L\'evy Sachdev-Ye-Kitaev Model

TL;DR

This paper investigates the spectral properties of a Le9vy-stable distribution-based Sachdev-Ye-Kitaev model, revealing a crossover from chaotic to integrable behavior linked to the fat-tailed nature of the distribution.

Contribution

It introduces a novel Le9vy distribution-based SYK model and analyzes its spectral crossover, highlighting many-body effects distinct from single-particle mobility edges.

Findings

Spectral crossover from chaos to integrability as distribution becomes fat-tailed

Eigenvalue correlations show a transition linked to the distribution's hierarchy

Model exhibits a many-body effect different from single-particle mobility edges

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.