Hard-core bosons in one-dimensional interacting topological bands

TL;DR

This study investigates hard-core bosons in 1D topological bands, revealing a superfluid to Mott insulator transition at certain fillings and identifying a bosonic fractional topological phase at others, with implications for cold-atom experiments.

Contribution

It demonstrates the absence of bosonic topological phases at certain fillings and identifies a fractional topological phase at others, contrasting with fermionic systems.

Findings

No bosonic topological phase at filling ν=1 with Hubbard interaction.

Superfluid to Mott-insulator transition driven by interactions.

Identification of a bosonic fractional topological phase at ν=1/3 with longer-range interactions.

Abstract

We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\nu=1$ and in the presence of on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid (SF) to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\nu=1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase (FTP) whose ground-states are characterized by the three-fold degeneracy and quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason of the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our these results can be realized in cold-atom experiments.