Screening cloud in the k-channel Kondo model: Perturbative and large-k results

We demonstrate the existence of a large Kondo screening cloud in the k-channel Kondo model using both renormalization-group improved perturbation theory and the large-k limit. We study position r-dependent spin Green's functions in both static and equal-time cases. The equal-time Green's function provides a natural definition of the screening-cloud profile, in which the large scale xi(K) drop upsilon(F)/T-K appears (upsilon(F) is the Fermi velocity; T-K is the Kondo temperature). At large distances it consists of both a slowly varying piece and a piece which oscillates at twice the Fermi wave vector, 2k(F). This function is calculated at all r in the large-k limit. Static Green's functions (Knight shift or susceptibility) consist only of a term oscillating at 2k(F), and appear to factorize into a function of r times a function of T for rT/upsilon(F) much less than 1, in agreement with NMR experiments. Most of the integrated susceptibility comes from the impurity-impurity part with conduction-electron contributions suppressed by powers of the bare Kondo coupling. The single-channel and overscreened multichannel cases are rather similar, although anomalous power laws occur in the latter case at large r and low T due to irrelevant operator corrections.