Hole doping and disorder effects on the one-dimensional Kondo lattice, for ferromagnetic Kondo couplings

We investigate the one-dimensional Kondo lattice model for ferromagnetic Kondo couplings. The so-called ferromagnetic two-leg spin ladder and the $S=1$ antiferromagnet occur as one-dimensional Kondo insulators. Both exhibit a spin gap. But, in contrast to the strong-coupling limit, the Haldane state which characterizes the two-leg spin-ladder Kondo insulator cannot fight against very weak exterior perturbations. First, by using standard bosonization techniques, we prove that an antiferromagnetic ground state occurs by doping with few holes; it is characterized by a form factor of the spin-spin correlation functions which exhibits two structures, respectively, at $q=\ensuremath{\pi}$ and ${q=2k}_{F}.$ Second, we prove precisely by using renormalization-group methods that the Anderson localization inevitably takes place in that weak-coupling Haldane system, by the introduction of quenched randomness; the spin-fixed point rather corresponds to a ``glass'' state. Finally, a weak-coupling analog of the $S=1$ antiferromagnet Kondo insulator is proposed; we show that the transition into the Anderson-localization state may be avoided in that unusual weak-coupling Haldane system.