The existence of a length-scale $\xi_K\sim 1/T_K$ (with $T_K$ the Kondotemperature) has long been predicted in quantum impurity systems. At lowtemperatures $T\ll T_K$, the standard interpretation is that aspin-$\tfrac{1}{2}$ impurity is screened by a surrounding `Kondo cloud' ofspatial extent $\xi_K$. We argue that renormalization group (RG) flow betweenany two fixed points (FPs) results in a characteristic length-scale, observedin real-space as a crossover between physical behaviour typical of each FP. Inthe simplest example of the Anderson impurity model, three FPs arise; and weshow that `free orbital', `local moment' and `strong coupling' regions of spacecan be identified at zero temperature. These regions are separated by twocrossover length-scales $\xi_{\text{LM}}$ and $\xi_K$, with the latterdiverging as the Kondo effect is destroyed on increasing temperature through$T_K$. One implication is that moment formation occurs inside the `Kondocloud', while the screening process itself occurs on flowing to the strongcoupling FP at distances $\sim \xi_K$. Generic aspects of the real-spacephysics are exemplified by the two-channel Kondo model, where $\xi_K$ nowseparates `local moment' and `overscreening' clouds.
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