Gauging non-invertible symmetries on the lattice

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Abstract
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 \mathbb{Z}_2 ℤ 2 , our gauging can be summarized by a gauging map, which is part of a larger, continuous non-invertible cosine symmetry.
Funding Information
  • National Science Foundation (DMR-2424315)
  • National Science Foundation (PHY-2210182)
  • Simons Foundation (651444)
  • U.S. Department of Energy (DE- SC0009988)

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