2025/06/04 by Budhaditya Bhattacharjee, William E. Salazar, Bhattacharjee, Budhaditya +5
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2506.04343
openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.