Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization

The screening of an impurity spin in the Kondo model occurs over a characteristic length scale $\xi_K$, that defines the size of the Kondo screening cloud or ``mist". The presence of such a length sc A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations depending on $r$, in terms of the single variable $r/\xi_K$ rather than depending on $r$ and $\xi_K$ separately. Here we study the paradigmatic one channel Kondo model using a spin chain representation, with an impurity spin at one end of the chain coupled with a strength $J_K'$. Using Fermi liquid theory combined with numerical results, we obtain new high precision estimates of the non-universal terms in the entanglement entropy which leads to a verification of the expected non-integer ground-state degeneracy, $g$. This then allows us to study the impurity contribution to the entanglement in detail. If the impurity coupling $J_K'$ is varied, a precise determination of $\xi_K$ can then be obtained. The length scale, $\xi_K$, is then shown to characterize the scaling of both the uniform and alternating part of a measure of the magnetization of part of an odd length chain with.