AI 中文总结
本研究在有限非阿贝尔群的量子双格点模型中构造非可逆1-形式算子，明确非阿贝尔拓扑序的非可逆1-形式对称性，确立其基态为自发非可逆1-形式对称性破缺的微观实现。
AI 中文摘要
高形式对称性是常规全局对称性的推广，作用于量子系统的低维子流形。阿贝尔拓扑相可由构成群的1-形式对称性来组织，而基于有限群的非阿贝尔拓扑相则要求1-形式对称算子受非可逆融合代数支配。本研究在有限非阿贝尔群G的量子双格点模型D(G)中明确了这一表述，直接在格点不动点构造了电、磁和 dyonic（双荷）1-形式算子，证明它们共同构成拓扑希尔伯特空间的完备非局域诊断代数。利用这些算子，我们明确确定了任意有限G对应的圆柱和圆环基态子空间。此外，我们计算了1-形式对称性的微观融合与胶合，证明其拓扑变形性质在投影到无缺陷拓扑子空间后显现。本研究结果确立了非阿贝尔量子双模型的基态为自发非可逆1-形式对称性破缺的具体微观实现，并提供了一种算子语言，或可用于表征量子处理器中的此类态。
英文摘要
Higher-form symmetries generalize conventional global symmetries and act on lower-dimensional submanifolds of a quantum system. While Abelian topological phases can be organized by 1-form symmetries that form a group, non-Abelian topological phases based on finite groups require 1-form symmetry operators governed by non-invertible fusion algebras. In this work, we make this statement precise in quantum double lattice models $\mathcal D(G)$ for finite non-Abelian groups $G$. We construct the electric, magnetic, and dyonic 1-form operators directly at the lattice fixed point and show that together they form a complete nonlocal diagnostic algebra for the topological Hilbert space. Using these operators, we explicitly determine the cylinder and torus ground-state subspaces for arbitrary finite $G$. Furthermore, we calculate the microscopic fusion and gluing of the 1-form symmetries and show that their topological deformation properties emerge after projection to the defect-free topological subspace. Our results establish ground states of non-Abelian quantum double models as a concrete microscopic realization of spontaneous non-invertible 1-form symmetry breaking and provide an operator language that may be useful for characterizing such states in quantum processors.
