| We study the ground state and low energy excitations of the one-dimensional Anderson lattice using the density matrix renormalization group technique. We first look at the half-filled case, with the purpose of modeling Kondo insulators. We calculate the charge gap, spin gap and quasiparticle gap as a function of the repulsive interaction U using open boundary conditions for lattices as large as 24 sites. We find that the charge gap is larger than the spin gap for all U for both the symmetric and asymmetric cases. RKKY interactions are evident in the f-spin-f-spin correlation functions at large U in the symmetric case, but are suppressed in the asymmetric case as the f-level approaches the Fermi energy. This suppression can also be seen in the staggered susceptibility {dollar}chi(q=2ksb{lcub}f{rcub}),{dollar} and it is consistent with neutron scattering measurements of {dollar}chi(q){dollar} in CeNiSn. We investigate the effect of a small dispersion in the f-band. We find that in the strong coupling limit the quasiparticle gap remains almost unaffected by the hopping of the f-electrons. However, the spin gap is strongly suppressed. We also consider the system away from half-filling (metallic case). We map out the phase diagram by studying the ground state magnetization as a function of band filling using the density matrix renormalization group technique. For strong coupling, we find that the quarter-filled system has an S{dollar}={dollar}0 ground state with strong antiferromagnetic correlations. As additional electrons are added, we find first a ferromagnetic phase, as reported by Moller and Wolfle, and then a phase in which the ground state has total spin S = 0. Within this S = 0 phase, we find RKKY oscillations in the spin-spin correlation functions. In addition, we study the case of a magnetic impurity in a semiconducting host. We compare the behavior of this system with the case of an impurity in a metal. |
