Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model

Abstract

We study the level statistics of a generalized Sachdev-Ye-Kitaev (SYK) model with two-body and one-body random interactions of finite range by exact diagonalization. Tuning the range of the one-body term, while keeping the two-body interaction sufficiently long-ranged, does not alter substantially the spectral correlations, which are still given by the random matrix prediction typical of a quantum chaotic system. However a transition to an insulating state, characterized by Poisson statistics, is observed by reducing the range of the two-body interaction. Close to the many-body metal-insulator transition, we show that spectral correlations share all features previously found in systems at the Anderson transition and in the proximity of the many-body localization transition. Our results suggest the potential relevance of SYK models in the context of many-body localization and also offer a starting point for the exploration of a gravity-dual of this phenomenon.

6 pages, 2 figures

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• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Chaos exponents of SYK traversable wormholes
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Sparse random matrices and Gaussian ensembles with varying randomness
• Towards quantum simulation of Sachdev-Ye-Kitaev model
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• Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit
• Superconducting gap ratio from strange metal phase in the absence of quasiparticles
• Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos
• Two-local modifications of SYK model with quantum chaos
• Electronic properties of the boson mode in a three-point fermion loop and the emergent SYK physics
• A sharp transition in quantum chaos and thermodynamics of mass deformed SYK model