Screening cloud in thek-channel Kondo model: Perturbative and large-kresults

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 ${\xi }_K\equiv v_F{/T}_K$ appears ${(v}_F$ 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 ${rT/v}_F\ll 1$, 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.