{"title":"The Double Semion State in Infinite Volume","authors":"Alex Bols, Boris Kjær, Alvin Moon","doi":"10.1007/s00023-024-01445-y","DOIUrl":null,"url":null,"abstract":"<p>We describe in a simple setting how to extract a braided tensor category from a collection of superselection sectors of a two-dimensional quantum spin system, corresponding to abelian anyons. We extract from this category its fusion ring as well as its F and R-symbols. We then construct the double semion state in infinite volume and extract the braided tensor category describing its semion, anti-semion, and bound state excitations. We verify that this category is equivalent to the representation category of the twisted quantum double <span>\\(\\mathcal {D}^{\\phi }(\\mathbb {Z}_2)\\)</span>.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"98 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://doi.org/10.1007/s00023-024-01445-y","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We describe in a simple setting how to extract a braided tensor category from a collection of superselection sectors of a two-dimensional quantum spin system, corresponding to abelian anyons. We extract from this category its fusion ring as well as its F and R-symbols. We then construct the double semion state in infinite volume and extract the braided tensor category describing its semion, anti-semion, and bound state excitations. We verify that this category is equivalent to the representation category of the twisted quantum double \(\mathcal {D}^{\phi }(\mathbb {Z}_2)\).
我们在一个简单的环境中描述了如何从二维量子自旋系统的超选扇区集合中提取一个编织张量范畴，该范畴与无边任子相对应。我们从这个范畴中提取其融合环以及 F 和 R 符号。然后，我们构建了无限体积的双半子态，并提取了描述其半子、反半子和束缚态激发的编织张量范畴。我们验证了这个范畴等价于扭曲量子双态的表示范畴（\mathcal {D}^{\phi }(\mathbb {Z}_2)\）。
期刊介绍：
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
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