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Higher categorical symmetries and gauging in two-dimensional spin systems
Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium, Krijgslaan 281.
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.ORCID iD: 0000-0003-4742-775X
2024 (English)In: SciPost Physics, E-ISSN 2542-4653, Vol. 16, no 4, article id 110Article in journal (Refereed) Published
Abstract [en]

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries. Our framework relies on an approach to dualities whereby dual quantum lattice models only differ in a choice of module 2-category over some input fusion 2-category. Given an arbitrary two-dimensional spin system with an ordinary symmetry, we explain how to perform the (twisted) gauging of any of its sub-symmetries. We then demonstrate that the resulting model has a symmetry structure encoded into the Morita dual of the input fusion 2-category with respect to the corresponding module 2-category. We exemplify this approach by specialising to certain finite group generalisations of the transversefield Ising model, for which we explicitly define lattice symmetry operators organised into fusion 2-categories of higher representations of higher groups.

Place, publisher, year, edition, pages
SciPost Foundation , 2024. Vol. 16, no 4, article id 110
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:kth:diva-346499DOI: 10.21468/SciPostPhys.16.4.110Scopus ID: 2-s2.0-85192355812OAI: oai:DiVA.org:kth-346499DiVA, id: diva2:1858415
Note

QC 20240520

Available from: 2024-05-16 Created: 2024-05-16 Last updated: 2024-05-20Bibliographically approved

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Tiwari, Apoorv

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