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理論物理前沿進展研討會(7月8日-9日)

報告人: 
兰天 (滑铁卢大学量子计算中心)、程蒙(耶魯大學物理系)、邹柳俊 (哈佛大学物理系)
題目: 
拓扑序与对称富化 (Workshop on topological order and symmetry enrichment)
地點: 
南校園冼爲堅堂111會議室
時間: 
2019年7月8日-9日

主持人:叶鹏 教授

? ? ? 由于是内部讨论,如果需要参加,请提前发邮件至yepeng5@mail.sysu.edu.cn(葉鵬教授),並明確參加的時間段。
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具體安排如下:

8日 (周一)上午 10:00-12:00

兰天 (滑铁卢大学量子计算中心)
讨论题目:Higher-dimensional topological order, higher category and a classification in 3+1D

【摘要】:Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitation of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n- category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of certain group. Such a "gauge group" is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying such boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above "gauge group" together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
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9日 ?(周二) 上午10:00-12:00

程蒙(耶魯大學物理系)
讨论题目:From translation-invariant symmetry-enriched topological order to fracton phases

【摘要】:I will discuss recent progress in the theory of two- and three-dimensional topological phases enriched by translation symmetry, and the connections to fracton topological order. I will first describe general aspects of topological phases with translation and other internal symmetries, as well as the associated Lieb-Schultz-Mattis quantum anomalies. I will discuss the relation between mobility of quasiparticles and their transformation under translation symmetry. With this point of view I will provide a systematic classification of fractonic excitations in three-dimensional U(1) spin liquids, possibly enforced by global symmetries, and their realizations in a gauged coupled layer construction.?
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9日 (周二) 下午 14:00-16:00

邹柳俊 (哈佛大学物理系)
讨论题目:Symmetry enriched U(1) quantum spin liquids and more

【摘要】:A U(1) quantum spin liquid (QSL) is an exotic gapless phase which can be described by a U(1) gauge theory at low energies. In the presence of symmetries, U(1) QSLs can be classified into different symmetry enriched U(1) QSLs. I will present systematic understanding of the characterization and classification of symmetry enriched U(1) QSLs. In particular, I will first present a physics-based approach to understand symmetry enriched U(1) QSLs. Next, I will take a more formal perspective on these phases. Finally, I will discuss some interesting applications based on the ideas developed along these lines.?

9日 (周二) 下午 16:00-18:00?

学生报告 Student session

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