Topological crystalline insulators are phases of matter where the crystalline symmetries solely protect the topology. In this work, we explore the effect of many-body interactions in a subclass of topological crystalline insulators, namely the mirror-symmetry protected topological crystalline insulator. Employing a prototypical mirror-symmetric quasi-one-dimensional model, we demonstrate the emergence of a mirror-symmetry protected topological phase and its robustness in the presence of short-range interactions. When longer-range interactions are introduced, we find an interaction-induced topological phase transition between the mirror-symmetry protected topological order and a trivial charge density wave. The results are obtained using density-matrix renormalization group and quantum Monte Carlo simulations in applicable limits.Topological crystalline insulators are phases of matter where the crystalline symmetries solely protect the topology. In this work, we explore the effect of many-body interactions in a subclass of topological crystalline insulators, namely the mirror-symmetry protected topological crystalline insulator. Employing a prototypical mirror-symmetric quasi-one-dimensional model, we demonstrate the emergence of a mirror-symmetry protected topological phase and its robustness in the presence of short-range interactions. When longer-range interactions are introduced, we find an interaction-induced topological phase transition between the mirror-symmetry protected topological order and a trivial charge density wave. The results are obtained using density-matrix renormalization group and quantum Monte Carlo simulations in applicable limits.

arXiv:2202.07436SciPost Physics CoreOct 10, 20222 citations

Symmetry-Protected Topological Phases

Bei Zeng, Xie Chen, D. L. Zhou +1 more

Quantum science and technologyJan 1, 20197 citations

Correlation effects on topological crystalline insulators

Tsuneya Yoshida, Akira Furusaki

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 ${Z}_{2}\ifmmode\times\else\texttimes\fi{}[\text{U(1)}\ensuremath{\rtimes}T]$ 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 $R\ifmmode\times\else\texttimes\fi{}[\text{U(1)}\ensuremath{\rtimes}T]$ symmetry is reduced from $\mathbb{Z}$ to ${\mathbb{Z}}_{8}$ by interactions.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 ${Z}_{2}\ifmmode\times\else\texttimes\fi{}[\text{U(1)}\ensuremath{\rtimes}T]$ 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 $R\ifmmode\times\else\texttimes\fi{}[\text{U(1)}\ensuremath{\rtimes}T]$ symmetry is reduced from $\mathbb{Z}$ to ${\mathbb{Z}}_{8}$ by interactions.

arXiv:1505.06598Physical Review BAug 7, 201528 citations

Topological phases protected by point group symmetry

Sheng-Jie Huang, Hao Song, Michael Hermele

Bulletin of the American Physical SocietyMar 16, 20160 citations

Theory of interacting topological crystalline insulators

Hiroki Isobe, Liang Fu

We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multivalley Dirac fermion surface states. We find that interactions reduce the integer classification of noninteracting TCIs in three dimensions, indexed by the mirror Chern number, to a finite group ${Z}_{8}$ . In particular, we explicitly construct a microscopic interaction Hamiltonian to gap eight flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. Our construction builds on interacting edge states of $U(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry-protected topological phases of fermions in two dimensions, which we classify. Our work reveals a deep connection between three-dimensional topological phases protected by spatial symmetries and two-dimensional topological phases protected by internal symmetries.We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multivalley Dirac fermion surface states. We find that interactions reduce the integer classification of noninteracting TCIs in three dimensions, indexed by the mirror Chern number, to a finite group ${Z}_{8}$. In particular, we explicitly construct a microscopic interaction Hamiltonian to gap eight flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. Our construction builds on interacting edge states of $U(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry-protected topological phases of fermions in two dimensions, which we classify. Our work reveals a deep connection between three-dimensional topological phases protected by spatial symmetries and two-dimensional topological phases protected by internal symmetries.

arXiv:1502.06962Physical Review BAug 10, 2015111 citations

Classification and Edge States of Symmetry Protected Topological Phases

Xie Chen

Bulletin of the American Physical SocietyMar 3, 20140 citations

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 ${Z}_{2}\ifmmode\times\else\texttimes\fi{}[\text{U(1)}\ensuremath{\rtimes}T]$ symmetry is reduced from

\mathbb{Z}

{\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 $R\ifmmode\times\else\texttimes\fi{}[\text{U(1)}\ensuremath{\rtimes}T]$ symmetry is reduced from

\mathbb{Z}

{\mathbb{Z}}_{8}

by interactions.

{Z}_{8}

. In particular, we explicitly construct a microscopic interaction Hamiltonian to gap eight flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. Our construction builds on interacting edge states of $U(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry-protected topological phases of fermions in two dimensions, which we classify. Our work reveals a deep connection between three-dimensional topological phases protected by spatial symmetries and two-dimensional topological phases protected by internal symmetries.