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Physical Review Letters

Ground-state properties of the periodic Anderson model

R. Blankenbecler, José R. Fulco, Wonpyong Gill, Douglas J. Scalapino

Published Jan 26, 1987• 74 citations
Publisher

Abstract

The ground-state energy, hybridization matrix element, local moment, and spin-density correlations of a one-dimensional, finite-chain, periodic, symmetric Anderson model are obtained by numerical simulations and compared with perturbation theory and strong-coupling results. We find that the local f-electron spins are compensated by correlation with other f electrons as well as band electrons leading to a nonmagnetic ground state.

DOI
10.1103/physrevlett.58.411

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The ground-state energy, hybridization matrix element, local moment, and spin-density correlations of a one-dimensional, finite-chain, periodic, symmetric Anderson model are obtained by numerical simulations and compared with perturbation theory and strong-coupling results. We find that the local f-electron spins are compensated by correlation with other f electrons as well as band electrons leading to a nonmagnetic ground state.
In an attempt to obtain a better description than the local-density approximation (LDA) for the electronic structure of realistic narrow-band systems, we have studied a perturbation-theory method for the self-energy and have tested it on the electronic properties of the periodic one-dimensional Anderson model. For a number of models we have calculated a wide range of properties such as quasiparticle energies, spectral densities, reduced hybridizations, and various magnetic correlation functions. For two different models we were able to compare with Monte Carlo results and found good agreement. In general, we have obtained a description of narrow-band systems that is more reasonable than the one given by the LDA.
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.
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The coupled-cluster method (CCM) is applied in obtaining the ground-state energy and the local moments of the localized orbitals of the periodic Anderson model. Starting with the state containing a filled Fermi sea of the conduction electrons plus a set of singly occupied and antiferromagnetically ordered f orbitals, the first-order hybridization from the f orbitals to the conduction band is included in the CCM transformation operator. A simple expression for the ground-state energy has been derived, and the calculated ground-state properties are compared with those obtained using a variational scheme and the Monte Carlo method.
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