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Europhysics Letters (EPL)

Ground-state magnetic properties of the Kondo lattice model at low electron densities

S. Caprara, Anders Rosengren

Published Jul 1, 1997• 24 citations
Publisher

Abstract

The infinite-size version of the density-matrix renormalization-group approach in real space is applied to the Kondo lattice model in one dimension, providing a more accurate determination of the zero-temperature magnetic properties for electron densities n ⩽ 0.5. The paramagnetic state of the free model evolves into a state with ferromagnetic correlations, by increasing the strength of the Kondo coupling, in agreement with previous numerical results. The change in the magnetic properties is produced by the competition between the RKKY mechanism, which favours the paramagnetic state in the weak-coupling region, and the Kondo screening, which leads to the formation of tightly bound singlets in the strong-coupling region, enforcing ferromagnetic correlations in the system.

DOI
10.1209/epl/i1997-00313-4

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We compute the magnetic structure factor, the singlet correlation function, and the momentum distribution of the one-dimensional Kondo lattice model at the density \ensuremath{\rho}=0.7. The density-matrix--renormalization-group method is used. We show that in the weak-coupling regime, the ground state is paramagnetic. We argue that a Luttinger-liquid description of the model in this region is consistent with our calculations. In the strong-coupling regime, the ground state becomes ferromagnetic. The conduction electrons show a spinless-fermionlik
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The Kondo effect in a one-dimensional spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ model in the gapless XY\mathrm{XY}XY regime $(\ensuremath{-}1<\ensuremath{\Delta}<~1)$ is studied both analytically and numerically. In our model an impurity spin (S=1/2)(S=1/2)(S=1/2) is coupled to a single spin in the XXZ\mathrm{XXZ}XXZ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host XXZ\mathrm{XXZ}XXZ chain. In the antiferromagnetic side $(0<\ensuremath{\Delta}<~1)$ the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side $(\ensuremath{-}1<\ensuremath{\Delta}<0),$ on the other hand, the host XXZ\mathrm{XXZ}XXZ chain remains as a single chain through ``healing'' of a weakened bond in the low-energy (long-distance) limit. The density-matrix renormalization-group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.
We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.