Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model

Abstract

We study spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, a variant of the $k$-body embedded random ensembles studied for several decades in the context of nuclear physics and quantum chaos. We show analytically that the fourth and sixth order energy cumulants vanish in the limit of large number of particles $N\to \infty$ which is consistent with a Gaussian spectral density. However, for finite $N$, the tail of the average spectral density is well approximated by a semi-circle law. The specific heat coefficient, determined numerically from the low temperature behavior of the partition function, is consistent with the value obtained by previous analytical calculations. For energy scales of the order of the mean level spacing we show that level statistics are well described by random matrix theory. Due to the underlying Clifford algebra of the model, the universality class of the spectral correlations depends on $N$. For larger energy separations we identify an energy scale that grows with $N$, reminiscent of the Thouless energy in mesoscopic physics, where deviations from random matrix theory are observed. Our results are a further confirmation that the Sachdev-Ye-Kitaev model is quantum chaotic for all time scales. According to recent claims in the literature, this is an expected feature in field theories with a gravity-dual.

arXiv comment29 pages, 11 figures, journal version

References in corpus (19)

• The Large N Limit of Superconformal Field Theories and Supergravity
• A bound on chaos
• Random Matrix Theories in Quantum Physics: Common Concepts
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Chaos in AdS${}_2$ holography
• The Spectrum in the Sachdev-Ye-Kitaev Model
• An Investigation of AdS${}_2$ Backreaction and Holography
• Bekenstein-Hawking Entropy and Strange Metals
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Bi-Local Holography in the SYK Model
• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
• Random free fermions: An analytical example of eigenstate thermalization
• Spectral Correlations from the Metal to the Mobility Edge
• Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices
• Thermalization in the Two-Body Random Ensemble
• Dirac Spectrum of the Wilson Dirac Operator for QCD with Two Colors
• Spectral statistics of the k-body random-interaction model

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