NUMERICAL EXACT-DIAGONALIZATION STUDY OF THE ONE-DIMENSIONAL SYMMETRICAL KONDO LATTICE

The one-dimensional symmetric (i.e., half-filled) Kondo lattice is studied by numerical exact diagonalization for a range of parameters. Chains of N = 4, 6, and 8 sites are considered, with both periodic and antiperiodic boundary conditions. Over the full parameter range the ground state is found to be a total spin singlet and the rms spin in the conduction electron and localized spin subsystems are found to be equal. Correlations between localized spins are of antiferromagnetic type and converge to a finite value in the limit of small exchange interaction J. When J-->0 a lower bound for nearest-neighbor spin correlations is determined in the limit of an infinite number of sites. For large J the spin correlation function appears to decay exponentially in space. As J increases, the crossover to behavior where Kondo compensation of the localized spins by conduction electrons dominates over correlations between the localized spins, occurs at a larger value of J than would be expected for the two impurity problem. The J dependence of the spin susceptibility is consistent with a Kondo (coherence) gap much larger than the impurity Kondo temperature. For large J the spectrum and nature of spin wave and quasiparticle/quasihole excitations are determined. The lowest excited state is the spin wave of wave vector k = pi reflecting the tendency towards antiferromagnetism for the half-filled conduction band. Spin-wave excitations have the character of waves in the localized spin subsystem. The quasiparticle effective mass renormalization is seen to increase from its J = infinity value of m*/m0 = 2 indicating the formation of heavy quasiparticles as J decreases. The k dependence of the conduction-electron self-energy function can contribute significantly to the effective mass.