Lévy Sachdev-Ye-Kitaev Model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908394191847424 |
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| author | Bhattacharjee, Budhaditya Salazar, William E. Rosa, Dario Andreanov, Alexei |
| author_facet | Bhattacharjee, Budhaditya Salazar, William E. Rosa, Dario Andreanov, Alexei |
| contents | We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a Lévy Stable (fat-tailed) distribution. Lévy random matrices are known to demonstrate non-ergodic behaviour through the emergence of a mobility edge. We study the eigenvalue distribution, focusing on long- and short-range correlations and extreme statistics. This model demonstrates a crossover from chaotic to integrable behaviour (in the spectral correlations) as the distribution becomes increasingly fat-tailed. We investigate this crossover through a hierarchical analysis of the eigenvalue spectrum, based on the multi-fractal hierarchy of the Lévy Stable distribution. The crossover is explained in terms of a genuine many-body effect, distinct from the transition (controlled by a mobility edge) in the Lévy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lévy Sachdev-Ye-Kitaev Model Bhattacharjee, Budhaditya Salazar, William E. Rosa, Dario Andreanov, Alexei Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a Lévy Stable (fat-tailed) distribution. Lévy random matrices are known to demonstrate non-ergodic behaviour through the emergence of a mobility edge. We study the eigenvalue distribution, focusing on long- and short-range correlations and extreme statistics. This model demonstrates a crossover from chaotic to integrable behaviour (in the spectral correlations) as the distribution becomes increasingly fat-tailed. We investigate this crossover through a hierarchical analysis of the eigenvalue spectrum, based on the multi-fractal hierarchy of the Lévy Stable distribution. The crossover is explained in terms of a genuine many-body effect, distinct from the transition (controlled by a mobility edge) in the Lévy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions. |
| title | Lévy Sachdev-Ye-Kitaev Model |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.04343 |