Nonperturbative renormnalization group in a hierarchical Kondo model
Trails in Quantum Mechanics and Surroundings, Como, Italy
July 9, 2015
Abstract
We consider a hierarchical version of the Kondo model, which consists in a 1dimensional chain of spin1/2 Fermions interacting magnetically with a single impurity. We approach the model using Wilson Renormalization Group techniques, in which we write the fields appearing in the corresponding Quantum Field Theory as a superposition of fields on different scales, and consider a hierarchical version of the model by assuming that a field on some scale does not fluctuate on smaller scales. Due to the Fermionic nature of the system, the hierarchical model is exactly solvable, in that the renormalization group flow equations are finite. In contrast to nonhierarchical models in which the flow equations are usually written as power series which only converge if the interaction is weak, the finite nature of the flow equations enables us to investigate the nonperturbative regime of the hierarchical model, i.e. when the renormalized interaction is not small. We show that if the interaction is antiferromagnetic, then the renormalization group flow tends to a nonGaussian fixed point, even for very small values of the interaction. This means that the behavior of the interacting system is qualitatively different from the noninteracting (Gaussian) one, which we illustrate by showing that the 0temperature magnetic susceptibility of the impurity, which is infinite in the noninteracting case, is finite for arbitrarily small antiferromagnetic interactions.
Joint work with Giuseppe Benfatto and Giovanni Gallavotti.
Slides
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 tarball: 15como1.0.3.tar.gz
 git repository: 15comogit (the git repository contains detailed information about the changes in the slides as well as the source code for all previous versions).
References
This presentation is based on

[BGJ15]: Kondo effect in a fermionic hierarchical model
Giuseppe Benfatto, Giovanni Gallavotti, Ian Jauslin, 2015
(published in Journal of Statistical Physics, volume 161, issue 5, pages 12031230, 2015)
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