发表机构
Universidade Estadual de Londrina; Purdue University（朗德里纳州立大学; 普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出d维晶格系统调制对称性及其规范变换的构造性框架，通过核构造获对称性允许的局域相互作用，实现阿贝尔晶体对称性富集拓扑相，适配文献中多个模型。
AI 中文摘要
我们开发了一个用于表征d维晶格系统中调制对称性及其规范变换的构造性框架。调制轮廓被组织为空间群在有限阿贝尔内部对称群上作用的有限维表示。由于对应的自同构群是有限的，非平凡空间作用通过空间群的有限商分解，从而产生周期性调制模式，并为离散阿贝尔调制对称性提供分类框架。对称性允许的局域相互作用可通过核构造系统地获得，该构造还产生开算子的代数。在规范变换时，其元素会转化为扩展的威尔逊算子和边界算子，同时保留其代数关系。在退禁闭 regime 中，所得代数实现了混合的't Hooft反常，为阿贝尔晶体对称性富集拓扑相（SETs）提供了微观途径。这些SETs不混合电 sector 和磁 sector，二者在互余表示中变换，从而保留它们的编织配对。我们通过具体示例说明该框架，并表明文献中的若干模型自然地适配于我们的构造中。
英文摘要
We develop a constructive framework for characterizing modulated symmetries and their gauging in $d$-dimensional lattice systems. The modulation profiles are organized as a finite-dimensional representation of the space group acting on a finite Abelian internal symmetry group. Since the corresponding automorphism group is finite, the nontrivial spatial action factors through a finite quotient of the space group, leading to periodic modulation patterns and providing a classification framework for discrete Abelian modulated symmetries. The symmetry-allowed local interactions are systematically obtained from a kernel construction, which also yields an algebra of open operators. Upon gauging, its elements are transmuted into extended Wilson and boundary operators while retaining their algebraic relations. In the deconfined regime, the resulting algebra realizes a mixed 't Hooft anomaly, providing a microscopic route to Abelian crystalline symmetry-enriched topological phases (SETs). These SETs do not mix electric and magnetic sectors, which transform in mutually contragredient representations, thereby preserving their braiding pairing. We illustrate the framework through explicit examples and show that several models present in the literature fit naturally within our construction.
Comments50 pages, 5 figures
