北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
会议
学术会议
工作坊
论坛
学院生活
住宿
交通
配套设施
周边旅游
新闻
新闻动态
通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > BIMSA TQFT and Higher Symmetries Seminar Extracting symmetry fractionalisation data from microscopics
Extracting symmetry fractionalisation data from microscopics
组织者
白岸斯 , 陈群皓 , 孔良 , 王亦龙 , 张智浩 , 郑浩
演讲者
Siddharth Vadnerkar
时间
2024年10月29日 09:40 至 11:40
地点
A3-2-301
线上
Zoom 468 248 1222 (BIMSA)
摘要
Based on "An operator algebraic approach to symmetry defects and fractionalisation", (arxiv:2411.XXXX). Joint work with Kyle Kawagoe and Daniel Wallick.

Symmetry has always played an important role in physics, and in the last 2 decades, the notion of topological order has taken the centre stage in many sub-disciplines of physics. A Symmetry Enriched Topological (SET) order is when one marries the concept of topological order and symmetry and considers sysems that have a global symmetry, as well as topological order. It is well known that gapped topological order in 2+1 dimensions is mathematically described by Unitary Modular Tensor Categories, and houses long-range quasi-particle excitations called anyons. It is natural to study the consequences of imposing a symmetry on such a system. The landmark paper by BBCW (arxiv:1410.4540) worked out the algebraic theory of such a resulting system, with the conclusion that such a theory must be a $G$-crossed braided monoidal category. This approach was based on a UMTC as a starting point and completely independent of microscopics.

In this talk, we take an entirely different approach. Starting from the algebra of local observables of any lattice system in 2+1D, we propose a "selection criterion" to extract global data of such system. We then work out the resultant theory of such data and it turns out to be a $G$-crossed braided monoidal category as expected. We will illustrate this technique using lattice models and see that the resultant category is equivalent to the algebraic theory one gets using the procedure of BBCW.
北京雁栖湖应用数学研究院
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