F eb 1 99 7 One - dimensional Kondo lattice at partial band filling

An effective Hamiltonian for the localized spins in the one-dimensional Kondo lattice model is derived via a unitary transformation involving a bosonization of delocalized conduction electrons. The effective Hamiltonian is shown to reproduce all the features of the model as identified in various numerical simulations, and provides much new information on the ferro-to-paramagnetic phase transition and the paramagnetic phase. PACS No. 71.27.+a, 71.28.+d, 75.20.Hr Typeset using REVTEX 1 The Kondo lattice model (KLM) describes the interaction between a conduction band and a half-filled narrow f -band, and is thought to capture the essential physics of some of the rare earth compounds [1]. Although intensively studied for two decades, the KLM is still far from being completely understood. Even in the simple one-dimensional (1D) model, and with the conduction band less than half-filled, there are only two limits in which the behavior has been analyzed successfully; in the limit of vanishing conduction electron (CE) density, and for antiferromagnetic Kondo couplings J > 0, the f -electrons (f -spins) form a ferromagnetic (FM) ground-state [2]; in the strong-coupling limit J → ∞, and for any filling of the conduction band, the unpaired f -spins are again found to be FM [3]. The intermediateto weak-coupling regime, away from half-filling but at finite CE density, has proved particularly difficult to analyze [3]. From the known limiting behavior [2,3], together with a consensus of recent numerical simulations using the density-matrix renormalization-group, exact numerical diagonalization, and quantum Monte Carlo [4–6], a successful theory of the less than half-filled 1D KLM will account for the following ground-state behavior of the f -spins: (i) At strongto intermediate-coupling the unpaired f -spins are FM at all fillings and show behavior in accord with the strong-coupling expansion [3]. (ii) As the coupling is lowered, and for finite CE density, the system undergoes a transition to a paramagnetic (PM) state, with a filling dependent critical coupling in the weak to intermediate range. (iii) At weak-coupling, the system is characterized by a strong peak in the f -spin structure factor at 2kF of the CEs. In this Letter we derive an effective Hamiltonian Heff from the 1D KLM which reproduces all the observed behavior in the intermediateto weak-coupling regime. Heff treats the f -spins exactly while the CEs are treated using bosonization techniques. The essential new ingredient in our work is an emphasis on describing delocalized CEs, as these are responsible for the observed magnetic behavior of the f -spins. The problem of accessing the intermediateto weak-coupling regime nonperturbatively is solved using a unitary transformation. The effective Hamiltonian maps to the quantum random transverse-field Ising spin chain near the FM-PM boundary, and using extensive work on this interesting model by