Fractional topological phase in one-dimensional flatbands with nontrivial topology

TL;DR

This paper demonstrates the existence of fractional topological phases in one-dimensional flatband models with nontrivial topology, characterized by degeneracy and Berry phase, and explores their stability and realization in cold-atom systems.

Contribution

It provides the first detailed analysis of fractional topological phases in 1D flatbands with nontrivial topology, including phase diagrams and physical interpretations.

Findings

FTP appears at filling factor 1/3 with nearest-neighbor interaction

FTP characterized by three-fold degeneracy and quantized Berry phase

Next-nearest-neighbor interaction destroys the FTP

Abstract

We show the existence of the fractional topological phase (FTP) in a one-dimensional interacting fermion model using exact diagonalization, in which the non-interacting part has flatbands with nontrivial topology. In the presence of the nearest-neighbouring interaction $V_{1}$, the FTP at filling factor $\nu =1/3$ appears. It is characterized by the three-fold degeneracy and the quantized total Berry phase of the ground-states. The FTP is destroyed by a next-nearest-neighbouring interaction $V_{2}$ and the phase diagrams in the $(V_{1},V_{2})$ plane is determined. We also present a physical picture of the phase and discuss its existence in the nearly flatband. Within the picture, we argue that the FTP at other filling factors can be generated by introducing proper interactions. The present study contributes to a systematic understanding of the FTPs and can be realized in cold-atom experiments.