FM 05-15; arXiv:1506.04381

Authors : Giuseppe Benfatto, Giovanni Gallavotti, Ian Jauslin

Title: Kondo effect in a fermionic hierarchical model

Sommario: 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.

Keywords: Renormalization group; Non-perturbative renormalization; Kondo effect; Fermionic hierarchical model; Quantum field theory

Giuseppe Benfatto
Università degli studi di Roma "Tor Vergata", 00133 Roma, Italy
benfatto@mat.uniroma2.it

Giovanni Gallavotti
INFN Fisica, Rutgers University e Accademia dei Lincei
Università di Roma Sapienza, 00185 Roma, Italy
giovanni.gallavotti@roma1.infn.it

Ian Jauslin
University of Rome "La Sapienza", 00185 Roma, Italy
ian.jauslin@roma1.infn.it
http://ian.jauslin.org

Supplementary material: The computation of the flow equation for the hierarchical Kondo model can be carried out using the meankondo program, available from http://ian.jauslin.org/software/meankondo