Fusion category symmetry-protected topological order in the generalized cluster state

Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be generalized at the microscopic level. In this work, we show that the generalized cluster state introduced in arXiv:1408.6237 is an SPT protected by categorical symmetry. We introduce a generalized Pauli stabilizer Hamiltonian which has the generalized cluster state as its ground state and study the generalization of several characteristic signatures of SPT order: string order, protected edge modes, algebraic structure under stacking, and topological response. We also discuss how the generalized cluster state can be used as a universal resource for measurement-based quantum computation (MBQC).

(Pizza and refreshments will be served after the talk.)