## 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/1904.08953v5 (pdf) |

Date accepted: | 2020-07-03 |

Date submitted: | 2020-06-04 |

Submitted by: | Cheng, Meng |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Theory |

Approach: | Theoretical |

### 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.

###### Current status:

Editorial decision:
For Journal SciPost Physics: Publish

(status: Editorial decision fixed and (if required) accepted by authors)

### List of changes

Major changes:

1. We have significantly expanded section 2 to include more background materials on concepts and ideas used in this work.

2. We renamed Section 5.5 to better reflect the actual content of the section.

3. Citations on gapping of null-vector type in a general Luttinger liquid are updated.

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2020-6-30 Invited Report

### Report

I join the other referee in recommending publication.

Referee 1: "The authors have addressed all the points I had raised in my report.

I recommend publication of their paper."