On gapless topological phases and their holographic duals
department or school: Science, Faculty of
department or school: Physics and Astronomy, Department of
data provider: DSpace
degree campus: UBCV
creator: Wen, Rui
issued: 2025-11-24T09:02:04Z
issued: 2025
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: Despite great success we have achieved in the past two decades on systematically understanding gapped topological phases, a firm foundation for understanding gapless topological phases is still lacking. In this dissertation I develop a general framework to describe, classify and construct gapped and gapless phases with or without symmetry. I then apply this framework to construct new gapless phases, and classify some classes of them completely. The first chapter is a non-technical summary of the subjects, ideas and results of the rest of the dissertation. In the first chapter I introduce the notion of gapless topological phases, and briefly discuss their general structures. We also discuss how topological holography can be useful for classifying and constructing gapless phases with generalized symmetries. In chapter two I develop a framework for understanding general quantum phases and phase transitions with generalized symmetries. After reviewing the established theory of gapped phases, we introduce two key notions: quantum order and symmetry-enriched quantum order. These concepts are the correct generalized of topological order and symmetry-enriched topological orders. I show that these new notions subsume conventional phase transitions, gapless spin liquids, and gapless symmetry-protected topological phases. For a class of symmetry-enriched quantum orders with finite many topological defects, we present a general classification using higher tensor category theory. The rest of the dissertation provides more detailed studies of specific gapless topological phases, including classification and lattice model construction of gapless symmetry-protected topological phases and the connection to the theory of topological holography.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/92978
note: ON GAPLESS TOPOLOGICAL PHASES AND THEIR HOLOGRAPHIC DUALSbyRui WenA DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)November 2025©Rui Wen, 2025The following individuals certify that they have read, and recommend to the Facultyof Graduate and Postdoctoral Studies for acceptance, the thesis entitled:On Gapless Topological Phases and Their Holographic Dualssubmitted by Rui Wen in partial fulfillment of the requirements forthe degree of Doctor of Philosophyin PhysicsExamining Committee:Andrew Potter, Assistant Professor, Physics, UBCSupervisorMoshe Rozali, Professor, Physics, UBCSupervisory Committee MemberFei Zhou, Professor, Physics, UBCUniversity ExaminerBen Williams, Associate Professor, Mathematics UBCUniversity ExaminerFiona Burnell , Professor, Physics, University of MinnesotaExternal ExaminerAdditional Supervisory Committee Members:Ziliang Ye, Assistant Professor, Physics, UBCSupervisory Committee MemberJulio Parra Martinez, Assistant Professor, Physics, UBCSupervisory Committee MemberiiAbstractDespite great success we have achieved in the past two decades on systematically un-derstanding gapped topological phases, a firm foundation for understanding gaplesstopological phases is still lacking. In this dissertation I develop a general framework todescribe, classify and construct gapped and gapless phases with or without symmetry.I then apply this framework to construct new gapless phases, and classify some classesof them completely.The first chapter is a non-technical summary of the subjects, ideas and resultsof the rest of the dissertation. In the first chapter I introduce the notion of gaplesstopological phases, and briefly discuss their general structures. We also discuss howtopological holography can be useful for classifying and constructing gapless phaseswith generalized symmetries.In chapter two I de…
has type: Thesis/Dissertation
date issued: 2026-05
is shown at: 10.14288/1.0450812
language: eng
degree discipline: Physics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Potter, Andrew
type: Text
identifier URI: http://hdl.handle.net/2429/92978