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arXiv:2104.07647 [hep-th]AbstractReferencesReviewsResources

The Wishart-Sachdev-Ye-Kitaev model: Exact spectral density, Q-Laguerre polynomials, and quantum chaos

Lucas Sá, Antonio M. Garcí a-Garcí a

Published 2021-04-15Version 1

We study the Wishart-Sachdev-Ye-Kitaev (WSYK) model consisting of two $\hat{q}$-body Sachdev-Ye-Kitaev (SYK) models with general complex couplings, one the complex conjugate of the other, living in off-diagonal blocks of the larger WSYK Hamiltonian. In the limit of large number $N$ of Majoranas and $\hat{q}\propto\sqrt{N}$, we employ diagrammatic techniques, and a generalized Riordan-Touchard formula, to show that the spectral density of the model is exactly given by the weight function of the Al-Salam-Chihara Q-Laguerre polynomials. For a fixed $\hat{q}$, the analytical spectral density, with $Q=Q(\hat{q},N)$ computed analytically, is still in excellent agreement with numerical results obtained by exact diagonalization. The spectrum is positive with a hard edge at zero energy and, for odd $\hat{q}$, low-energy excitations grow as a stretched exponential, though the functional form is different from that of the supersymmetric SYK model. The microscopic spectral density and level statistics close to the hard edge are very well approximated by that of an ensemble of random matrices belonging to non-standard universality classes which indicates quantum chaotic dynamics. The observed features of the model are consistent with the existence of a gravity dual in the low-energy limit.

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