A Unified Mean-field Understanding of Fractional Chern Insulator Stability

Resolving the ground state and the phase diagram of strongly correlated phases such as fractional Chern insulators (FCI) are known to be computationally expensive. In this work, we develop a mean-field theory of fractional Chern insulators based on the dipole picture of composite fermions (CF), and propose it as a unified description to the FCI phase stability. We construct CFs by binding vortices to Bloch electrons and derive a CF single-particle Hamiltonian that describes a Hofstadter problem in the enlarged CF Hilbert space, with the band dispersion and the well-known trace-condition term emerging naturally in the small-q limit, and a CF effective mass driven by the Coulomb interaction and affected by the band projection details. Going beyond the small-q regime, we compute the full-q CF spectrum for twisted MoTe2 and obtain its CF phase diagram. The CF phase boundary matches closely with the exact diagonalization result, and the projected many-body wavefunctions achieve exceptionally high overlaps with the latter. Our theory thus provides both a microscopic understanding and a computationally efficient tool for identifying fractional Chern insulators.