IAS CMP/QFT Group Meeting

Abstract: I will talk about the adiabatic cycles of one-dimensional gapped Hamiltonians with non-invertible symmetry. Using quasiadiabatic evolution and the results of gapped phase classification, the adiabatic cycles can be classified by the autoequivalences of module categories. This result extends Kitaev's pumping picture and confirms conjectures in the literature. I will present the generalized Thouless pumps in explicit lattice realizations of non-invertible SPT states. Finally, I will talk about the constructions of Floquet drives, which lead to dynamical phases protected by non-invertible symmetries.