Show simple item record

dc.contributor.advisorKorepin, Vladimir Een_US
dc.contributor.authorParaan, Francis Norman Claridadesen_US
dc.contributor.otherDepartment of Physicsen_US
dc.date.accessioned2013-05-24T16:38:19Z
dc.date.available2013-05-24T16:38:19Z
dc.date.issued1-Dec-12en_US
dc.date.submitted12-Decen_US
dc.identifierStonyBrookUniversityETDPageEmbargo_20130517082608_116839en_US
dc.identifier.urihttp://hdl.handle.net/1951/60267
dc.description116 pg.en_US
dc.description.abstractWe present analytic results for the ground state properties and entanglement in the Lieb-Liniger model and q-deformed Affleck-Kennedy-Lieb-Tasaki (AKLT) models. The translational invariance of the Lieb-Liniger model is broken by an external harmonic potential in one case and by coarse-grained measurements of particle number in another. Meanwhile, anisotropy is introduced into the AKLT model by generalizing its SU(2) invariant hamiltonian into one that is SU<sub>q</sub>(2) invariant. The Lieb-Liniger model describes a one-dimensional gas of bosons that mutually interact by a zero-range interaction term. Under longitudinal harmonic confinement, the exact spectrum of the hamiltonian is known only for free and impenetrable bosons. We use a pseudopotential approach and perturbation theory to calculate the ground state energy of this gas near the limit of infinite repulsion. We further study entanglement in the periodic homogeneous Lieb-Liniger model. When the particle number in a spatial partition of the ground state is measured, entanglement in the resulting state arises only from interparticle interactions. We demonstrate that entanglement in these projected states increases monotonically with the strength of interactions. Finally, we discuss how anisotropy reduces entanglement in the valence-bond-solid ground state of the q-deformed AKLT model. We propose effective thermal models that describe block entanglement in terms of boundary degrees of freedom. The anisotropy parameter q enters these models as an effective temperature.en_US
dc.description.sponsorshipStony Brook University Libraries. SBU Graduate School in Department of Physics. Charles Taber (Dean of Graduate School).en_US
dc.formatElectronic Resourceen_US
dc.language.isoen_USen_US
dc.publisherThe Graduate School, Stony Brook University: Stony Brook, NY.en_US
dc.subject.lcshPhysicsen_US
dc.titleSome Results on One-Dimensional Models with Broken and Deformed Symmetriesen_US
dc.typeDissertationen_US
dc.description.advisorAdvisor(s): Korepin, Vladimir E. Committee Member(s): Schneble, Dominik A; Wei, Tzu-Chieh ; Kirillov, Jr., Alexander.en_US
dc.mimetypeApplication/PDFen_US
dc.embargo.releaseDec-14en_US
dc.embargo.period2 Yearsen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record