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Physical Review Letters

Phase Diagram of the Two-Channel Kondo Lattice Model in One Dimension

T. Schauerte, Daniel Lee Cox, R. M. Noack, P. G. J. van Dongen, Cristian D. Batista

Published Apr 11, 2005• 21 citations
Publisher

Abstract

Employing the density matrix renormalization group method and strong-coupling perturbation theory, we study the phase diagram of the SU(2)xSU(2) Kondo lattice model in one dimension. We show that, at quarter filling, the system can exist in two phases depending on the coupling strength. The weak-coupling phase is dominated by RKKY exchange correlations, while the strong-coupling phase is characterized by strong antiferromagnetic correlations of the channel degree of freedom. These two phases are separated by a quantum critical point. For conduction-band fillings of less than one-quarter, we find a paramagnetic metallic phase at weak coupling and a ferromagnetic phase at moderate to strong coupling.

DOI
10.1103/physrevlett.94.147201

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Employing the density matrix renormalization group method and strong-coupling perturbation theory, we study the phase diagram of the SU(2)xSU(2) Kondo lattice model in one dimension. We show that, at quarter filling, the system can exist in two phases depending on the coupling strength. The weak-coupling phase is dominated by RKKY exchange correlations, while the strong-coupling phase is characterized by strong antiferromagnetic correlations of the channel degree of freedom. These two phases are separated by a quantum critical point. For conduction-band fillings of less than one-quarter, we find a paramagnetic metallic phase at weak coupling and a ferromagnetic phase at moderate to strong coupling.
Employing the density matrix renormalization group method and strong-coupling perturbation theory, we study the phase diagram of the SU(2)xSU(2) Kondo lattice model in one dimension. We show that, at quarter filling, the system can exist in two phases depending on the coupling strength. The weak-coupling phase is dominated by RKKY exchange correlations while the strong-coupling phase is characterized by strong antiferromagnetic correlations of the channel degree of freedom. These two phases are separated by a quantum critical point. For conduction-band fillings of less than one quarter, we find a paramagnetic metallic phase at weak coupling and a ferromagnetic phase at moderate to strong coupling.
We study the ground state of the one-dimensional ``$t\text{\ensuremath{-}}{J}_{s}\text{\ensuremath{-}}{J}_{\ensuremath{\tau}}$ model,'' which is a variant of the $t\text{\ensuremath{-}}J$ model with an additional channel degree of freedom. The model is not only a generalization of the $t\text{\ensuremath{-}}J$ model but also an effective model of the two-channel Kondo lattice model in the strong-coupling region. The low-energy excitations and correlation functions are systematically calculated by the density matrix renormalization group method, and the ground-state phase diagram at quarter filling consisting of a Tomonaga-Luttinger liquid, spin-gap state, channel-gap state, insulator, and phase separation is determined. We find that weak channel fluctuations stabilize the spin-gap state, while strong channel fluctuations lead to the transition to the insulator.
We study higher-spin ($S\ensuremath{\ge}1$) generalization of the one-dimensional Kondo-Heisenberg model, in which the local spin-SSS moments of the Kondo-lattice model interact with each other via the antiferromagnetic Heisenberg interaction (JH{J}_{\text{H}}JH​), by analytical and numerical methods. The strong-coupling (i.e., large Kondo coupling) expansion maps out an insulating phase at half-filling whose magnetic correlation depends on the parity of 2S2S2S as well as a ferromagnetic metallic phase which dominates the strong-coupling region at generic fillings. Then, we carried out the density-matrix renormalization-group simulations for S=1S=1S=1 to closely investigate the phase structure at large but finite Kondo coupling. At half-filling, the Kondo coupling and JH{J}_{\text{H}}JH​ do not compete and the insulating spin-gapless phase is stable, while the competition of the two leads to a stepwise collapse of the strong-coupling ferromagnetism via an intervening dimerized insulating phase with power-law spin correlation at quarter-filling.
We map out the phase diagram of the one-dimensional Anderson lattice by studying the ground-state magnetization as a function of band filling using the density matrix renormalization group technique. For strong coupling, we find that the quarter-filled system has an S=0 ground state with strong antiferromagnetic correlations. As additional electrons are put in, we find first a ferromagnetic phase, as reported by M\"oller and W\"olfle, and then a phase in which the ground state has total spin S=0. Within this S=0 phase, we find Ruderman-Kittel-Kasuya-Yosida oscillations in the spin-spin correlation functions. \textcopyright{} 1996 The American Physical Society.
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 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