Real-space renormalization group flow in quantum impurity systems:local moment formation and the Kondo screening cloud Phys. Rev. B 84, 115120 (2011)
Andrew K. Mitchell, Michael Becker, Ralf Bulla
The existence of a length-scale xi_K~1/T_K (with T_K the Kondo temperature) has long been predicted in quantum impurity systems. At low temperatures T < T_K, the standard interpretation is that a spin-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_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 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.
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