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 scale in experimental and numerical results is rather subtle. A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations in terms of the single variable, r/xi K instead of the correlations 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 JK ' . 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 JK ' 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.