A Unifying Framework for Fractional Chern Insulator Stabilization

We present a theory of fractional Chern insulator stabilization against charge-ordered states. We argue that the phase competition is captured by an effective interaction range, which depends on both the bare interaction range and quantum geometric properties. We argue that short effective interaction ranges stabilize fractional states while longer-range interactions favor charge-ordered states. To confirm our hypothesis, we conduct a numerical study of the generalized Hofstadter model using the density matrix renormalization group. Our theory offers a new interpretation of the geometric stability hypothesis and generalizes it, providing a unifying framework for several approaches to fractional phase stabilization. Finally, we propose a route towards experimental verification of the theory and possible implications for fractional states in bands with higher Chern numbers.