{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Algebraic Bethe Ansatz and Tensor Networks","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76686"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"We consider several exactly solvable models of strongly correlated electrons in one dimension, such as the Heisenberg XXX model, the supersymmetric t-J model and the Hubbard model. These models can be solved by using the method of graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product State. This overcomes a major shortcoming of current density matrix renormalization group (DMRG) methods which work well on the ground states, but have difficulty working with the excited states of such models. In addition, observables such as correlation functions are important as they are experimentally measurable, but have been analytically described in the double scaling limit only. Moreover, these analytical results are mostly expressed in the form of determinants, which are numerically inefficient to compute. With the tensor network description of the spin models, we can efficiently compute any expectation value of the eigenstates on finite length lattices for direct comparison with laboratory results. As a proof of principle, we calculate correlation functions of ground states and excited states of such models on finite lattices of lengths in an intermediate regime which are of experimental interest."},{"label":"dcterms.available","value":"2017-09-20T16:50:59Z"},{"label":"dcterms.contributor","value":"Wei, Tzu-Chieh"},{"label":"dcterms.creator","value":"Chong, You Quan"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:59Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:59Z"},{"label":"dcterms.description","value":"Department of Physics."},{"label":"dcterms.extent","value":"108 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76686"},{"label":"dcterms.issued","value":"2015-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:59Z (GMT). No. of bitstreams: 1\nChong_grad.sunysb_0771E_12269.pdf: 1181213 bytes, checksum: 7b1135a7a71495fe97d6bae720b5e8b7 (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Physics"},{"label":"dcterms.title","value":"Algebraic Bethe Ansatz and Tensor Networks"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/14%2F32%2F28%2F143228940623876282205270345357187079342/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/14%2F32%2F28%2F143228940623876282205270345357187079342","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}