标题： 自由费米子与相互作用晶体对称性保护拓扑相之间的联系 显示英文标题

标题： Connection between Free-Fermion and Interacting Crystalline Symmetry-Protected Topological Phases

摘要： 我们提出一个框架，用于研究相互作用对晶体对称性保护拓扑（SPT）相的影响。 在该框架中，可以建立自由费米子系统与其相应相互作用类之间的直接联系。 该框架的核心组成部分是Atiyah-Hirzebruch谱序列，它提供了一种系统的方法，将晶体SPT相表示为子空间上的具有内部对称性的SPT相。 我们通过不同维度中的例子展示了这种方法的应用：具有U(1)和反射对称性的1d系统，具有U(1)和C_{n}旋转对称性的2d系统，以及具有U(1)和反演对称性的3d系统。 显示英文摘要

摘要： We present a framework for investigating the effects of interactions on crystalline symmetry-protected topological (SPT) phases. Within this framework, one can establish a direct connection between the equivalence classes of free-fermion systems and their corresponding interacting classes. A central component of this framework is the Atiyah-Hirzebruch spectral sequence, which provides a systematic way to represent crystalline SPT phases as SPT phases with internal symmetries on subspaces. We demonstrate the application of this approach through examples in various dimensions: 1d systems with U(1) and reflection symmetry, 2d systems with U(1) and C_{n} rotation symmetry, and 3d systems with U(1) and inversion symmetry.