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Updated: May 28, 2026
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Published on: December 4, 2017
Criticality without self-similarity: a 2D system with random long-range hopping
Summary
This study explores quantum disorder in 2D systems, revealing that eigenfunctions at the metal-insulator transition exhibit multifractal behavior at small hopping amplitudes but not at large amplitudes.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Disordered Systems
Background:
- Understanding metal-insulator transitions is crucial in condensed matter physics.
- Quantum disorder significantly impacts electronic properties of materials.
- Eigenfunction localization is a hallmark of insulating states.
Purpose of the Study:
- To investigate the nature of eigenfunctions at a metal-insulator transition in a 2D disordered system.
- To analyze the influence of hopping amplitude on eigenfunction properties.
- To compare the transition with related models in 1D and higher dimensions.
Main Methods:
- Modeling a 2D system with long-range site-to-site hopping.
- Analyzing the behavior of eigenfunctions at the transition point.
- Examining density moments and their scaling with system size.
Main Results:
- Eigenfunction nature depends on hopping amplitude magnitude.
- Strong multifractality observed at small hopping amplitudes.
- Absence of multifractality at large amplitudes; density moments scale logarithmically with system size.
Conclusions:
- The 2D transition differs from 1D systems and conventional Anderson transitions.
- Logarithmic scaling of density moments suggests a unique localization mechanism.
- Hopping amplitude is a critical parameter determining transition characteristics.
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