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arXiv · 2506.04343

L\'evy Sachdev-Ye-Kitaev Model

Budhaditya Bhattacharjee·William E. Salazar·Dario Rosa·Alexei Andreanov
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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.

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Budhaditya Bhattacharjee, William E. Salazar, Dario Rosa, Alexei Andreanov. 2025-06-04. L\'evy Sachdev-Ye-Kitaev Model. https://arxiv.org/abs/2506.04343

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