2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155937Using a controlled analytic treatment, we derive a model that generically describes cooperative strong electron-phonon interaction (EPI) in one-band and two-band Jahn-Teller (JT) systems. The model involves a {\em next-nearest-neighbor} hopping and a nearest-neighbor repulsion. Rings with odd number of sites (o-rings) belong to a different universality class compared to rings with even number (e-rings). The e-rings, upon tuning repulsion, undergo a dramatic discontinuous transition to a {\em conducting commensurate} charge density wave (CDW) state with a period independent of filling.Added Jahn-Teller systemStrongly Correlated ElectronsMaterials Sciencetext