标题： 在格点上对非可逆对称性进行规范化 显示英文标题

标题： Gauging non-invertible symmetries on the lattice

摘要： 我们提供了一种在1+1d格点哈密顿量系统中规范有限非可逆对称性的通用方法。 我们的主要例子是由Kennedy-Tasaki变换生成的Rep(D$_8$)融合范畴，这是自旋链上最简单的无异常的非可逆对称性。 我们显式计算了其格点F符号，并展示了对该对称性的特定（非最大）规范化的方案。 在我们的规范过程中，我们在每个链接周围引入两个量子比特，起到“规范场”的作用，以施加新的高斯定律。 类似于用于规范普通$\mathbb{Z}_2$的Kramers-Wannier变换，我们的规范可以通过一个规范映射来总结，该映射是更大、连续的非可逆余弦对称性的一部分。 显示英文摘要

摘要： 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.