The one dimensional Kondo lattice model at partial band filling

TL;DR

This review provides a detailed bosonization-based analysis of the one-dimensional Kondo lattice model at partial band filling, exploring its phases, interactions, and the effects of disorder, with emphasis on ferromagnetic phase destruction.

Contribution

It offers a comprehensive, pedagogic bosonization approach to understanding the phase diagram and interactions in the 1D Kondo lattice model at partial band filling, including recent numerical insights.

Findings

Analysis of phase diagram and ferromagnetic phase destruction

Description of Kondo singlet formation and RKKY interaction

Comparison of antiferromagnetic and ferromagnetic cases

Abstract

The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds, called heavy fermion systems, and as such has been studied intensively by a wide variety of techniques for more than a quarter of a century. This review focuses on the one dimensional case at partial band filling, in which the number of conduction electrons is less than the number of localized moments. The theoretical understanding, based on the bosonized solution, of the conventional Kondo lattice model is presented in great detail. This review divides naturally into two parts, the first relating to the description of the formalism, and the second to its application. After an all-inclusive description of the bosonization technique, the bosonized form of the Kondo lattice hamiltonian is constructed in detail. Next the double-exchange ordering, Kondo singlet formation, the RKKY interaction and spin polaron formation are described comprehensively. An in-depth analysis of the phase diagram follows, with special emphasis on the destruction of the ferromagnetic phase by spin-flip disorder scattering, and of recent numerical results. The results are shown to hold for both antiferromagnetic and ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.