Description
Symmetry protected topological (SPT) phase is a new type of phases beyond Landau's paradigm and is related to the anomaly on the boundary. In recent year, the notion of symmetry has been generalized and therefore it is interesting to ask about SPT phases with these generalized symmetries. In this talk, I will discuss how to classify a noninvertible SPT phases and construct concrete lattice models realizing these new phases. Through a duality transformation, Kramers-Wannier duality in our case, the models with non-invertible symmetry are dual to models with a group symmetry and therefore the classification problem is translated into the classification of gapped phases with group symmetry. We illustrate this method with the example of Rep(D_{2n}) symmetry in (1+1)d and 2-Rep(Z_{n}^{(1)}\rtimes Z_{2}^{(0)}) symmetry in (2+1)d. We also discuss the anomalous boundaries at the interfaces of different SPT phases, which realizes the anomaly inflow picture of non-invertible symmetry.
