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

Bosonization Solution of the Falicov-Kimball Model

“…(10). Near the SEG phase we can use the same values for S α (x j ) and L α (x j ) as in the CP analysis; for MVS behaviour both these objects vanish.…”

“…(3) satisfies the conditions Λ α (k) ≈ 1 for |k| < π α and Λ α (k) ≈ 0 otherwise. Λ α (k) enforces the finite minimum wavelength α > a of the bosonic density fluctuations ρ ν (k): taking into account this wavelength limit is essential for preserving the lattice structure of the FKM [10]. Since the Bose fields cannot 'resolve' distances less than α, we find that the usual field commutators are 'smeared' over this length scale:…”

Peierls and Spin-Peierls Instabilities in the Per2[M(mnt)2] Series of One-Dimensional Organic Conductors; Experimental Realization of a 1D Kondo Lattice for M = Pd, Ni and Pt

“…Note also since, as shown in Figure 2, magnetic chains are spatially decoupled from the conducting chains that α-Per 2 [M(mnt) 2 ] belongs to the category of two-chain 1D Kondo lattices. In this respect α-Per 2 [M(mnt) 2 ] differs from standard one chain Kondo lattices where, because of the presence of several electron species, spin localized and conducting electrons are located on the same chain such as in metal-phthalo-cyanine-iodine Cu(pc)I [57] or BaVS 3 [58] There is an abundant literature on 1D Kondo lattices based on elaborated theoretical considerations [51,59]. However, experimental clear-cut evidence of 1D Kondo lattice effects are quite sparse in the literature.…”

“…[51]). The mediated interaction (Expression (14)) provides in particular an indirect AF coupling between spins located on every second molecules (m = 2) on the dithiolate stack (note in Expression (14) at RT) [9] with a quarter-filled hole (or a three quarter filled electron) conduction band-see Figure 3a.…”

Ferromagnetic order in the one-dimensional Anderson lattice

“…(the effective width of the f-levels due to hybridization), the single-impurity Anderson model can be perturbatively mapped onto the Kondo impurity [4,5]. As the f 1 -level lies far below the Fermi energy and the f 2 -level lies far above, the ion is always singly occupied, thus maintaining a spin-1/2 moment.…”