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Kondo effect in the hierarchical s-d model

Giovanni Gallavotti, Ian Jauslin

2015

Abstract

The s-d model describes a chain of spin-1/2 electrons interacting magnetically with a two-level impurity. It was introduced to study the Kondo effect, in which the magnetic susceptibility of the impurity remains finite in the 0-temperature limit as long as the interaction of the impurity with the electrons is anti-ferromagnetic. A variant of this model was introduced by Andrei, which he proved was exactly solvable via Bethe Ansatz. A hierarchical version of Andrei's model was studied by Benfatto and the authors. In the present letter, that discussion is extended to a hierarchical version of the $s-d$ model. The resulting analysis is very similar to the hierarchical Andrei model, though the result is slightly simpler.

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PDF:

• Gallavotti_Jauslin_2015.pdf

LaTeX source:

• tarball: 15gj-1.1.tar.gz
• git repository: 15gj-git (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: arXiv-1507.05678
• peer-reviewed version, published in the Journal of Statistical Physics, Volume 161, issue 5, page 1231-1235, doi:10.1007/s10955-015-1370-2

Related articles

• [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 1203-1230, 2015)
  pdf, source

Talks

This work has been presented at the following conferences:

• [IAS16]: Strong-coupling renormalization group in the hierarchical Kondo model
  Institute for Advanced Study, Princeton, USA, Sep 21 2016
  video, pdf


• [Zur16]: Strong-coupling renormalization group in a hierarchical Kondo model
  University of Zurich, Switzerland, Mar 24 2016
  pdf


• [PhD16]: The renormalization group in the weak- and strong-coupling regimes
  PhD defense, University of Rome "Sapienza", Rome, Italy, Jan 22 2016
  pdf


• [Rut15]: Non-perturbative renormalization group in a hierarchical Kondo model
  Rutgers University, New Brunswick, New Jersey, USA, Sep 03 2015
  pdf