Emergent multifractality in power-law decaying eigenstates
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909671006142464 |
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| author | Das, Adway Kumar Ghosh, Anandamohan Khaymovich, Ivan M. |
| author_facet | Das, Adway Kumar Ghosh, Anandamohan Khaymovich, Ivan M. |
| contents | Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates which allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1d tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions which are in agreement with numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergent multifractality in power-law decaying eigenstates Das, Adway Kumar Ghosh, Anandamohan Khaymovich, Ivan M. Disordered Systems and Neural Networks High Energy Physics - Theory Mathematical Physics Quantum Physics Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates which allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1d tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions which are in agreement with numerical simulations. |
| title | Emergent multifractality in power-law decaying eigenstates |
| topic | Disordered Systems and Neural Networks High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2501.17242 |