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One-Dimensional Quasicrystals with Power-Law Hopping.

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Summary
This summary is machine-generated.

One-dimensional quasiperiodic systems with power-law hopping exhibit unique behaviors. Long-range hops (a≤1) lead to ergodic-to-multifractal transitions, unlike localization seen in other models.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Disordered Systems

Background:

  • Standard Aubry-André (AA) model describes a transition from ergodic to localized states in quasiperiodic systems.
  • Power-law hopping (1/r^a) introduces unique characteristics compared to uncorrelated disorder.
  • Distinguishing between short-range and long-range hopping is crucial for understanding system behavior.

Purpose of the Study:

  • To investigate the behavior of one-dimensional quasiperiodic systems with power-law hopping.
  • To differentiate the effects of short-range (a>1) versus long-range (a≤1) power-law hopping.
  • To identify novel phase transitions and edge phenomena in these systems.

Main Methods:

  • Analysis of one-dimensional quasiperiodic systems.
  • Theoretical modeling of power-law hopping interactions (1/r^a).
  • Comparison with standard Aubry-André model and uncorrelated disorder systems.

Main Results:

  • Short-range power-law hops (a>1) can lead to mobility edges.
  • Long-range power-law hops (a≤1) show no localization, contrasting with uncorrelated disorder.
  • Systems with long-range hops exhibit ergodic-to-multifractal edges and phase transitions.

Conclusions:

  • Power-law hopping in quasiperiodic systems introduces distinct phenomena beyond standard localization.
  • The nature of hopping (short-range vs. long-range) dictates the system's edge and transition properties.
  • Observed mobility and ergodic-to-multifractal edges can be experimentally verified through expansion dynamics.