We provide a general prescription for gauging finite non-invertible symmetries in 1+1d lattice Hamiltonian systems. Our primary example is the Rep (D ₈ 8) fusion category generated by the Kennedy-Tasaki transformation, which is the simplest anomaly-free non-invertible symmetry on a spin chain of qubits. We explicitly compute its lattice F-symbols and illustrate our prescription for a particular (non-maximal) gauging of this symmetry. In our gauging procedure, we introduce two qubits around each link, playing the role of “gauge fields” for the non-invertible symmetry, and impose novel Gauss’s laws. Similar to the Kramers-Wannier transformation for gauging an ordinary Z₂ ℤ2, our gauging can be summarized by a gauging map, which is part of a larger, continuous non-invertible cosine symmetry.
Seifnashri et al. (Fri,) studied this question.