Graduate Theory Seminar - Sahand Seifnashri - “Topological phases protected by non-invertible symmetries”

We will discuss the simplest example of SPT phases protected by non-invertible symmetries. We show that the 1+1d cluster model has a Rep(D8) non-invertible symmetry, thereby identifying it as a non-invertible SPT phase. We find two other commuting Pauli Hamiltonians for the other two Rep(D8) SPT phases, matching the classification in field theory and mathematics. Finally, we identify the projective algebra and edge modes at the interfaces between such two phases.