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arXiv:cond-mat/9704226 · Physical review. B, Condensed matter

Phase transition in the one-dimensional Kondo lattice model with attractive electron-electron interaction

Naokazu Shibata, Manfred Sigrist, Elmar Heeb

Published Nov 1, 1997• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.56.11084

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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.
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.
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.
The ground state properties of the one-dimensional Kondo lattice with an f^2 configuration at each site are studied by the density matrix renormalization group method. At half-filling, competition between the Kondo exchange J and the antiferromagnetic intra f-shell exchange I leads to reduction of energy gaps for spin, quasi-particle and charge excitations. The attractive force among conduction electrons is induced by the competition and the bound state is formed. As J/I increases the f^2 singlet gives way to the Kondo singlet as the dominant local correlation. The remarkable change of the quasi-particle gap is driven by the change of the spin-1/2 excitation character from the itinerant one to the localized one. Possible metal-insulator transition is discussed which may occur as the ratio J/I is varied by reference to mean-field results in the f^2 lattice system and the two impurity Kondo system.
Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and specific heat are calculated down to T=0.1t for various exchange constants. The obtained results clearly show crossover behavior from the high temperature regime of nearly independent localized spins and conduction electrons to the low temperature regime where the two degrees of freedom couple strongly. The low temperature energy scales of the charge and spin susceptibilities are determined and shown to be equal to the quasiparticle gap and the spin gap, respectively, for weak exchange couplings.
The density-matrix renormalization-group method is applied to the one-dimensional Kondo-lattice model with the Coulomb interaction between the conduction electrons. The spin and charge gaps are calculated as a function of the exchange constant JJJ and the Coulomb interaction Uc{U}_{c}Uc​. It is shown that both the spin and charge gaps increase with increasing JJJ and Uc{U}_{c}Uc​. The spin gap vanishes in the limit of $J\ensuremath{\rightarrow}0$ for any Uc{U}_{c}Uc​ with an exponential form, ${\ensuremath{\Delta}}_{s}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\frac{1}{\ensuremath{\alpha}({U}_{c})J\ensuremath{\rho}}]$. The exponent, $\ensuremath{\alpha}({U}_{c})$, is determined as a function of Uc{U}_{c}Uc​. The charge gap is generally much larger than the spin gap. In the limit of $J\ensuremath{\rightarrow}0$, the charge gap vanishes as ${\ensuremath{\Delta}}_{c}=\frac{1}{2}J$ for Uc=0{U}_{c}=0Uc​=0 but for a finite Uc{U}_{c}Uc​ it tends to a finite value, which is the charge gap of the Hubbard model.
The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.