Eigenstate thermalization in the Sachdev-Ye-Kitaev model

TL;DR

This paper demonstrates that the Sachdev-Ye-Kitaev (SYK) model satisfies the eigenstate thermalization hypothesis, showing that individual eigenstates exhibit thermal behavior and information scrambling, with implications for black hole physics.

Contribution

The study provides exact diagonalization evidence that the SYK model obeys ETH and analyzes thermalization and scrambling in its eigenstates, linking to dual black hole theories.

Findings

Two-point functions in eigenstates match thermal predictions

Eigenstates exhibit information scrambling

Results support the SYK model as a black hole analog

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.