Chaos and random matrices in supersymmetric SYK

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.

27 pages, 7 figures; v2: typos fixed, references added. Published version

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• Many-body quantum chaos in stroboscopically-driven cold atoms
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• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model
• Spectral form factor and semi-circle law in the time direction
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Probing quantum chaos in multipartite systems
• Spectral form factor in the double-scaled SYK model
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
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• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• Quantum complexity and the virial theorem
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• A route from maximal chaoticity to integrability
• Comparing quantum complexity and quantum fidelity