Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices

TL;DR

This paper explores how tunable longer-range hopping in 2D lattice models can induce band topology transitions and fractional quantum Hall states, offering insights into topological phases and potential experimental realizations.

Contribution

It demonstrates that band topology transitions can be achieved through tunable longer-range hopping in Hofstadter-like models and confirms the existence of fractional quantum Hall states in various topological phases.

Findings

Band topology transitions are controllable via tunable longer-range hopping.

Fractional quantum Hall states exist in bands with different Chern numbers.

The model provides a pathway for realizing topological phases in optical lattices.

Abstract

Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C|=1 and |C|>1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.