The one dimensional Kondo lattice model at partial band filling

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.

Review, 258 pages, 19 figures

References in corpus (11)

• Localized spin ordering in Kondo lattice models
• Dimerization induced by the RKKY interaction
• Charge and spin inhomogeneous phases in the Ferromagnetic Kondo Lattice Model
• Small Fermi surface in the one-dimensional Kondo lattice model
• A Coulomb gas approach to the anisotropic one-dimensional Kondo lattice model at arbitrary filling
• Magnetic Polarons in the 1D FM Kondo Model
• Zero Temperature Series Expansions for the Kondo Lattice Model
• Phase diagram of the anisotropic Kondo chain
• Magnetism in the dilute Kondo lattice model
• Finite temperature bosonization
• Competing interactions of spin and lattice in the Kondo lattice model

Cited by in corpus (33)

• Ferromagnetic state in the one-dimensional Kondo lattice model
• New possibility of the ground state of quarter-filled one-dimensional strongly correlated electronic system interacting with localized spins
• Lifshitz phase transitions in the ferromagnetic regime of the Kondo lattice model
• Spin-incoherent behavior in the ground state of strongly correlated systems
• Strong-coupling limit of depleted Kondo- and Anderson-lattice models
• Double Exchange Ferromagnetism in the Peierls Insulator State
• Magnetic phase diagram of the Kondo lattice model with quantum localized spins
• Orbital-driven melting of a bosonic Mott insulator in a shaken optical lattice
• Quantum Phase Transition and Protected Ideal Transport in a Kondo Chain
• Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model
• Hubbard-Shastry lattice models
• Interplay of localized and itinerant behavior in the one-dimensional Kondo-Heisenberg model
• Faithful fermionic representations of the Kondo lattice model
• Physics of Arbitrary Doped Kondo Lattices: from a Commensurate Insulator to a Heavy Luttinger Liquid and a Protected Helical Metal
• Absence of a true long-range orbital order in a two-leg Kondo ladder
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• Low Energy Properties of the Kondo chain in the RKKY regime
• Pair-density-wave and $s\pm \mathrm{i}d$ superconductivity in a strongly coupled, lightly doped Kondo insulator
• Majorana fermion description of the Kondo lattice: Variational and Path integral approach
• Charge Order in the Falicov-Kimball Model
• The one-dimensional Kondo lattice model at quarter-filling
• Kondo lattice model at half-filling
• Nontrivial topology and localization in the double exchange model with possible applications to perovskite manganites
• Hybridization oscillation in the one-dimensional Kondo-Heisenberg model with Kondo holes
• Bosonization solution of the Falicov-Kimball model
• Hidden hyperspace geometry and long-distance quantum coupling
• Electric and Magnetic Properties of Higher-Spin Kondo-Heisenberg Models at Strong Coupling
• Transport in Magnetically Doped One-Dimensional Wires: Can the Helical Protection Emerge without the Global Helicity?
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Ferromagnetism in the one-dimensional Kondo lattice: mean-field approach via Majorana fermion canonical transformation
• Quadratic operators used in deducing exact ground states for correlated systems: ferromagnetism at half filling provided by a dispersive band
• Solution of one-dimensional Kondo lattice model, ground state calculation
• Electronic polarons in an extended Falicov-Kimball model