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The study of many-electron systems

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dc.contributor.authorZhou, Yuen
dc.contributor.committeecochairBowen, Samuel P.en
dc.contributor.committeecochairWilliams, Clayton D.en
dc.contributor.committeememberLee, Ting-Kuoen
dc.contributor.committeememberMancini, Jay D.en
dc.contributor.committeememberRoper, L. Daviden
dc.contributor.committeememberZia, Royce K. P.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2014-03-14T21:21:14Zen
dc.date.adate2005-10-14en
dc.date.available2014-03-14T21:21:14Zen
dc.date.issued1991en
dc.date.rdate2005-10-14en
dc.date.sdate2005-10-14en
dc.description.abstractVarious 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.en
dc.description.degreePh. D.en
dc.format.extentxi, 144 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10142005-103108en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10142005-103108/en
dc.identifier.urihttp://hdl.handle.net/10919/39876en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1991.Z469.pdfen
dc.relation.isformatofOCLC# 25611911en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1991.Z469en
dc.subject.lcshAnderson modelen
dc.subject.lcshCondensed matteren
dc.subject.lcshHubbard modelen
dc.subject.lcshParticles (Nuclear physics) -- Multiplicityen
dc.titleThe study of many-electron systemsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplinePhysicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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