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

Abstract

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.

41 pages, 5 figures

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Cited by in corpus (1)

• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly