Cluster state as a non-invertible SPT phase

Abstract: We study the simplest lattice realizations of SPT phases protected by non-invertible symmetries. We show that the well-known 1+1d cluster model has a Rep(D8) non-invertible symmetry, thereby identifying it as a non-invertible SPT phase. We also find commuting Pauli Hamiltonians for the remaining two Rep(D8) SPT phases, matching the classification in field theory and mathematics. Finally, we determine the projective algebra and edge modes at the interfaces between these three non-invertible SPT phases.

HEP - phenomenologyHEP - theorymathematical physicscategory theory

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.