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arXiv:cond-mat/0209624 · Physical review. B, Condensed matter

Small Fermi surface in the one-dimensional Kondo lattice model

J. C. Xavier, E. Novais, E. Miranda

Published May 17, 2002• 24 citations
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Abstract

We study the one-dimensional Kondo lattice model through the density-matrix renormalization group. Our results for the spin-correlation function indicate the presence of a small Fermi surface in large portions of the phase diagram, in contrast to some previous studies that used the same technique. We argue that the discrepancy is due to the open boundary conditions, which introduce strong charge perturbations that strongly affect the spin Friedel oscillations.

DOI
10.1103/physrevb.65.214406

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We study the one-dimensional Kondo lattice model through the density-matrix renormalization group. Our results for the spin-correlation function indicate the presence of a small Fermi surface in large portions of the phase diagram, in contrast to some previous studies that used the same technique. We argue that the discrepancy is due to the open boundary conditions, which introduce strong charge perturbations that strongly affect the spin Friedel oscillations.
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.
Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.
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.
In order to better understand Kondo insulators, we have studied both the symmetric and asymmetric Anderson lattices at half filling in one dimension using the density-matrix formulation of the numerical renormalization group. The asymmetric case is treated in the mixed-valence regime. We have calculated the charge gap, the spin gap, and the quasiparticle gap as a function of the repulsive interaction U using open boundary conditions for lattices as large as 24 sites. We find that the charge gap is larger than the spin gap for all U for both the symmetric and asymmetric cases. Ruderman-Kittel-Kasuya-Yosida interactions are evident in the f-spin--f-spin correlation functions at large U in the symmetric case, but are suppressed in the asymmetric case as the f level approaches the Fermi energy. This suppression can also be seen in the staggered susceptibility \ensuremath{\chi}(q=2kF{\mathit{k}}_{\mathit{F}}kF​) and it is consistent with neutron scattering measurements of \ensuremath{\chi}(q) in CeNiSn.
We use the density matrix renormalization group method to study the properties of the one-dimensional Kondo-Heisenberg model doped with Kondo holes. We find that the perturbation of the Kondo holes to the local hybridization exhibits spatial oscillation pattern and its amplitude decays exponentially with distance away from the Kondo hole sites. The hybridization oscillation is correlated with both the charge density oscillation of the conduction electrons and the oscillation in the correlation function of the Heisenberg spins. In particular, we find that the oscillation wavelength for intermediate Kondo couplings is given by the Fermi wavevector of the large Fermi surface even before it is formed. This suggests that heavy electrons responsible for the oscillation are already present in this regime and start to accumulate around the to-be-formed large Fermi surface in the Brillouin zone.