The Study of ManyElectron Systems
Abstract
Various methods and approximation schemes are used to study manyelectron interacting systems. Two important manyparticle 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 singleimpurity model Hamiltonian based calculation of the magnetic susceptibility is performed for YbN in the presence of crystal fields using an alteration of the NonCrossing 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 manyelectron 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 onedimensional Hubbard model has been solved exactly for smallsize clusters by diagonalizing the Hamiltonian in the basis of manyelectron Bloch states. The results for the energy spectrum and eigenfunctions of the ground state and lowlying excited states are presented. Also, mean field calculations of the twodimensional singleband Hubbard model and CuO lattice model (threeband 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 manyparticle 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 February 1991
 Bibcode:
 1991PhDT........65Z
 Keywords:

 ANDERSON MODEL;
 HUBBARD MODEL;
 Physics: Condensed Matter