Stability of Correlated Phases under Band Hybridization: A Neural‑Network Quantum‑State Study

Correlated phases in flat bands are often treated within a single-band approximation due to computational cost. In this work, We study how hybridization with nearby bands, i.e., multiband effects, modifies the energy spectra and the ground-state degeneracy of fractional Chern insulators (FCIs). Using neural-network quantum states such as those from FermiNet, we probe the momentum-resolved spectra and structure factors on system sizes beyond exact diagonalization, across tunable parameters of realistic models realizing FCIs. Our results reveal systematic trends linking the evolution and eventual breakdown of topological orders, together with the emergence of competing textures of nearby phases. This study offers a controlled perspective on how band geometry interplays with the multi-band effects in setting FCI stability, and highlight neural-network ansatz states as physics-driven computational probes for strongly correlated phases.