Liouville resolvent methods applied to highly correlated systems

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dc.contributor.authorHoltz, Susan Ladyen
dc.contributor.committeechairBowen, Samuel P.en
dc.contributor.committeememberTipsword, R.F.en
dc.contributor.committeememberWilliams, Clayton D.en
dc.contributor.committeememberZallen, R.H.en
dc.contributor.committeememberZia, R.K.P.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2014-08-13T14:38:25Zen
dc.date.available2014-08-13T14:38:25Zen
dc.date.issued1986en
dc.description.abstractIn this dissertation we report on the application of the Liouville Operator Resolvent technique (LRM) to two hamiltonians used to model highly correlated systems: Falicov-Kimball and Anderson Lattice. We calculate specific heats, magnetic susceptibilities, thermal averages of physical operators, and energy bands. We demonstrate that the LRM is a viable method for investigating many body problems. For the Falicov-Kimball, an exact calculation of the atomic limit shows no sharp metal-insulator transition. A truncation approximation for the full hamiltonian has a smooth evolution from the atomic limit with the opening of a band for the conduction electrons. No phase transition was observed. A bose space calculation using the proper boson norm indicates that the conduction band induces a correlation between localized electrons on nearest-neighbor sites. It is not known if this effect is real or a by-product of the approximation. We applied the LRM to the Anderson Lattice and several of its limiting cases. In the limit of no hybridization, for both the symmetric and asymmetric (mixed-valence) parameter sets, we found that the thermodynamics could be described as competition between closely-lying energy levels. The effects that dominate are those that minimize the thermal average of the hamiltonian. A simple model is presented in which only hybridization between two localized orbitals is allowed. It shows that hybridization can give rise to mixed valence phenomena as the temperature approaches zero. For the full Anderson Lattice hybridization causes relatively small shifts in the occupation numbers of the localized and conduction electrons. However, these shifts can have dramatic effects on the physical properties as demonstrated by the magnetic susceptibilities. Band structures of the eigenenergies of the Liouville operator, for both parameter sets, reveal that low-lying excitations associated with some of the basis vector operators may split out from the fermi level and become significant at low temperatures. In addition, we report on progress toward extending the calculation to bose space using a commutator norm.en
dc.description.adminincomplete_metadataen
dc.description.degreePh. D.en
dc.format.extentxii, 264 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/10919/49795en
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 14471587en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1986.H647en
dc.subject.lcshMany-body problemen
dc.subject.lcshMetal-insulator transitionsen
dc.subject.lcshThermodynamicsen
dc.subject.lcshHamiltonian operatoren
dc.titleLiouville resolvent methods applied to highly correlated 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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