1204.2365 (Huaiming Guo et al.)

Fractional topological phase in one-dimensional flatbands with
nontrivial topology    [PDF]

Huaiming Guo, Shun-Qing Shen, Shiping Feng

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, and is characterized by the three-fold degeneracy of the ground states. Although a next-nearest-neighbouring interaction $% V_{2}$ destroys the FTP at $\nu =1/3$, the FTP at $\nu =1/4$ is generated, which is further destroyed by next-next-nearest-neighbouring interaction $V_{3}$. We study the total Berry phase of the low-energy states at both filling factors, and determine the phase diagrams in the $% (V_{1},V_{2})$ and $(V_{2},V_{3})$ planes, respectively. 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 may be helpful in understanding the relevant physics in higher dimensions and realized in cold-atom experiments.

View original: http://arxiv.org/abs/1204.2365