{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/139158"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/139158","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Implementing a Lattice Formulation of the Schwinger Modelwith Periodic Boundary Conditions Using Tensor Networks","abstract":"I attempt to develop a simple tensor network formulation of the Schwinger model with periodic boundary conditions. The primary challenge is to enforce the local constraints imposed by Gauss's Law. I do this by combining global conservation of a specially defined quantum number with the local optimization steps used in the density matrix renormalization group (DMRG) algorithm for finding the ground state of a quantum system. However, due to practical constraints, I still use matrix product states and matrix product operators with open boundary conditions. I demonstrate the efficacy of the model in computing the bulk limit (the limit as the number of lattice sites goes to infinity) for the energy density, chiral condensate, and electric field energy density of the ground state. Future investigation should begin with recreating the model using periodic matrix product states and matrix product operators and using a version of DMRG that has been optimized for periodic boundary conditions.","abstract_html":"I attempt to develop a simple tensor network formulation of the Schwinger model with periodic boundary conditions. The primary challenge is to enforce the local constraints imposed by Gauss's Law. I do this by combining global conservation of a specially defined quantum number with the local optimization steps used in the density matrix renormalization group (DMRG) algorithm for finding the ground state of a quantum system. However, due to practical constraints, I still use matrix product states and matrix product operators with open boundary conditions. I demonstrate the efficacy of the model in computing the bulk limit (the limit as the number of lattice sites goes to infinity) for the energy density, chiral condensate, and electric field energy density of the ground state. Future investigation should begin with recreating the model using periodic matrix product states and matrix product operators and using a version of DMRG that has been optimized for periodic boundary conditions.","abstract_has_math":false,"creators":["Kazi, Sujay"],"institution":"Massachusetts Institute of Technology","degree_name":"Bachelor","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Physics","school":null,"contributors":[],"advisors":["Shanahan, Phiala"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-06","date_published":"2021-06","updated_at":"2026-07-22T22:22:18Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"rights_urls":["https://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/139158","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Shanahan, Phiala"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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The primary challenge is to enforce the local constraints imposed by Gauss's Law. I do this by combining global conservation of a specially defined quantum number with the local optimization steps used in the density matrix renormalization group (DMRG) algorithm for finding the ground state of a quantum system. However, due to practical constraints, I still use matrix product states and matrix product operators with open boundary conditions. I demonstrate the efficacy of the model in computing the bulk limit (the limit as the number of lattice sites goes to infinity) for the energy density, chiral condensate, and electric field energy density of the ground state. Future investigation should begin with recreating the model using periodic matrix product states and matrix product operators and using a version of DMRG that has been optimized for periodic boundary conditions."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.B."]},{"key":"dc:title","label":"Title","values":["Implementing a Lattice Formulation of the Schwinger Modelwith Periodic Boundary Conditions Using Tensor Networks"]}]}],"canonical_facts":{"dc:contributor.advisor":["Shanahan, Phiala"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Physics"],"dc:creator":["Kazi, Sujay"],"dc:date.accessioned":["2022-01-14T14:53:32Z"],"dc:date.available":["2022-01-14T14:53:32Z"],"dc:date.issued":["2021-06"],"dc:description.abstract":["I attempt to develop a simple tensor network formulation of the Schwinger model with periodic boundary conditions. The primary challenge is to enforce the local constraints imposed by Gauss's Law. I do this by combining global conservation of a specially defined quantum number with the local optimization steps used in the density matrix renormalization group (DMRG) algorithm for finding the ground state of a quantum system. However, due to practical constraints, I still use matrix product states and matrix product operators with open boundary conditions. I demonstrate the efficacy of the model in computing the bulk limit (the limit as the number of lattice sites goes to infinity) for the energy density, chiral condensate, and electric field energy density of the ground state. Future investigation should begin with recreating the model using periodic matrix product states and matrix product operators and using a version of DMRG that has been optimized for periodic boundary conditions."],"dc:description.degree":["S.B."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/139158"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Implementing a Lattice Formulation of the Schwinger Modelwith Periodic Boundary Conditions Using Tensor Networks"],"dc:type":["Thesis"],"thesis:degree_name":["Bachelor","Bachelor of Science in Physics"]},"updated_at":"2026-07-22T22:22:18Z"}