One-Dimensional Quasicrystals with Power-Law Hopping

X. Deng, S. Ray, S. Sinha, G. V. Shlyapnikov, L. Santos

Research output: Contribution to journalArticlepeer-review

102 Scopus citations


One-dimensional quasiperiodic systems with power-law hopping, 1/ra, differ from both the standard Aubry-André (AA) model and from power-law systems with uncorrelated disorder. Whereas in the AA model all single-particle states undergo a transition from ergodic to localized at a critical quasidisorder strength, short-range power-law hops with a>1 can result in mobility edges. We find that there is no localization for long-range hops with a≤1, in contrast to the case of uncorrelated disorder. Systems with long-range hops rather present ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but nonergodic) states. Both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.

Original languageEnglish
Article number025301
JournalPhysical Review Letters
Issue number2
StatePublished - 10 Jul 2019
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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