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

We investigate the one-dimensional Kondo lattice model (1D KLM) for ferromagnetic Kondo couplings. The so-called ferromagnetic 2-leg spin ladder and the S=1 antiferromagnet occur as new one-dimensional Kondo insulators. Both exhibit a spin gap. But, in contrast to the strong coupling limit, the Haldane state which characterizes the 2-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 $q=\pi$ 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 ``analogue'' 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.