## SciPost Submission Page

# Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions

### by Joseph Sullivan, Meng Cheng

### Submission summary

As Contributors: | Meng Cheng |

Arxiv Link: | https://arxiv.org/abs/1904.08953v3 |

Date submitted: | 2019-08-23 |

Submitted by: | Cheng, Meng |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Condensed Matter Physics - Theory |

### Abstract

Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge states of such an intrinsically interacting fermionic SPT phase in two spatial dimensions, protected by $\mathbb{Z}_4\times\mathbb{Z}_2^T$ symmetry. We model the edge Hilbert space by replacing the internal $\mathbb{Z}_4$ symmetry with a spatial translation symmetry, and design an exactly solvable Hamiltonian for the edge model. We show that at low-energy the edge can be described by a two-component Luttinger liquid, with nontrivial symmetry transformations that can only be realized in strongly interacting systems. We further demonstrate the symmetry-protected gaplessness under various perturbations, and the bulk-edge correspondence in the theory.