Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N

Abstract

We show analytically that the spectral density of the $q$-body Sachdeev-Ye-Kitaev (SYK) model agrees with that of Q-Hermite polynomials with Q a non-trivial function of $q\ge 2$ and the number of Majorana fermions $N\gg 1$. Numerical results, obtained by exact diagonalization, are in excellent agreement with the analytical spectral density even for relatively small $N\sim 8$. For $N\gg 1$ and not close to the edge of the spectrum, we find the macroscopic spectral density simplifies to $\rho (E)\sim \exp [2{\arcsin }^2(E/E_0)/\log \eta ]$, where $\eta$ is the suppression factor of the contribution of intersecting Wick contractions relative to nested contractions. This spectral density reproduces the known result for the free energy in the large $q$ and $N$ limit. In the infrared region, where the SYK model is believed to have a gravity-dual, the spectral density is given by $\rho (E)\sim \sinh [2\pi \sqrt{2}\sqrt{(1-E/E_0)/(-\log \eta )}]$. It therefore has a square-root edge, as in random matrix ensembles, followed by an exponential growth, a distinctive feature of black holes and also of low energy nuclear excitations. Results for level-statistics in this region confirm the agreement with random matrix theory. Physically this is a signature that, for sufficiently long times, the SYK model and its gravity dual evolve to a fully ergodic state whose dynamics only depends on the global symmetry of the system. Our results strongly suggest that random matrix correlations are a universal feature of quantum black holes and that the SYK model, combined with holography, may be relevant to model certain aspects of the nuclear dynamics.

18 pages, 5 figures, corrected typos, added references and an explicit calculation of the partition function

References in corpus (10)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Higher Dimensional Generalizations of the SYK Model
• Quantum Chaos and Holographic Tensor Models
• A Supersymmetric SYK-like Tensor Model
• Deformations of the Almheiri-Polchinski model
• Dynamical thermalization in isolated quantum dots and black holes

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