Gauging non-invertible symmetries on the lattice

• URL: http://arxiv.org/abs/2503.02925v1
• Date: Tue, 04 Mar 2025 19:00:00 GMT
• Title: Gauging non-invertible symmetries on the lattice
• Authors: Sahand Seifnashri, Shu-Heng Shao, Xinping Yang,
• Abstract summary: We provide a prescription for gauging finite non-invertible symmetries in 1+1d lattice Hamiltonian systems.<n>In our gauging procedure, we introduce two qubits around each link, playing the cosine of "gauge fields" for non-invertible symmetry.<n>Similar to the Kramers-Wannier transformation for gauging an ordinary $bbZ$, our gauging can be summarized by a gauging map.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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$_8$) 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 $\mathbb{Z}_2$, our gauging can be summarized by a gauging map, which is part of a larger, continuous non-invertible cosine symmetry.

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