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Correlation exponent Kr of the one-dimensional Kondo lattice model

J. C. Xavier, E. Miranda

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

We present results for the correlation exponent Kr of the Tomonaga-Luttinger liquid description of the one-dimensional Kondo lattice as a function of conduction-electron density and coupling constant. Kr is obtained from the first derivative of the Fourier transform of the charge-charge correlation function. We also show that the spin correlation function can only be described in this picture if we include logarithmic corrections, a feature that had been previously overlooked. A consistent description of both charge and spin sectors is then obtained. Finally, we show evidence that the spin sector of the dimerized phase at quarter-filling is gapless.

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We present results for the correlation exponent Kr of the Tomonaga-Luttinger liquid description of the one-dimensional Kondo lattice as a function of conduction-electron density and coupling constant. Kr is obtained from the first derivative of the Fourier transform of the charge-charge correlation function. We also show that the spin correlation function can only be described in this picture if we include logarithmic corrections, a feature that had been previously overlooked. A consistent description of both charge and spin sectors is then obtained. Finally, we show evidence that the spin sector of the dimerized phase at quarter-filling is gapless.
We present results for the correlation exponent ${K}_{\ensuremath{\rho}}$ of the Tomonaga-Luttinger liquid description of the one-dimensional Kondo lattice as a function of conduction-electron density and coupling constant. ${K}_{\ensuremath{\rho}}$ is obtained from the first derivative of the Fourier transform of the charge-charge correlation function. We also show that the spin correlation function can only be described in this picture if we include logarithmic corrections, a feature that had been previously overlooked. A consistent description of both charge and spin sectors is then obtained. Finally, we show evidence that the spin sector of the dimerized phase at quarter-filling is gapless.
The one-dimensional Kondo lattice model with attractive interaction among the conduction electrons is analyzed in the case of half-filling. It is shown that there are three distinct phases depending on the coupling constants of the model. Two phases have a spin and charge gap. While one shows a clear distinction of the spin and charge excitation spectrum the other phase may be characterized as a band insulator type where both excitations are due to two-particle states. The third phase is gapless in both channels and has quasi-long-range order in the spin- and charge-density-wave correlation. In this phase the spin and charge excitations have a clearly separated spectrum. For the analysis we discuss first two limiting cases. Then a density matrix renormalization group calculation on finite systems is applied to determine the phase diagram and the correlation functions in the gapped and gapless phase for general coupling constants.
The paramagnetic metallic phase of the one-dimensional Kondo lattice model is studied by the density matrix renormalization group method. We observe charge and spin Friedel oscillations. They reflect the long- range charge-charge and spin-spin correlation functions. The observed oscillations are consistent with a Tomonaga-Luttinger liquid. From the period of the oscillations it is concluded that the Fermi surface is large, including both the conduction electrons and the localized spins, kF{\mathit{k}}_{\mathit{F}}kF​=\ensuremath{\pi}(1+nc{\mathit{n}}_{\mathit{c}}nc​)/2, where nc{\mathit{n}}_{\mathit{c}}nc​ is the density of conduction electrons. \textcopyright{} 1996 The American Physical Society.
Recent developments in the theoretical investigation of the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given of the zero-temperature DMRG method, the finite-temperature DMRG method, and also the application of the finite- T DMRG to dynamic quantities. Away from half-filling, the paramagnetic metallic state is shown to be a Tomonaga-Luttinger liquid with a large Fermi surface. The size of the large Fermi surface is determined by the sum of the densities of the conduction electrons and the localized spins. The correlation exponent of this metallic phase is smaller than 1/2. At half-filling the ground state is insulating. The excitation gaps are different, depending on the channels, the spin gap, the charge gap and the quasiparticle gap. The temperature dependence of the spin and charge susceptibilities and the specific heat are discussed. Particularly interesting is the temperature dependence of various excitation spectra, which indicates unusual properties for the Kondo insulators.
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
The finite-T DMRG method is applied to the one-dimensional Kondo lattice model to calculate dynamic correlation functions. Dynamic spin and charge correlations, S_f(omega), S_c(omega), and N_c(omega), and quasiparticle density of states rho(omega) are calculated in the paramagnetic metallic phase for various temperatures and hole densities. Near half filling, it is shown that a pseudogap grows in these dynamic correlation functions below the crossover temperature characterized by the spin gap at half filling. A sharp peak at omega=0 evolves at low temperatures in S_f(omega) and N_c(omega). This may be an evidence of the formation of the collective excitations, and this confirms that the metallic phase is a Tomonaga-Luttinger liquid in the low temperature limit.