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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.04213 |
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| _version_ | 1866916829038903296 |
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| author | Wang, Jundi Chen, Yuxiao Huang, Huaqing |
| author_facet | Wang, Jundi Chen, Yuxiao Huang, Huaqing |
| contents | The quantum metric, a key component of quantum geometry, plays a central role in a wide range of physical phenomena and has been extensively studied in periodic crystals and moiré materials. Here, we systematically investigate quantum geometry in one-dimensional (1D) quasiperiodic systems and uncover novel properties that fundamentally distinguish them from both periodic crystals and disordered media. Our comparative analysis reveals that quasiperiodicity significantly enhances the quantum metric -- despite the absence of translational symmetry -- due to the presence of critical wavefunctions with long-range spatial correlations. In the Aubry-André-Harper model, we show that the quantum metric serves as a sensitive probe of localization transitions, exhibiting sharp changes at the critical point and distinct behaviors near mobility edges. In the Fibonacci chain, characterized by a singular continuous spectrum, we discover an anomalous enhancement of the quantum metric when the Fermi level lies within the minimal gaps of the fractal energy spectrum. Using a perturbative renormalization group framework, we trace this enhancement to the hierarchical structure of the spectrum and the bonding-antibonding nature of critical states across narrow gaps. Our findings establish a fundamental connection between wavefunction criticality, spectral fractality, and quantum geometry, suggesting quasiperiodic systems as promising platforms for engineering enhanced quantum geometric properties beyond conventional crystalline paradigms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Metric Enhancement and Hierarchical Scaling in One-Dimensional Quasiperiodic Systems Wang, Jundi Chen, Yuxiao Huang, Huaqing Mesoscale and Nanoscale Physics The quantum metric, a key component of quantum geometry, plays a central role in a wide range of physical phenomena and has been extensively studied in periodic crystals and moiré materials. Here, we systematically investigate quantum geometry in one-dimensional (1D) quasiperiodic systems and uncover novel properties that fundamentally distinguish them from both periodic crystals and disordered media. Our comparative analysis reveals that quasiperiodicity significantly enhances the quantum metric -- despite the absence of translational symmetry -- due to the presence of critical wavefunctions with long-range spatial correlations. In the Aubry-André-Harper model, we show that the quantum metric serves as a sensitive probe of localization transitions, exhibiting sharp changes at the critical point and distinct behaviors near mobility edges. In the Fibonacci chain, characterized by a singular continuous spectrum, we discover an anomalous enhancement of the quantum metric when the Fermi level lies within the minimal gaps of the fractal energy spectrum. Using a perturbative renormalization group framework, we trace this enhancement to the hierarchical structure of the spectrum and the bonding-antibonding nature of critical states across narrow gaps. Our findings establish a fundamental connection between wavefunction criticality, spectral fractality, and quantum geometry, suggesting quasiperiodic systems as promising platforms for engineering enhanced quantum geometric properties beyond conventional crystalline paradigms. |
| title | Quantum Metric Enhancement and Hierarchical Scaling in One-Dimensional Quasiperiodic Systems |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2507.04213 |