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Journal of Applied Physics

Magnetic properties of the lattice Anderson model

Hsueh‐Ju Lin, H. Chen, J. Callaway

Published May 15, 1994• 2 citations
Publisher

Abstract

We perform exact diagonalization studies of the one-dimensional lattice Anderson model for various clusters. The ground state energy and spin–spin correlation functions are calculated as functions of Hubbard U, hybridization V, and f level occupancies. For the symmetric case, we compare our results with weak and strong coupling perturbation theory.

DOI
10.1063/1.356719

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We perform exact diagonalization studies of the one-dimensional lattice Anderson model for various clusters. The ground state energy and spin–spin correlation functions are calculated as functions of Hubbard U, hybridization V, and f level occupancies. For the symmetric case, we compare our results with weak and strong coupling perturbation theory.
Various methods and approximation schemes are used to study many-electron interacting systems. Two important many-particle models, the Anderson model and the Hubbard model, and their electromagnetic properties have been investigated in many parameter regimes, and applied to physical systems. An Anderson single-impurity model Hamiltonian based calculation of the magnetic susceptibility is performed for YbN in the presence of crystal fields using an alteration of the Non-Crossing Approximation proposed by Zwicknagl et.al., incorporating parameters obtained from ab initio band structure calculations. It yields good agreement with experimental data. For the Anderson lattice model, a variational scheme which uses specific many-electron wavefunctions as basis is applied to both one- and two-dimensional systems represented by symmetric Anderson lattice Hamiltonians. Without much computational effort, the ground state energy is well approximated, especially in strong-coupling limit. Some electronic properties are examined using the variational ground state wavefunction. The one-dimensional Hubbard model has been solved exactly for small-size clusters by diagonalizing the Hamiltonian in the basis of many-electron Bloch states. The results for the energy spectrum and eigenfunctions of the ground state and low-lying excited states are presented. Also, mean field calculations of the two-dimensional single-band Hubbard model and Cu-O lattice model (three-band Hubbard model) are carried out for various physical quantities including the energy, occupation probability, staggered magnetization, momentum distribution Fermi surface and density of states, by using a projection operator formalism. To develop a systematic approach to solving many-electron problems, the many-particle partition function for the free electron gas system is explored using a cumulant expansion scheme. Starting from the ground state, the partition function can be approximated to any order in terms of excitation energy. Its application to interacting systems such as the Anderson model and the Hubbard model is briefly discussed.
Ground-state properties of the asymmetric Hubbard model are studied on one-dimensional clusters (rings) with N=6, 8, and 10 sites. The ground-state energy, correlation functions, and phase diagrams are determined for various sets of model parameters. Computations are performed both by exact diagonalization (for N=6) and by an approximate method by which correlation effects can be examined on larger clusters than exact diagonalization allows. In the limiting cases (one limit corresponds to the spinless Falicov-Kimball model and the other to the Hubbard model) our results agree quite well with those obtained analytically for infinite systems.
The ground-state properties of the periodic Anderson model on one-dimensional chains from three to six sites are studied by exact diagonalization. An appropriate average over boundary conditions is found to be necessary in order to eliminate finite-size oscillations. In the weak-coupling limit, the results for the short-range correlations suggest a smooth transition from a ferromagnetic state at low electron concentration to an antiferromagnetic state at half-filling, rather than a sudden jump at a critical concentration.