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Physical review. B, Condensed matter

Real-space density-matrix renormalization-group study of the Kondo necklace

S. Moukouri, Laurent G. Caron, C. Bourbonnais, L. Hubert

Published Jun 1, 1995• 28 citations
Publisher

Abstract

A recently proposed density-matrix renormalization group is used to investigate the ground-state properties of the Kondo-necklace Hamiltonian. It represents a chain of XY interacting pseudospins that are Kondo coupled (J) to localized spins. The spin gap as well as the short- and long-range spin correlation functions are consistent with the existence of a smooth crossover at J\ensuremath{\approxeq}0.5. For J\ensuremath{\le}0.5, the gap depends exponentially on ${\mathit{J}}^{\mathrm{\ensuremath{-}}1/2}$ and the in-plane correlation function of the localized spins shows RKKY oscillations while the z one falls monotonically in contrast to the XY behavior. The correlation length diverges at J=0. For J\ensuremath{\ge}0.5, the gap is linearly increasing with J, and the system is made of nearly independent singlets.

DOI
10.1103/physrevb.51.15920

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arXiv:cond-mat/9808301•Journal of Physics Condensed Matter•Jan 1, 1999•71 citations
A recently proposed density-matrix renormalization group is used to investigate the ground-state properties of the Kondo-necklace Hamiltonian. It represents a chain of XY interacting pseudospins that are Kondo coupled (J) to localized spins. The spin gap as well as the short- and long-range spin correlation functions are consistent with the existence of a smooth crossover at J\ensuremath{\approxeq}0.5. For J\ensuremath{\le}0.5, the gap depends exponentially on J\ensuremath−1/2{\mathit{J}}^{\mathrm{\ensuremath{-}}1/2}J\ensuremath−1/2 and the in-plane correlation function of the localized spins shows RKKY oscillations while the z one falls monotonically in contrast to the XY behavior. The correlation length diverges at J=0. For J\ensuremath{\ge}0.5, the gap is linearly increasing with J, and the system is made of nearly independent singlets.
We have studied the one-dimensional Kondo chain at half filling using a density matrix formulation of the numerical renormalization group. The charge gap is larger than the spin gap for all antiferromagnetic values of the exhange coupling J. A new type of excitation, a neutral spin singlet, consists of a particle and a hole which are repulsive for J\ensuremath{\gtrsim}5t and attractive for J\ensuremath{\lesssim}5t. As J\ensuremath{\rightarrow}0, RKKY interactions become more important and the staggered susceptibility \ensuremath{\chi}(q=2kF{\mathit{k}}_{\mathit{F}}kF​) diverges. We have also studied \ensuremath{\chi}(q) and the dispersion of the low-lying spin excitations as a function of wave vector q.
The projector Monte Carlo method and finite-size scaling are applied to the solution of the ground-state properties of the ``Kondo necklace'' Hamiltonian. The energy and various spin-spin correlation functions are calculated for chains up to 16 sites in length. Correlations between the spins on different sites are evaluated, and the nature of the ground-state phase as a function of the ratio of the exchange coupling J to the bandwidth W is examined. Evaluation of the correlation function 〈S\ensuremath{\rightarrow}(i)\ensuremath{\cdot}\ensuremath{\tau}\ensuremath{\rightarrow}(i)〉 shows that as the coupling between the localized S spins and the \ensuremath{\tau} spin chain increases, the system becomes composed of independent singlets on each site. Contrary to both mean-field and various approximate renormalization-group calculations, we find that our results are consistent with an absence of magnetic order as soon as J is different from 0.
We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter $\ensuremath{\eta}$ in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with $\ensuremath{\eta}$, but when $\ensuremath{\eta}$ approaches zero, they drop abruptly.
"We use the density matrix renormalization group to calculate the von Neumann block entropy in the Kondo necklace model. We have included two anisotropies: η in the exchange interaction between conduction spins, and ∆ in the coupling between localized and conduction spins. Calculating the energy gap for the one-dimensional model at zero temperature, it was obtained that when η > 0, a quantum phase transition between Kondo singlet and antiferomagnetic states for finite couplings occurs, and as ∆ increases the Kondo singlet phase is favoured. Now we observe that the quantum critical points of the model can be identified by a maximum of the von Neumann block entropy, so entanglement measures can be useful for determining the phase diagram of the anisotropic Kondo necklace model."
Abstract Using the density matrix renormalization group method, we study the one‐dimensional Kondo necklace model including two anisotropies: η in the XY interaction of the conduction chain, and Δ in the local Kondo coupling between localized and conduction spins. For different values of the anisotropies, we calculate the energy gap and estimate the quantum critical points in which a phase transition from antiferromagnetic to spin liquid states takes place, assuming a Kosterlitz–Thouless‐like behavior. For the case η=0\eta = 0η=0 , the system remains in a spin liquid state for the different Δ considered, but when η≠0\eta \ne 0η=0 , Δ markedly affects the location of the critical points. We also calculate correlation functions for a specific case, in order to support our gap results.
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.