Lévy Sachdev-Ye-Kitaev Model

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Main Authors: Bhattacharjee, Budhaditya, Salazar, William E., Rosa, Dario, Andreanov, Alexei
Format: Preprint
Published: 2025
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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