Metal-insulator transition in the one-dimensional Kondo lattice model

Abstract

We study the usual one-dimensional Kondo lattice model (1D KLM) using the non-Abelian bosonization. At half filling, we obtain a Kondo insulator with a gap in both charge and spin excitations that varies quite linearly with the Kondo exchange ${J}_{K}.$ It consists of a spin-density glass state, or a $q=\ensuremath{\pi}$ spin density wave weakly pinned by a nearly antiferromagnetically ordered spin array. We will study the stability of this Kondo insulator against both quenched disorder and interactions between conduction electrons. Away from half filling, the metallic system now yields a very small spin gap that is equal to the one-impurity Kondo gap ${T}_{k}^{(\mathrm{imp})}.$ Unlike the one-impurity Kondo model, we will show that this Kondo phase cannot rule the fixed point of the 1D KLM, away from half filling. We rather obtain a heavy-fermion metallic state controlled by the energy scale ${T}_{\mathrm{coh}}\ensuremath{\propto}{(T}_{k}^{(\mathrm{imp})}{)}^{2}/t$ $(t$ is the hopping term) with a quite long-range antiferromagnetic polarization.