标题： 交错构造界面和费米子对称保护拓扑相的反常边界 显示英文标题

标题： Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases

摘要： 我们使用拉回平凡化技术系统地构建费米子对称保护拓扑（FSPT）态的带隙界面和反常边界，通过将其对称群$G_f = \mathbb{Z}_2^f \times_{\omega_2} G$扩展到更大的群。 这些FSPT态可能涉及马约拉纳链和复杂费米子的装饰层。 我们为（2+1）维和（3+1）维系统明确推导出一般的一致性公式，在这些系统中，非平凡的扭曲来源于确保上链水平的余边界消失的费米子对称局部酉变换或“规范变换”。 此外，我们给出了一个具有马约拉纳链装饰的（3+1）维 FSPT 的具体例子，其对称群为$G_f=\mathbb{Z}_2^f \times \mathbb{Z}_4 \times \mathbb{Z}_4$。 显示英文摘要

摘要： We use the pullback trivialization technique to systematically construct gapped interfaces and anomalous boundaries for fermionic symmetry-protected topological (FSPT) states by extending their symmetry group $G_f = \mathbb{Z}_2^f \times_{\omega_2} G$ to larger groups. These FSPT states may involve decoration layers of both Majorana chains and complex fermions. We derive general consistency formulas explicitly for (2+1)D and (3+1)D systems, where nontrivial twists arise from fermionic symmetric local unitaries or "gauge transformations" that ensure coboundaries vanish at the cochain level. Additionally, we present explicit example for a (3+1)D FSPT of symmetry group $G_f=\mathbb{Z}_2^f \times \mathbb{Z}_4 \times \mathbb{Z}_4$ with Majorana chain decorations.