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 1-dimensional lattice gas of spin-1/2 electrons interacting with a spin-1/2 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 0-temperature limit, whereas it diverges if the interaction is ferromagnetic. Such an effect is therefore inherently non-perturbative. 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: 15bgj-1.2.tar.gz
- git repository: 15bgj-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-1506.04381
- peer-reviewed version, published in the Journal of Statistical Physics, Volume 161, issue 5, page 1203-1230, doi:10.1007/s10955-015-1378-7
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[GJ15]: Kondo effect in the hierarchical s-d model
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(published in Journal of Statistical Physics, volume 161, issue 5, pages 1231-1235, 2015)
pdf, source
Talks
This work has been presented at the following conferences:
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[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 -
[ICMP15]: Non-perturbative renormalization group in a hierarchical Kondo model
XVIII International Congress of Mathematical Physics, Santiago, Chile, Jul 30 2015
pdf -
[TQMS15]: Non-perturbative renormalization group in a hierarchical Kondo model
Trails in Quantum Mechanics and Surroundings, Como, Italy, Jul 09 2015
pdf