Non-invertible symmetries in 2+1d lattice models and SPT states
Abstract:
We will discuss an example of fusion 2-category symmetry that involves 1-form symmetry and non-invertible symmetry on the lattice with a tensor product Hilbert space. We start by motivating why realizing generalized symmetries on the lattice with tensor product Hilbert space is an interesting and non-trivial question. After highlighting the difference of “topological” and “non-topological” 1-form symmetry on the lattice, we discuss how non-invertible symmetry naturally appears in a simple family of lattice models. This non-invertible symmetry is shown to be anomaly free, by finding mutually commuting Hamiltonians with unique ground state. Such Hamiltonians describe the SPT phases with non-invertible symmetry, which we partially identify.