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

Chen-Shen Lee^1*, Ken Shiozaki², Chang-Tse Hsieh¹

¹Department of Physics, National Taiwan University, Taipei, Taiwan
²Yukawa Institute of Theoretical Physics, Kyoto University, Kyoto, Japan

* Presenter:Chen-Shen Lee, email:d13222002@ntu.edu.tw

We propose a prescription to investigate the interaction effects on crystalline symmetry-protected topological (SPT) phases. Specifically, using this method, one can establish a clear connection between the equivalence class a free-fermion system falls into and its corresponding interacting class. A key element of this prescription is the Atiyah-Hirzebruch spectral sequence (AHSS), which enables crystalline SPT phases to be represented as SPT phases on subspace manifolds.

Keywords: Symmetry-protected topological phase, generalized (co)homology, topological insulator