标题： 广义全局对称性的交织顺序 显示英文标题

标题： Intertwined order of generalized global symmetries

摘要： 我们通过引入一个格点模型来研究2+1维中的广义全局对称性的相互作用，该模型通过拓扑相互作用将$\mathbb{Z}_N$时钟模型与$\mathbb{Z}_N$规范理论耦合。 这种耦合将一种对称性的电荷绑定到另一种对称性的无序算符上，当这些复合物体凝聚时，会产生具有混合't Hooft反常的涌现广义对称性。 这些反常导致了具有普通对称性破缺、拓扑序和对称性保护拓扑（SPT）序的相，其中不同类型的序不是独立的，而是紧密相关的。 我们进一步探讨了这些奇异相的无能隙边界态，并发展了它们之间相变的理论。 此外，我们将格点模型扩展以包含一个非可逆全局对称性，该对称性可以被自发破缺，从而产生具有非平凡融合规则的域墙。 显示英文摘要

摘要： We investigate the interplay of generalized global symmetries in 2+1 dimensions by introducing a lattice model that couples a $\mathbb{Z}_N$ clock model to a $\mathbb{Z}_N$ gauge theory via a topological interaction. This coupling binds the charges of one symmetry to the disorder operators of the other, and when these composite objects condense, they give rise to emergent generalized symmetries with mixed 't Hooft anomalies. These anomalies result in phases with ordinary symmetry breaking, topological order, and symmetry-protected topological (SPT) order, where the different types of order are not independent but intimately related. We further explore the gapped boundary states of these exotic phases and develop theories for phase transitions between them. Additionally, we extend our lattice model to incorporate a non-invertible global symmetry, which can be spontaneously broken, leading to domain walls with non-trivial fusion rules.