Solution of effective Hamiltonian of impurity hopping between two sites in a metal

TL;DR

This paper thoroughly analyzes the fixed points of an effective Hamiltonian for a non-magnetic impurity hopping between two sites in a metal, revealing a continuum of non-Fermi liquid states and their relation to known Kondo fixed points.

Contribution

It identifies a line of non-Fermi liquid fixed points interpolating between 2-channel and 2-impurity Kondo fixed points, extending understanding of impurity behavior in metals.

Findings

Discovery of a continuous line of non-Fermi liquid fixed points.

Derivation of scaling functions for measurable quantities.

Analysis of effects of particle-hole symmetry breaking and magnetic fields.

Abstract

We analyze in detail all the possible fixed points of the effective Hamiltonian of a non-magnetic impurity hopping between two sites in a metal obtained by Moustakas and Fisher(MF). We find a line of non-fermi liquid fixed points which continuously interpolates between the 2-channel Kondo fixed point(2CK) and the one channel, two impurity Kondo (2IK) fixed point. The additional non-fermi liquid fixed point found by MF has the same symmetry as the 2IK, The system is shown to flow to a line of fermi-liquid fixed points which continuously interpolates between the non-interacting fixed point and the 2 channel spin-flavor Kondo fixed point (2CSFK) discussed by the author previously. The effect of particle-hole symmetry breaking is discussed. The effective Hamiltonian in the external magnetic field is analysed. The scaling functions for the physical measurable quantities are derived in the different regimes; their predictions for the experiments are given. Finally the implications are given for a non-magnetic impurity hopping around three sites with triangular symmetry discussed by MF.