behavior if characteristics of quasiparticles are not analytic near the Fermi surface. Prompted by this observation, we divide Fermi liquids into two categories: regular Fermi liquids and singular Fermi Liquids. The difference between regular Fermi liquids, singular Fermi liquids, and non-Fermi liquids fixed points is explained using properties of the many-body S-matrix for impurity quasiparticle scattering. Using the Bethe-Ansatz and numerical RG, we show that whereas the ordinary Kondo Model is a regular Fermi liquid the underscreened Kondo model is a a singular Fermi liquid. This results in a breakdown of Nozieres' Fermi liquid picture for the underscreened and explains the singular thermodynamic behavior noticed in Bethe Ansatz and large-N calculations. Furthermore, we show that conventional regular Fermi liquid behavior is re-established in an external magnetic field H, but with a density of states which diverges as 1/H. Possible connections with the field-tuned quantum criticality recently observed in heavy electron materials are also discussed.