Correlation effects on topological crystalline insulators

TL;DR

This paper investigates how interactions affect the classification of topological crystalline insulators, revealing that their topological classifications are reduced from infinite groups to finite cyclic groups in both two and three dimensions.

Contribution

The study extends the understanding of interaction effects on topological crystalline insulators, showing a reduction in classification groups from  to  and from  to  in 2D and 3D respectively, using bosonization and symmetry analysis.

Findings

2D classification reduced from  to  by interactions

3D classification reduced from  to  by interactions

Edge state stability analyzed via bosonization

Abstract

We study interaction effects on the topological crystalline insulators protected by time-reversal ($T$) and reflection symmetry ($R$) in two and three spatial dimensions. From the stability analysis of the edge states with bosonization, we find that the classification of the two-dimensional SPT phases protected by $Z_2\times[\mbox{U(1)}\rtimes T]$ symmetry is reduced from $\mathbb{Z}$ to $\mathbb{Z}_4$ by interactions, where the $Z_2$ symmetry denotes the reflection whose mirror plane is the two-dimensional plane itself. By extending the approach recently proposed by Isobe and Fu, we show that the classification of the three-dimensional SPT phases (i.e., topological crystalline insulators) protected by $R\times[\mbox{U(1)}\rtimes T]$ symmetry is reduced from $\mathbb{Z}$ to $\mathbb{Z}_8$ by interactions.