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Physical review. B, Condensed matter

Effect of dispersion in thefband of the one-dimensional Anderson lattice model

M. Guerrero, Hervé M. Carruzzo

Published Dec 15, 1996• 1 citation
Publisher

Abstract

We study the effect of a small dispersion in the f band on the elementary excitations of the one-dimensional Anderson lattice at half filling. We use the density-matrix renormalization-group technique to study the strong-coupling case (large Coulomb repulsion U) and an analytic renormalization-group calculation for weak coupling. When U=0, even a small dispersion in the f band can close the hybridization gap. In contrast, when U is large, the quasiparticle gap remains open and is almost independent of the dispersion in the f band. This means that for a given value of the dispersion, there is a metal-insulator transition for some value of the Coulomb repulsion U. The analytic calculation shows that the transition occurs at U=0. In contrast to the quasiparticle gap, the spin gap is strongly suppressed by the dispersion in the f band. This suppression is associated with the enhancement of antiferromagnetic correlations. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.16562

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We study the effect of a small dispersion in the f band on the elementary excitations of the one-dimensional Anderson lattice at half filling. We use the density-matrix renormalization-group technique to study the strong-coupling case (large Coulomb repulsion U) and an analytic renormalization-group calculation for weak coupling. When U=0, even a small dispersion in the f band can close the hybridization gap. In contrast, when U is large, the quasiparticle gap remains open and is almost independent of the dispersion in the f band. This means that for a given value of the dispersion, there is a metal-insulator transition for some value of the Coulomb repulsion U. The analytic calculation shows that the transition occurs at U=0. In contrast to the quasiparticle gap, the spin gap is strongly suppressed by the dispersion in the f band. This suppression is associated with the enhancement of antiferromagnetic correlations. \textcopyright{} 1996 The American Physical Society.
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 investigate the inter-play of f-electron band dispersion and inter-f electron interactions on the gap in the one electron density of states (DOS) of the periodic Anderson model. The calculations are based on dynamical mean field theory and the numerical renormalization group method for the model in infinite dimensions. The local f-electron DOS at low energies for the electron-hole symmetric model with interactions is found to have a complete-gap, a pseudo-gap or to be gap-less, whenever these structures occur for the non-interacting model but the parameters that characterize these features are strongly renormalized. As the degree of f-electron dispersion is increased, when there is a complete gap, the many-body renormalization remains almost constant, but in the pseudo-gap case the renormalization increases. We calculate the sizes of gaps both in the local DOS and in the dynamic local susceptibilities. When the gap width is defined by the edges in the spectrum for the complete-gap model, the widths of the indirect gap and the spin gap are equal, independent of the degree of electron correlation. However, if the width is defined as the excitation energy between the peaks in the spectrum, then the ratio of the indirect gap to the spin gap increases and eventually saturates as the correlation increases. The value of this ratio depends on the f-electron band dispersion. We have also investigated the dependence of the shape of the interacting DOS on the f-band filling for different forms of f-band dispersion. When the f-band dispersion is small, the gap structure in the symmetric model vanishes as the filling factor decreases. When the model, including the dispersion, has no gap structure, the filling dependence on the DOS in low energies is similar to that for a single impurity Anderson model. The energy dispersion of the quasi-particle in the range, ε f < ε < ε f + U , is approximately explained by the renormalized band model in the cases of both large and small f-band dispersion.
The spin gap of a one-dimensional repulsive Hubbard model is numerically calculated with the density-matrix renormalization group, with a special emphasis on the effect of a next-nearest-neighbor hopping ${(t}^{\ensuremath{'}})$ and the nearest-neighbor ferromagnetic exchange (J)(J)(J) interaction. At half filling, a significant spin gap opens if $|{t}^{\ensuremath{'}}|\ensuremath{\simeq}|t|$ and J=0J=0J=0, in agreement with the weak-coupling theory, while the gap is strongly suppressed by the introduction of JJJ. On the other hand, the quarter-filled system has very small spin gaps regardless of the values of ${t}^{\ensuremath{'}}$ and JJJ. Implications for the CuO2{\mathrm{CuO}}_{2}CuO2​ chain in Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ and related materials are discussed.
We have studied the ground-state properties of the symmetric and asymmetric one-dimensional periodic Anderson model as a function of band filling and the model parameters (V,U,(V,U,(V,U,and Ef){E}_{f})Ef​) using the local mean-field (LMF) approach. We have constructed the phase diagram for both cases and have calculated the energy, local moment, and occupation number of the f level. The LMF approach can reveal the basic properties of the system throughout the entire parameter space. For the symmetric case ${(E}_{f}=\ensuremath{-}U/2),$ close to quarter and half filling the antiferromagnetic phase is the ground state. For intermediate band-filling there is a second-order phase transition to a ferromagnetic state. At quarter filling there is a transition from a metallic paramagnetic state to an insulating antiferromagnetic state as the on-site Coulomb interaction increases. The asymmetric case is treated in the mixed-valence regime (Ef=0).{(E}_{f}=0).(Ef​=0). At half filling the ground state is antiferromagnetic while at or close to quarter filling it is paramagnetic. Below half filling the ground state becomes ferromagnetic, suggesting that doping destroys rapidly the antiferromagnetic $f\ensuremath{-}f$ spin correlations. For small values of U we find a paramagnetic state at all band fillings. Results for the average occupation number of the f level compare well with density matrix renormalization group calculations.
Correlation effects in the one-dimensional Hubbard model are studied by application of the L-resolvent method. The calculations are well beyond one-particle mean field approximation. All correlations involving two neighboring sites are included exactly and higher order correlations are approximated. The effects of varying temperature, band filling, Coulomb repulsion and external magnetic field are investigated. Two-site correlations for non-half-filled band fillings are calculated for the first time. Some exact relations between correlation functions are derived by electron-hole symmetry. Results indicate that short-range spin correlations always favor antiferromagnetic order. Large Coulomb repulsion induces a gap in the excitation spectrum and a metal-insulator transition is predicted as the Coulomb repulsion parameter is changed.
Heavy-fermion or Kondo lattice materials are considered to be typical strongly correlated systems, for which mean-field approximations have shown that the Coulomb interaction increases the effective mass and narrows the band gap. In this paper, to clarify interaction effects on the electronic excitation, the spectral function of the Kondo lattice and periodic Anderson models is studied around Kondo insulators in the strong-coupling regime, by using the non-Abelian dynamical density-matrix renormalization group method and perturbation theory. Upon doping a Kondo insulator, an electronic mode emerges in the Kondo insulating gap, exhibiting the momentum-shifted magnetic dispersion relation. Although the ground-state properties are similar to those of a doped band insulator, the emergence of the electronic mode reflecting spin-charge separation of the Kondo insulator is a crucial interaction effect that allows us to regard the Kondo-insulator--metal transition as a type of Mott transition. In addition, electronic modes emerge even in the high-energy regime by doping in the periodic Anderson model. These strong-correlation effects have not been expected in conventional mean-field approximations and would bring a different perspective on heavy-fermion or Kondo lattice systems.