자료유형  

 학위논문

Control Number  

0017163909

International Standard Book Number  

9798342718745

Dewey Decimal Classification Number  

530

Main Entry-Personal Name  

Li, Yabo.

Publication, Distribution, etc. (Imprint  

[S.l.] : State University of New York at Stony Brook., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

218 p.

General Note  

Source: Dissertations Abstracts International, Volume: 86-05, Section: B.

General Note  

Advisor: Wei, Tzu-Chieh;Cano, Jennifer.

Dissertation Note  

Thesis (Ph.D.)--State University of New York at Stony Brook, 2024.

Summary, Etc.  

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.

Subject Added Entry-Topical Term  

Physics.

Subject Added Entry-Topical Term  

Statistical physics.

Subject Added Entry-Topical Term  

Applied mathematics.

Subject Added Entry-Topical Term  

Theoretical physics.

Index Term-Uncontrolled  

Gauging

Index Term-Uncontrolled  

Twisted quantum double

Index Term-Uncontrolled  

Kramers-Wannier

Index Term-Uncontrolled  

Topological phases

Index Term-Uncontrolled  

Symmetry fractionalization

Added Entry-Corporate Name  

State University of New York at Stony Brook Physics

Host Item Entry  

Dissertations Abstracts International. 86-05B.

Electronic Location and Access  

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Control Number  

joongbu:656865