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SUMMARY:Non-invertible SPTs: an on-site realization of (1+1)d anomaly-free
  fusion category symmetry - Xinping  Yang (Yale University)
DTSTART:20251203T130000Z
DTEND:20251203T143000Z
UID:TALK241468@talks.cam.ac.uk
DESCRIPTION:We investigate (1+1)d symmetry-protected topological (SPT) pha
 ses with fusion category symmetries. We emphasize that the UV description 
 of an anomaly-free fusion category symmetry must include the fiber functor
 \, giving rise to a local symmetry action\, a charge category and a trivia
 l phase. We construct an "onsite'' matrix-product-operator (MPO) version o
 f the Hopf algebra symmetry operators in a lattice model with tensor-produ
 ct Hilbert space. In particular\, we propose a systematic framework for cl
 assifying and constructing SPTs with non-invertible symmetries. An SPT pha
 se corresponds to a Q-system in the charge category\, such that the Q-syst
 em becomes a matrix algebra when the symmetry is forgotten. As an example\
 , we provide an explicit microscopic realization of all three 
LOCATION:Seminar Room 2\, Newton Institute
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