The Band Geometry of Band Mixing

Fractional topological phases in lattice systems are typically studied within an isolated, nearly flat Chern band. However, experimental platforms featuring flat Chern bands often feature other nearby bands that can affective the ground state significantly — a phenomena called band mixing in the Landau level context. This work examines the role of remote bands in stabilizing or destabilizing fractional states in flat Chern bands beyond Landau levels. Using Schrieffer–Wolff transformations, we derive effective Hamiltonians that systematically incorporate the influence of adjacent bands, establishing a direct connection between the single-particle geometry of remote bands and the many-body properties of fractional states. We verify the analytical insights obtained from this framework in many-body numerical simulations.