Interaction-driven plateau transition between integer and fractional Chern Insulators

We present numerical evidence of an interaction-driven quantum Hall plateau transition between a |C|>1 Chern Insulator (CI) and a ν=1/3 Laughlin state in the Harper-Hofstadter model. We study the model at flux densities p/q, where the lowest Landau level (LLL) manifold comprises p magnetic sub-bands. For weak interactions, the model realises integer CIs corresponding to filled sub-bands, while strongly interacting candidate states include fractional quantum Hall (FQH) states at LLL filling fractions ν=r/t. These phases may compete at the same particle density when p=t. As a concrete example, we numerically explore the physics at flux density nϕ=3/11, where we show evidence that a direct transition occurs between a CI and a ν=1/3 Laughlin state, which we characterise in terms of its critical, topological and entanglement properties. We also show that strong interactions generically stabilise a ν=1/3 Laughlin state even when the LLL is split into multiple bands, and introduce a powerful methodology to extract its topological entanglement entropy by exploiting the scaling of magnetic length with nϕ.