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

## TL;DR

This paper investigates the edge states of a novel two-dimensional fermionic symmetry-protected topological phase, revealing interaction-driven gapless modes and their robustness, which cannot be realized in non-interacting systems.

## Contribution

It introduces an exactly solvable model for the edge of an interacting fermionic SPT phase with $ ext{Z}_4 imes ext{Z}_2^T$ symmetry, highlighting unique strongly interacting features.

## Key findings

- Edge modeled by a two-component Luttinger liquid
- Symmetry transformations only realizable in strongly interacting systems
- Edge remains gapless under various perturbations

## 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.