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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Hierarchical Structures of Quantum Geometric Spectrum in Quasicrystals: A Renormalization-Group Study
Jundi Wang1, Yuxiao Chen1, Huaqing Huang1,2,3
1Peking University, School of Physics, Beijing 100871, China.
Physical Review Letters
|July 26, 2026
Summary
We discovered a universal mechanism for enhancing the quantum metric in 1D quasiperiodic systems. This quantum geometric effect is linked to wave function criticality and spectral fractality, offering new insights into quasicrystals.
Area of Science:
- Condensed Matter Physics
- Quantum Materials
- Nonperiodic Systems
Background:
- Quantum geometry, using quantum metric and Berry curvature, is key to understanding quantum materials.
- Its behavior in nonperiodic systems is not well understood.
- Quasicrystals offer unique properties due to their nonperiodic atomic structure.
Purpose of the Study:
- To uncover the behavior of quantum geometry in 1D quasiperiodic systems.
- To investigate the enhancement of the quantum metric in these systems.
- To link quantum geometric effects to critical phenomena in quasicrystals.
Main Methods:
- Analysis of the Fibonacci chain as a paradigmatic quasiperiodic system.
- Real-space renormalization-group analysis.
- Investigation of the Aubry-André-Harper model in its critical, localized, and extended phases.
Main Results:
- A universal mechanism for divergent enhancement of the quantum metric in 1D quasiperiodic systems was found.
- The quantum metric exhibits hierarchical scaling mirroring the fractal energy spectrum.
- A power-law scaling G∝(ΔE)^{-k} was derived, with the exponent k linked to self-similarity.
Conclusions:
- The quantum metric serves as a sensitive indicator of quasiperiodic criticality.
- Quasicrystals are promising platforms for giant quantum geometric effects.
- This work bridges quantum geometry, criticality, and the physics of nonperiodic systems.
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