Single-Polaron Physics in Flat Bands: Exact Solution and Spectral Properties

Flat bands host unique correlated electronics states. Efforts have predominantly focused on the effects of direct electron-electron interactions such as Coulomb and Hubbard. Here, we study flat bands in the presence of electron-phonon coupling (EPC) and solve the single-polaron problem exactly in a class of flat band models with uniform quantum geometry. We show that the spectral function is nonperturbatively renormalized and exhibits exotic features like repeated poles with a non-integer power law divergence: a direct experiment observable. Our results provide a rare example of an exactly solvable electron–phonon problem and establish a foundation for exploring phonon-mediated correlations in flat-band systems.