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 $\nu = 1/3$ 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 with occupation in all subbands of the LLL, and overall LLL filling fractions $\nu=r/t$. These phases may compete at the same particle density when the number of sub-bands $p$ matches the denominator $t$. As a concrete example, we numerically explore a direct interaction-driven transition between a CI and a $\nu = 1/3$ Laughlin state at a flux density $n_{\phi} = 3/11$, and characterise the transition in terms of its critical, topological and entanglement properties.