{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/157573"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/157573","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Explorations in two dimensional strongly correlated quantum matter: from exactly solvable models to conformal bootstrap","abstract":"This dissertation presents two projects that touch upon the role of quantum mechanics in classifying phases of matter and their transitions. In the first project, we set out to answer: is it possible to find a lattice model in the Ising universality class that realizes the Kramers Wannier symmetry in such a way that it squares to 1, rather than a lattice translation as in the usual Ising model? Using insights from symmetry-protected topological phases of matter, we answer in the affirmative, with the caveat that the symmetry, beyond being non-onsite, actually acts on a Hilbert space that is not a local tensor product. The second concerns the nature of the Neel-VBS deconfined quantum critical point. This is thought to be described by the noncompact CP¹ model, which we argue to be continuously connected to the theory accessed by the 2 + ε expansion for the O(3) NLSM. To shed light on the nature of the DQCP, we perform conformal bootstrap studies of the O(3) model in 2 < d < 3.","abstract_html":"This dissertation presents two projects that touch upon the role of quantum mechanics in classifying phases of matter and their transitions. In the first project, we set out to answer: is it possible to find a lattice model in the Ising universality class that realizes the Kramers Wannier symmetry in such a way that it squares to 1, rather than a lattice translation as in the usual Ising model? Using insights from symmetry-protected topological phases of matter, we answer in the affirmative, with the caveat that the symmetry, beyond being non-onsite, actually acts on a Hilbert space that is not a local tensor product. The second concerns the nature of the Neel-VBS deconfined quantum critical point. This is thought to be described by the noncompact CP¹ model, which we argue to be continuously connected to the theory accessed by the 2 + ε expansion for the O(3) NLSM. To shed light on the nature of the DQCP, we perform conformal bootstrap studies of the O(3) model in 2 &lt; d &lt; 3.","abstract_has_math":false,"creators":["Jones, Robert A."],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Physics","school":null,"contributors":[],"advisors":["Metlitski, Max A."],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-09","date_published":"2024-09","updated_at":"2026-07-22T22:21:45Z","subjects":[],"languages":[],"rights":["Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","Copyright retained by author(s)"],"rights_urls":["https://creativecommons.org/licenses/by-nc-nd/4.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/157573","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Metlitski, Max A."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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In the first project, we set out to answer: is it possible to find a lattice model in the Ising universality class that realizes the Kramers Wannier symmetry in such a way that it squares to 1, rather than a lattice translation as in the usual Ising model? Using insights from symmetry-protected topological phases of matter, we answer in the affirmative, with the caveat that the symmetry, beyond being non-onsite, actually acts on a Hilbert space that is not a local tensor product. The second concerns the nature of the Neel-VBS deconfined quantum critical point. This is thought to be described by the noncompact CP¹ model, which we argue to be continuously connected to the theory accessed by the 2 + ε expansion for the O(3) NLSM. To shed light on the nature of the DQCP, we perform conformal bootstrap studies of the O(3) model in 2 < d < 3."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Explorations in two dimensional strongly correlated quantum matter: from exactly solvable models to conformal bootstrap"]}]}],"canonical_facts":{"dc:contributor.advisor":["Metlitski, Max A."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Physics"],"dc:creator":["Jones, Robert A."],"dc:date.accessioned":["2024-11-18T19:11:45Z"],"dc:date.available":["2024-11-18T19:11:45Z"],"dc:date.issued":["2024-09"],"dc:description.abstract":["This dissertation presents two projects that touch upon the role of quantum mechanics in classifying phases of matter and their transitions. In the first project, we set out to answer: is it possible to find a lattice model in the Ising universality class that realizes the Kramers Wannier symmetry in such a way that it squares to 1, rather than a lattice translation as in the usual Ising model? Using insights from symmetry-protected topological phases of matter, we answer in the affirmative, with the caveat that the symmetry, beyond being non-onsite, actually acts on a Hilbert space that is not a local tensor product. The second concerns the nature of the Neel-VBS deconfined quantum critical point. This is thought to be described by the noncompact CP¹ model, which we argue to be continuously connected to the theory accessed by the 2 + ε expansion for the O(3) NLSM. To shed light on the nature of the DQCP, we perform conformal bootstrap studies of the O(3) model in 2 < d < 3."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/157573"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","Copyright retained by author(s)"],"dc:rights.uri":["https://creativecommons.org/licenses/by-nc-nd/4.0/"],"dc:title":["Explorations in two dimensional strongly correlated quantum matter: from exactly solvable models to conformal bootstrap"],"dc:type":["Thesis"],"thesis:degree_name":["Doctoral","Doctor of Philosophy"]},"updated_at":"2026-07-22T22:21:45Z"}