We study a one-dimensional n -channel highly correlated electron model (based on the supersymmetric t-J model) with a magnetic impurity of arbitrary spin S that can hybridize with up to one itinerant electron per channel. The model extends the multichannel Kondo problem to correlations in the host and to the mixed valence regime. The Bethe ansatz equations are derived and solved for the ground state and for low temperatures. We conclude that the critical non-Fermi-liquid (overscreened) behaviour cannot be reached for this interacting electron system. Possible applications of the model are discussed.
The Hubbard chain with a magnetic impurity of arbitrary spin
S is studied using the Bethe ansatz technique. We consider two kinds of impurities which interact with itinerant electrons on the neighboring lattice sites without destroying the integrability. The correlations in the host always induce valence fluctuations at the impurity site. For a repulsive Hubbard
U, an impurity coupled via antiferromagnetic exchange to the host reveals magnetic properties similar to those of the ordinary Kondo effect. In contrast, a hybridization impurity (Anderson-like) embedded into the attractive Hubbard model gives rise to essentially different magnetic behavior. This difference is a consequence of the spin gap in the host.
We consider the one-dimensional gas of electrons interacting via an attractive δ-function potential. The attractive potential leads to the formation of Cooper-pair-like bound states with a spin gap. Without destroying the integrability, we introduce a finite concentration of mixed-valence impurities with two magnetic configurations of spin S and S + {{1}/{2}}, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the system for the correlated host with impurities and discuss the ground-state properties as functions of the concentration of impurities and the Kondo coupling. For a sufficiently large density of electrons the spin gap is reduced by the impurities and is closed at a critical concentration which depends on the impurity spin and the coupling strength. A ferromagnetic phase of unpaired spin-polarized itinerant electrons is induced for impurity concentrations larger than the critical one. The critical behaviour of the correlation functions is studied in the gapped and gapless regions using the mesoscopic energy spectrum and conformal field theory.