论文标题
关键的分类对称性
Categorical Symmetries at Criticality
论文作者
论文摘要
我们研究了最近引入的“分类对称性”的概念，在最基本的意义上是指一对双对称性，例如$ 1D $ Quantum Ising模型的Ising对称性及其自动对手。在本手稿中，我们研究了在较高维点和无间隙阶段的离散分类对称性。在这些选定的物质无间隙状态下，我们可以分析分类对称性的行为。我们在以下关键示例中分析了分类对称性：（1）$（2+1）d $ Quantum ising系统的LifShit临界点； （2）$（3+1）d $光子阶段作为拓扑顺序与3D $ z_2 $量子量规理论之间的中间间隔相； （3）$ 2D $和$ 3D $的系统示例具有分类对称性（0形或1形式的分类对称性）和子系统对称性。我们证明，在这些物质的某些无间隙状态下，分类对称性的行为与附近的间隙阶段大不相同。
We study the concept of "categorical symmetry" introduced recently, which in the most basic sense refers to a pair of dual symmetries, such as the Ising symmetries of the $1d$ quantum Ising model and its self-dual counterpart. In this manuscript we study discrete categorical symmetry at higher dimensional critical points and gapless phases. At these selected gapless states of matter, we can evaluate the behavior of categorical symmetries analytically. We analyze the categorical symmetry at the following examples of criticality: (1) Lifshit critical point of a $(2+1)d$ quantum Ising system; (2) $(3+1)d$ photon phase as an intermediate gapless phase between the topological order and the confined phase of 3d $Z_2$ quantum gauge theory; (3) $2d$ and $3d$ examples of systems with both categorical symmetries (either 0-form or 1-form categorical symmetries) and subsystem symmetries. We demonstrate that at some of these gapless states of matter the categorical symmetries have very different behavior from the nearby gapped phases.
