{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/51601"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/51601","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Effective action approach to quantum phase transitions in bosonic lattices","abstract":"In this thesis, I develop a new, field-theoretic method for describing the quantum phase transition between Mott insulating and superfluid states observed in bosonic optical lattices. I begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, I then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced, and the underlying effective action is derived via a Legendre transformation. After determining the Ginzburg-Landau expansion of the effective action to first order in the tunneling term. expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator - superfluid phase boundary to first order in the tunneling, the predictions of the effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase.","abstract_html":"In this thesis, I develop a new, field-theoretic method for describing the quantum phase transition between Mott insulating and superfluid states observed in bosonic optical lattices. I begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, I then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced, and the underlying effective action is derived via a Legendre transformation. After determining the Ginzburg-Landau expansion of the effective action to first order in the tunneling term. expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator - superfluid phase boundary to first order in the tunneling, the predictions of the effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase.","abstract_has_math":false,"creators":["Bradlyn, Barry J"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Physics.","school":null,"contributors":[],"advisors":["Roman Jackiw."],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-22T22:21:56Z","subjects":["Physics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/51601","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Roman Jackiw."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Physics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Dept. of Physics."]},{"key":"dc:creator","label":"Author","values":["Bradlyn, Barry J"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2010-02-09T16:49:54Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2010-02-09T16:49:54Z"]},{"key":"dc:date.issued","label":"Date","values":["2009"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/51601"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2009.","Includes bibliographical references (p. 51-54)."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, I develop a new, field-theoretic method for describing the quantum phase transition between Mott insulating and superfluid states observed in bosonic optical lattices. I begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, I then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced, and the underlying effective action is derived via a Legendre transformation. After determining the Ginzburg-Landau expansion of the effective action to first order in the tunneling term. expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator - superfluid phase boundary to first order in the tunneling, the predictions of the effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.B."]},{"key":"dc:title","label":"Title","values":["Effective action approach to quantum phase transitions in bosonic lattices"]}]}],"canonical_facts":{"dc:contributor.advisor":["Roman Jackiw."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Physics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Physics."],"dc:creator":["Bradlyn, Barry J"],"dc:date.accessioned":["2010-02-09T16:49:54Z"],"dc:date.available":["2010-02-09T16:49:54Z"],"dc:date.issued":["2009"],"dc:description":["Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2009.","Includes bibliographical references (p. 51-54)."],"dc:description.abstract":["In this thesis, I develop a new, field-theoretic method for describing the quantum phase transition between Mott insulating and superfluid states observed in bosonic optical lattices. I begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, I then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced, and the underlying effective action is derived via a Legendre transformation. After determining the Ginzburg-Landau expansion of the effective action to first order in the tunneling term. expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator - superfluid phase boundary to first order in the tunneling, the predictions of the effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase."],"dc:description.degree":["S.B."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/51601"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Physics."],"dc:title":["Effective action approach to quantum phase transitions in bosonic lattices"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:56Z"}