Connection between free-fermion and interacting crystalline symmetry-protected topological phases
Journal
Physical Review B
Journal Volume
113
Journal Issue
4
Start Page
1
End Page
17
ISSN
2469-9950
2469-9969
Date Issued
2026-01-21
Author(s)
Abstract
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 Cn rotation symmetry, and 3d systems with U(1) and inversion symmetry.
Publisher
American Physical Society (APS)
Type
journal article