# On lattice models of gapped phases with fusion category symmetries

@inproceedings{Inamura2021OnLM, title={On lattice models of gapped phases with fusion category symmetries}, author={Kansei Inamura}, year={2021} }

We construct topological quantum field theories (TQFTs) and commuting projector Hamiltonians for any 1+1d gapped phases with non-anomalous fusion category symmetries, i.e. finite symmetries that admit SPT phases. The construction is based on two-dimensional state sum TQFT whose input datum is anH-simple leftH-comodule algebra, whereH is a finite dimensional semisimple Hopf algebra. We show that the actions of fusion category symmetries C on the boundary conditions of these state sum TQFTs are…

## One Citation

Non-Invertible Duality Defects in 3+1 Dimensions

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For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the…

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