Eigenstate thermalization in the Sachdev-Ye-Kitaev model

Abstract

The eigenstate thermalization hypothesis (ETH) explains how closed unitary quantum systems can exhibit thermal behavior in pure states. In this work we examine a recently proposed microscopic model of a black hole in AdS${}_2$, the so-called Sachdev-Ye-Kitaev (SYK) model. We show that this model satisfies the eigenstate thermalization hypothesis by solving the system in exact diagonalization. Using these results we also study the behavior, in eigenstates, of various measures of thermalization and scrambling of information. We establish that two-point functions in finite-energy eigenstates approximate closely their thermal counterparts and that information is scrambled in individual eigenstates. We study both the eigenstates of a single random realization of the model, as well as the model obtained after averaging of the random disordered couplings. We use our results to comment on the implications for thermal states of the dual theory, i.e. the AdS${}_2$ black hole.

36 pages, many figures; references added; matches published version

References in corpus (10)

• Thermalization and its mechanism for generic isolated quantum systems
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Chaos, Complexity, and Random Matrices
• The complete $1/N$ expansion of a SYK--like tensor model
• Quantum quench of the Sachdev-Ye-Kitaev Model
• Higher Dimensional Generalizations of the SYK Model
• Three Dimensional View of the SYK/AdS Duality
• From Conformal Blocks to Path Integrals in the Vaidya Geometry
• Towards a Finite-$N$ Hologram
• Black Holes, Entanglement and Random Matrices