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One-Dimensional Quasicrystals with Power-Law Hopping
1Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover, Germany.
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.
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.
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