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Aspects of Gauging in Topological Phases of Matter
Aspects of Gauging in Topological Phases of Matter
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152808
- ISBN
- 9798342718745
- DDC
- 530
- 저자명
- Li, Yabo.
- 서명/저자
- Aspects of Gauging in Topological Phases of Matter
- 발행사항
- [Sl] : State University of New York at Stony Brook, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 218 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-05, Section: B.
- 주기사항
- Advisor: Wei, Tzu-Chieh;Cano, Jennifer.
- 학위논문주기
- Thesis (Ph.D.)--State University of New York at Stony Brook, 2024.
- 초록/해제
- 요약The gauging (Kramers-Wannier) duality plays a crucial role in the study of topological phases of matter. This dissertation explores various aspects of gauging duality in different topological phases. In the first part, we examine the gauging of a finite symmetry on a lattice, demonstrating that applying dualities to a G symmetry-protected topologically ordered (SPT) state results in symmetry-enriched topologically ordered (SET) states. We construct generic lattice parent Hamiltonians for these states and show that they form an entangled superposition of twisted quantum double (TQD) ground states with SPT ordered states. A general formula is derived to characterize the SET phases through this entanglement.In the second part, we investigate the role of measurement in topological quantum field theories (TQFTs), which is closely related to the Kramers-Wannier duality. We present a field-theoretic framework to describe states and phases post-measurement, focusing on emergent symmetries and potential mixed anomalies between them and the remaining symmetries.Finally, we treat gauging dualities as symmetries and explore topological phases under these non-invertible symmetries. Utilizing Kramers-Wannier operators, we construct lattice models with Rep(G) symmetry, including non-invertible SPT phases on a 1d tensor product Hilbert space. Upon dualization, a complex interplay between onsite symmetries, non-onsite symmetries, non-abelian symmetries, and non-invertible symmetries emerges. This interplay is elucidated through symmetry fractionalization in the 2+1d bulk SET.
- 일반주제명
- Physics
- 일반주제명
- Statistical physics
- 일반주제명
- Applied mathematics
- 일반주제명
- Theoretical physics
- 키워드
- Gauging
- 키워드
- Kramers-Wannier
- 기타저자
- State University of New York at Stony Brook Physics
- 기본자료저록
- Dissertations Abstracts International. 86-05B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008250123s2024 us c eng d■001000017163909
■00520250211152808
■006m o d
■007cr#unu||||||||
■020 ▼a9798342718745
■035 ▼a(MiAaPQ)AAI31557440
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aLi, Yabo.
■24510▼aAspects of Gauging in Topological Phases of Matter
■260 ▼a[Sl]▼bState University of New York at Stony Brook▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a218 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-05, Section: B.
■500 ▼aAdvisor: Wei, Tzu-Chieh;Cano, Jennifer.
■5021 ▼aThesis (Ph.D.)--State University of New York at Stony Brook, 2024.
■520 ▼aThe gauging (Kramers-Wannier) duality plays a crucial role in the study of topological phases of matter. This dissertation explores various aspects of gauging duality in different topological phases. In the first part, we examine the gauging of a finite symmetry on a lattice, demonstrating that applying dualities to a G symmetry-protected topologically ordered (SPT) state results in symmetry-enriched topologically ordered (SET) states. We construct generic lattice parent Hamiltonians for these states and show that they form an entangled superposition of twisted quantum double (TQD) ground states with SPT ordered states. A general formula is derived to characterize the SET phases through this entanglement.In the second part, we investigate the role of measurement in topological quantum field theories (TQFTs), which is closely related to the Kramers-Wannier duality. We present a field-theoretic framework to describe states and phases post-measurement, focusing on emergent symmetries and potential mixed anomalies between them and the remaining symmetries.Finally, we treat gauging dualities as symmetries and explore topological phases under these non-invertible symmetries. Utilizing Kramers-Wannier operators, we construct lattice models with Rep(G) symmetry, including non-invertible SPT phases on a 1d tensor product Hilbert space. Upon dualization, a complex interplay between onsite symmetries, non-onsite symmetries, non-abelian symmetries, and non-invertible symmetries emerges. This interplay is elucidated through symmetry fractionalization in the 2+1d bulk SET.
■590 ▼aSchool code: 0771.
■650 4▼aPhysics
■650 4▼aStatistical physics
■650 4▼aApplied mathematics
■650 4▼aTheoretical physics
■653 ▼aGauging
■653 ▼aTwisted quantum double
■653 ▼aKramers-Wannier
■653 ▼aTopological phases
■653 ▼aSymmetry fractionalization
■690 ▼a0605
■690 ▼a0753
■690 ▼a0217
■690 ▼a0364
■71020▼aState University of New York at Stony Brook▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g86-05B.
■790 ▼a0771
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17163909▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
