Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Physics

Background:

• Quasiperiodic systems bridge ordered and disordered states, exhibiting unique critical behaviors.
• One-dimensional models breaking self-dual symmetry often show a mobility edge, akin to higher-dimensional disordered systems.

Purpose of the Study:

• To determine critical localization properties of single particles in shallow, one-dimensional, quasiperiodic models.
• To correlate these properties with the fractal nature of the energy spectrum.
• To investigate implications for Anderson localization and related phenomena in ultracold atoms.

Main Methods:

• Analysis of single-particle localization in one-dimensional quasiperiodic potentials.
• Determination of the mobility edge separating localized and extended phases.
• Calculation of the critical potential amplitude and spectral Hausdorff dimension.

Main Results:

• A clear mobility edge is identified, delineating distinct localized and extended phases.
• A universal critical exponent ν ≈ 1/3 is found for the critical potential amplitude.
• The spectral Hausdorff dimension is nonuniversal and always less than unity, indicating a nowhere-dense spectrum.

Conclusions:

• The study elucidates the critical localization phenomena in one-dimensional quasiperiodic systems.
• Findings provide insights into Anderson localization, Bose-glass physics, and many-body localization.
• Results are relevant for ongoing research with ultracold atoms in quasiperiodic potentials.