An operator-algebraic framework proves that boundary conditions in (1+1)D gapped phases with categorical symmetry are classified by objects of the module category M_Q^op via an equivalence of categories, yielding a bulk-boundary correspondence as the enriched center.
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String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
Introductory lecture notes on tensor networks with emphasis on matrix-product states, their algorithms, higher-dimensional generalizations, and applications to mixed states and open quantum systems, accompanied by Julia code.
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Bulk-boundary correspondence of (1+1)D symmetric gapped phases
An operator-algebraic framework proves that boundary conditions in (1+1)D gapped phases with categorical symmetry are classified by objects of the module category M_Q^op via an equivalence of categories, yielding a bulk-boundary correspondence as the enriched center.