Emergent extended states in an unbounded quasiperiodic lattice

TL;DR

This paper introduces a quasiperiodic lattice model with unbounded potentials and hopping amplitudes, demonstrating the emergence of extended states due to unbounded hopping overcoming localization, supported by analytical and numerical analysis.

Contribution

It presents a novel quasiperiodic system where unbounded hopping induces extended states, contrasting prior models that only exhibited localized or multifractal states.

Findings

Extended states emerge from unbounded hopping overcoming potential localization.

Analytical phase boundaries derived using Avila's global theory.

Discovery of a hidden self-duality linking to the Aubry-André model.

Abstract

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.