Archive ouverte HAL – One-Dimensional Quasicrystals with Power-Law Hopping

X. DengS. RayS. Sinha 1 G. v. Shlyapnikov 2 L. Santos

X. Deng, S. Ray, S. Sinha, G. v. Shlyapnikov, L. Santos. One-Dimensional Quasicrystals with Power-Law Hopping. Physical Review Letters, American Physical Society, 2019, 123 (2), ⟨10.1103/PhysRevLett.123.025301⟩. ⟨hal-02291885⟩

One-dimensional quasi-periodic systems with power-law hopping, $1/r^a$, differ from both the standard Aubry-Azbel-Harper (AAH) model and from power-law systems with uncorrelated disorder. Whereas in the AAH model all single-particle states undergo a transition from ergodic to localized at a critical quasi-disorder strength, short-range power-law hops with $a>1$ can result in mobility edges. Interestingly, there is no localization for long-range hops with $a\leq 1$, in contrast to the case of uncorrelated disorder. Systems with long-range hops are rather characterized by ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but non ergodic) states. We show that both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.

• 1. TU/e - Eindhoven University of Technology [Eindhoven]
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques