Correlation effects on topological crystalline insulators

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 symmetry-protected topological (SPT) phases protected by Z₂×[U(1)T] symmetry is reduced from Z to Z₄ by interactions where the Z₂ 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×[U(1)T] symmetry is reduced from Z to Z₈ by interactions.