The ground-state phase diagram of the one-dimensional Kondo lattice model

The periodic Anderson and Kondo lattice model describe the physics of conduction electrons in extended orbitals interacting with strongly correlated electrons in localized orbitals. These models are relevant for the so-called heavy-fermion and related systems such as the Kondo insulators. In this review we summarize recent progress in the understanding of these models, in particular, the one-dimensional Kondo lattice model. The ground-state phase diagram for the one-dimensional Kondo lattice model is determined and shows three distinct phases: a ferromagnetic metallic, an insulating spin liquid, and a paramagnetic metallic state. We present results on these phases obtained from rigorous and approximate analytical calculations supported by various extensive numerical studies on finite-size systems. The ferromagnetic phase appears in the limit of low density of conduction electrons and for strong Kondo coupling away from half filling. On the other hand, the half-filled Kondo lattice has a gap in both spin and charge excitations, i.e., it has a spin-liquid ground state. The paramagnetic phase may be considered as the generic heavy-fermion state and appears in the weak-coupling limit away from half filling. While the former two phases are well understood, the physics of the paramagnetic phase is not worked out in detail yet. In this context various questions will be considered here: Does the Fermi surface include conduction electrons only or also the localized electrons? Does the concept of Luttinger liquid apply in this case? The extension of these results to higher dimensions is also discussed. It is important to notice that the ground states of the Kondo lattice and the periodic Anderson model involve complicated effects, which cannot be understood by simple extension of the single- or two-impurity problem.