Non-invertible SPT order in a group-based cluster state

Abstract: The one-dimensional cluster state is a paradigmatic example of a symmetry-protected topological (SPT) state protected by Z2xZ2 symmetry in 1+1D. I will show that a generalization of the cluster state to finite groups is an example of an SPT state protected by a non-invertible GxRep(G) symmetry, belonging to a distinct phase from the symmetric product state. In this example, the signatures of SPT phases: protected edge modes, string order parameters, and topological response can be naturally generalized. Along the way, I will highlight the deep relation between the cluster state and gauging (the Kramers-Wannier transformation), the generalization of the Pauli matrices from the group Z2 to finite groups, and the power of tensor networks to express microscopic realizations of non-invertible symmetries. This talk is based on arXiv:2312.09272

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.