Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials

Hepeng Yao, Alice Khoudli, Léa Bresque, and Laurent Sanchez-Palencia
Phys. Rev. Lett. 123, 070405 – Published 16 August 2019
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Abstract

Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility edge, similarly as truly disordered systems in a dimension strictly higher than two. Here, we determine the critical localization properties of single particles in shallow, one-dimensional, quasiperiodic models and relate them to the fractal character of the energy spectrum. On the one hand, we determine the mobility edge and show that it separates the localized and extended phases, with no intermediate phase. On the other hand, we determine the critical potential amplitude and find the universal critical exponent ν1/3. We also study the spectral Hausdorff dimension and show that it is nonuniversal but always smaller than unity, hence showing that the spectrum is nowhere dense. Finally, applications to ongoing studies of Anderson localization, Bose-glass physics, and many-body localization in ultracold atoms are discussed.

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  • Received 2 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.070405

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Hepeng Yao, Alice Khoudli, Léa Bresque, and Laurent Sanchez-Palencia

  • CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Route de Saclay, F-91128 Palaiseau, France

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Issue

Vol. 123, Iss. 7 — 16 August 2019

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