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This research investigates the spectral properties of a four-fermion Sachdev-Ye-Kitaev model driven by Lévy stable distributions, revealing a crossover from chaotic to integrable behavior. The study highlights how fat-tailed interactions induce non-ergodicity and distinct many-body effects separate from standard mobility edge transitions in random matrices. These findings advance the theoretical understanding of quantum chaos and spectral statistics in strongly correlated systems.
L\'evy Sachdev-Ye-Kitaev Model
arXiv:2506.04343v2 Announce Type: replace Abstract: We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a L\'evy Stable (fat-tailed) distribution. L\'evy 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 L\'evy 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 L\'evy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions.
Abstract: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.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
arXiv:2506.04343 [quant-ph]
(or arXiv:2506.04343v2 [quant-ph] for this version)
Phys.Rev.B 114 (2026) 15, 154205
https://doi.org/10.1103/g35t-x778 DOI(s) linking to related resources
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