Emergent extended states in an unbounded quasiperiodic lattice

• DOI: 10.48550/arxiv.2502.13503
• Publication Date: 2025-02-19
• Authors: Jia-Ming Zhang; Shan-Zhong Li; Shi-Liang Zhu; Zhi Li
• Keywords: Lattice (music)

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 system incorporates both hopping amplitudes, where states emerge as direct consequence terms overcoming localization constraints imposed by potential, thereby facilitating enhanced particle transport. By using Avila's global theory, derive analytical expressions for phase boundaries, exact results aligning closely numerical simulations.Intriguingly, uncover hidden self-duality in proposed model establishing mapping to Aubry-Andr\'e model, revealing profound structural connection between these systems.