AI 中文总结
该研究利用代数拓扑和范畴论构建晶体拓扑相的连续介质极限框架，揭示部分晶格相无连续介质极限、部分拓扑数据坍缩等规律，并将其应用于多种拓扑相及退禁闭量子临界点的反常研究。
AI 中文摘要
连续介质极限是一种广泛应用的理论构造，用于获取晶体系统的连续介质场论。我们研究有能隙玻色子相的连续介质极限的构建，并探讨其拓扑性质在过渡到连续介质时是否保留。利用代数拓扑和范畴论方法，我们给出了连续介质极限的严格构建，并构造了一个满射全局映射，将所有有限点群对称性下的晶体拓扑相与连续介质可逆拓扑相关联起来。因此，我们发现部分晶格相不存在连续介质极限，而部分确实存在连续介质极限的不同晶格相可共享相同的连续介质像，这意味着部分晶格拓扑数据会发生坍缩。相反，我们发现每个连续介质可逆相都存在忠实的晶体实现。除了一般框架外，我们将其应用于多个示例，包括二维旋转对称相、高阶拓扑相，以及反铁磁体与价键固体之间退禁闭量子临界点的混合自旋-晶格反常研究。
英文摘要
The continuum limit is a widely used theoretical construct for obtaining continuum field-theories of crystalline systems. We study the formulation of a continuum limit for gapped bosonic phases and ask whether their topological properties survive passage to the continuum. Using methods in algebraic topology and category theory, we give a rigorous formulation of the continuum limit and construct a surjective global map relating crystalline topological phases across all finite point-group symmetries to continuum invertible topological phases. Consequently, we find that some lattice phases admit no continuum limit, while distinct lattice phases that do admit a continuum limit can share the same continuum image, hence implying that some lattice topological data can collapse. Conversely, we find that every continuum invertible phase admits a faithful crystalline realization. In addition to the general framework, we apply it to several examples, including studies of a 2D rotation-symmetric phase, higher-order topological phases, and the mixed spin-lattice anomaly of the deconfined quantum critical point between an antiferromagnet and valence bond solid.
Comments55+70 pages, 16+1 figures
