Chaos and random matrices in supersymmetric SYK

TL;DR

This paper investigates chaos in supersymmetric quantum systems using random matrix theory, revealing unique spectral features and slower randomization compared to non-supersymmetric models.

Contribution

It applies Wishart-Laguerre ensembles to supersymmetric SYK models, providing new insights into their spectral properties and chaotic behavior.

Findings

Absence of a dip regime in spectral form factors

Slower approach to Haar-random dynamics

Agreement with supersymmetric SYK predictions

Abstract

We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.