Real-space renormalization group flow in quantum impurity systems: local moment formation and the Kondo screening cloud

Abstract

The existence of a length-scale ${\xi }_K\sim 1/T_K$ (with $T_K$ the Kondo temperature) has long been predicted in quantum impurity systems. At low temperatures $T\ll T_K$, the standard interpretation is that a spin-$\frac{1}{2}$ impurity is screened by a surrounding `Kondo cloud' of spatial extent ${\xi }_K$. We argue that renormalization group (RG) flow between any two fixed points (FPs) results in a characteristic length-scale, observed in real-space as a crossover between physical behaviour typical of each FP. In the simplest example of the Anderson impurity model, three FPs arise; and we show that `free orbital', `local moment' and `strong coupling' regions of space can be identified at zero temperature. These regions are separated by two crossover length-scales ${\xi }_{\text{LM}}$ and ${\xi }_K$, with the latter diverging as the Kondo effect is destroyed on increasing temperature through $T_K$. One implication is that moment formation occurs inside the `Kondo cloud', while the screening process itself occurs on flowing to the strong coupling FP at distances $\sim {\xi }_K$. Generic aspects of the real-space physics are exemplified by the two-channel Kondo model, where ${\xi }_K$ now separates `local moment' and `overscreening' clouds.

6 pages; 5 figures

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