Lévy Sachdev-Ye-Kitaev model
Phys. Rev. B 114, 154205 – Published 22 September, 2026
DOI: https://doi.org/10.1103/g35t-x778
Abstract
We explore the spectral properties of the four-fermion Sachdev-Ye-Kitaev model with interaction sourced from a Lévy stable (fat-tailed) distribution. We study the eigenvalue distribution, focusing on long- and short-range correlations and extreme statistics. Our analysis uncovers a crossover from chaotic to integrable behavior (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 multifractal hierarchy of the Lévy stable distribution. The crossover is explained in terms of a genuine many-body effect, which is distinct from the single-particle transition (controlled by a mobility edge) of the underlying Lévy random matrices. We conclude with comments on the model's solvability and discussion of possible models with exact transitions.
