Integrable one-dimensional heavy fermion lattice model

Abstract

We consider a one-dimensional lattice gas of interacting electrons embedding a finite concentration of magnetic impurities. The host electrons propagate with nearest neighbor hopping t, constrained by the excluded multiple occupancy of the lattice sites, and interact with electrons on neighboring sites via spin exchange J and a charge interaction ( t- J model). The host is integrable at the supersymmetric point, J = 2 t, where charges and spin form a graded FFB superalgebra. Without destroying the integrability we introduce a finite concentration of mixed-valent impurities with two magnetic configurations of spin S and (S + 1 2 ) , respectively, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the correlated host with impurities and discuss the ground-state properties as a function of magnetic field and the Kondo exchange coupling. While for an isolated impurity the ground state is magnetic of effective spin S, a finite concentration of impurities introduces an additional Dirac sea (the impurity band), which gives rise to a singlet ground state. The impurities are antiferromagnetically correlated and frustrated in zero-field. As a function of field first the narrow impurity band is spin polarized. The van Hove singularities of the spindashrapidity bands define critical fields at which the susceptibility diverges. The number of itinerant electrons and the concentration of impurities can be varied continuously, so that the Kondo problem, the supersymmetric t- J model and the antiferromagnetic Heisenberg chain are contained as special limits. The properties of the model are related to heavy fermion alloys and the Kondo lattice.