Kondo effect in a fermionic hierarchical model
Giuseppe Benfatto, Giovanni Gallavotti, Ian Jauslin
2015
Abstract
In this paper, a fermionic hierarchical model is defined, inspired by the Kondo model, which describes a 1dimensional lattice gas of spin1/2 electrons interacting with a spin1/2 impurity. This model is proved to be exactly solvable, and is shown to exhibit a Kondo effect, i.e. that, if the interaction between the impurity and the electrons is antiferromagnetic, then the magnetic susceptibility of the impurity is finite in the 0temperature limit, whereas it diverges if the interaction is ferromagnetic. Such an effect is therefore inherently nonperturbative. This difficulty is overcome by using the exact solvability of the model, which follows both from its fermionic and hierarchical nature.
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 tarball: 15bgj1.2.tar.gz
 git repository: 15bgjgit (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).
Supplementary material
 Some of the computations were carried out using a program called meankondo, which is available at http://ian.jauslin.org/software/meankondo.
Other releases
 arXiv preprint: arXiv1506.04381
 peerreviewed version, published in the Journal of Statistical Physics, Volume 161, issue 5, page 12031230, doi:10.1007/s1095501513787
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[GJ15]: Kondo effect in the hierarchical sd model
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(published in Journal of Statistical Physics, volume 161, issue 5, pages 12311235, 2015)
pdf, source
Talks
This work has been presented at the following conferences:

[IAS16]: Strongcoupling renormalization group in the hierarchical Kondo model
Institute for Advanced Study, Princeton, USA, Sep 21 2016
video, pdf 
[Zur16]: Strongcoupling renormalization group in a hierarchical Kondo model
University of Zurich, Switzerland, Mar 24 2016
pdf 
[PhD16]: The renormalization group in the weak and strongcoupling regimes
PhD defense, University of Rome "Sapienza", Rome, Italy, Jan 22 2016
pdf 
[Rut15]: Nonperturbative renormalization group in a hierarchical Kondo model
Rutgers University, USA, Sep 03 2015
pdf 
[ICMP15]: Nonperturbative renormalization group in a hierarchical Kondo model
XVIII International Congress of Mathematical Physics, Santiago, Chile, Jul 30 2015
pdf 
[TQMS15]: Nonperturbative renormalization group in a hierarchical Kondo model
Trails in Quantum Mechanics and Surroundings, Como, Italy, Jul 09 2015
pdf