The kondo screening cloud

Abstract

The spin-1=2 Kondo model describes an antiferromagnetic exchange interaction between an impurity spin and the spin-density of a Fermi gas. Although the thermodynamics of this system have been resolved, there are still some unanswered questions regarding its spatial features. The spatial region of correlation between the impurity spin and the spin-density of the Fermi gas is referred to as the Kondo screening cloud. For the case of anisotropic couplings, the cloud consists of four distinct components. In this dissertation we use the bosonization technique to derive both an exact numeric and an approximate analytic expression for the forward scattering longitudinal cloud at the Toulouse point. The expressions are then extended to incorporate the effects of a time-independent external magnetic field. The non-magnetic case displays universal scaling behavior, while the addition of an external magnetic field only slightly spoils the scaling in the vicinity of the crossover length (B) K , but remarkably not deep inside or outside the cloud.