Eur. Phys. J. B 84, 273-281 (2011)
https://doi.org/10.1140/epjb/e2011-20727-3

Regular Article

Numerical calculation of the fidelity for the Kondo and the Friedel-Anderson impurities

Department of Physics & Astronomy, University of Southern California, Los Angeles, 90089-0484 California, USA

^a e-mail: gerd.bergmann@gmail.com

Received: 2 September 2011
Received in final form: 9 October 2011
Published online: 16 November 2011

Abstract

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N_eff of states. A plot of ln(F) versus N ∝ ln(N_eff) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F) – ln(N_eff) plot for the Kondo impurity diverges for large N_eff. On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N_eff when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime.