Disorder in the Sachdev-Yee-Kitaev Model

Abstract

We give qualitative arguments for the mesoscopic nature of the Sachdev-Yee-Kitaev (SYK) model in the holographic regime with $q^2/N\ll 1$ with $N$ Majorana particles coupled by antisymmetric and random interactions of range $q$. Using a stochastic deformation of the SYK model, we show that its characteristic determinant obeys a viscid Burgers equation with a small spectral viscosity in the opposite regime with $q/N=1/2$, in leading order. The stochastic evolution of the SYK model can be mapped onto that of random matrix theory, with universal Airy oscillations at the edges. A spectral hydrodynamical estimate for the relaxation of the collective modes is made.

7 pages, 1 figure

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Cited by in corpus (31)

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• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Three Dimensional View of Arbitrary $q$ SYK models
• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Towards a Finite-$N$ Hologram
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Topological Sachdev-Ye-Kitaev Model
• Sachdev-Ye-Kitaev model on a noisy quantum computer
• Scale-invariant critical dynamics at eigenstate transitions
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• Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes
• Conformality of $1/N$ corrections in SYK-like models
• On the replica structure of Sachdev-Ye-Kitaev model
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• What is the Simplest Linear Ramp?
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Probing quantum chaos in multipartite systems
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• Stochastic Operator Variance: an observable to diagnose noise and scrambling
• Violation of the viscosity/entropy bound in translationally invariant non-Fermi liquids
• Single-Particle Universality of the Many-Body Spectral Form Factor
• Exact spectral form factors of non-interacting fermions with Dyson statistics
• Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model