Xinping Yang (Perimeter Institute) – Non-invertible SPTs: an on-site realization of (1+1)d anomaly-free fusion category symmetry

Abstract - Symmetry and its anomaly constrain a system's dynamics and provide a universal characterization of its behaviors. It serves as a powerful tool to understand exotic phases of matter, especially symmetry-protected topological (SPT) orders. The notion of generalized symmetries requires extending our previous understanding of topological phases to those enriched by fusion category symmetries, yet new mathematical formalism is needed to implement unitary fusion category symmetries in a quantum many-body system. In this talk, I will introduce a general fixed-point lattice construction of (1+1)d SPTs with unitary fusion category symmetries, realized in a tensor-product Hilbert space with an “onsite” matrix-product-operator (MPO) version of the Hopf C*-algebra symmetry operators. Within this construction, I will address 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 trivial phase, and discuss an alternative characterization of SPT phases using the Q-system in the charge category. As an example, I will provide an explicit microscopic realization of all three 𝖱𝖾𝗉(D8) SPT phases, including a trivial phase, and further demonstrate the S3-duality among these three SPT phases.