Emergent extended states in an unbounded quasiperiodic lattice

Previous studies have established that quasiperiodic lattice models with unbounded potentials can exhibit localized and multifractal states, yet preclude the existence of extended states. In this work, we introduce a quasiperiodic system that incorporates both unbounded potentials and unbounded hopping amplitudes, where extended states emerge as a direct consequence of the unbounded hopping terms overcoming the localization constraints imposed by the unbounded potential, thereby facilitating enhanced particle transport. By using Avila's global theory, we derive analytical expressions for the phase boundaries, with exact results aligning closely with numerical simulations.Intriguingly, we uncover a hidden self-duality in the proposed model by establishing a mapping to the Aubry-Andr\'e model, revealing a profound structural connection between these systems.