标题： 广义整体对称性的交织序 显示英文标题

标题： Intertwined order of generalized global symmetries

摘要： 我们研究了2+1维晶格模型中广义整体对称性的相互作用，该模型通过拓扑相互作用将一个$\mathbb{Z}_N$时钟模型与一个$\mathbb{Z}_N$规范理论耦合起来。这种耦合将一个对称性的电荷绑定到另一个对称性的无序算符上，当这些复合对象凝聚时，会产生具有混合't Hooft异常的新兴广义对称性。这些异常导致具有普通对称性破缺、拓扑序和对称保护的拓扑(SPT)序的相，不同类型的序并非独立，而是紧密相关。我们进一步探索了这些奇异相的能隙边界态，并发展了它们之间相变的理论。此外，我们将此晶格模型扩展以纳入一种非可逆的整体对称性，它可以自发破缺，从而产生具有非平凡融合规则的域壁。 显示英文摘要

摘要： We investigate the interplay of generalized global symmetries in 2+1 dimensions in 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 this lattice model to incorporate a non-invertible global symmetry, which can be spontaneously broken, leading to domain walls with non-trivial fusion rules.