Year: 2024
Type: article
Abstract: We show that the Levin-Wen model of a unitary fusion category $${\mathcal {C}}$$ C is a gauge theory with gauge symmetry given by the tube algebra $${\text {Tube}}({\mathcal {C}})$$ Tube ( C ) . In particular, we define a model corresponding to a $${\text {Tube}}({\mathcal {C}})$$ Tube ( C ) symmetry protected topological phase, and we provide a gauging procedure which results in the corresponding Levin-Wen model. In the case $${\mathcal {C}}=\textsf{Hilb}(G,\omega )$$ C = Hilb ( G , ω ) , we show how our procedure reduces to the twisted gauging of a trival G-SPT to produce the Twisted Quantum Double. We further provide an example which is outside the bounds of the current literature, the trivial Fibbonacci SPT, whose gauge theory results in the doubled Fibonacci string-net. Our formalism has a natural topological interpretation with string diagrams living on a punctured sphere. We provide diagrams to supplement our mathematical proofs and to give the reader an intuitive understanding of the subject matter.
Authors: Kyle Kawagoe, Corey Jones, Sean Sanford, David Green, David Penneys
Institutions: The Ohio State University, North Carolina State University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
Awards: Categorical Symmetries of Operator Algebras, G2493428800, G266914229, G3062877667, G330644682, Quantum Symmetries: Subfactors, Topological Phases, and Higher Categories, G5934961879, G5956625161, Center for Emergent Materials, an NSF MRSEC, G7928636825, CAREER: Representing and Classifying Enriched Quantum Symmetry
OpenAlex ID: W4403349298