On thermalization in the SYK and supersymmetric SYK models

This work addresses the question of whether the eigenstate thermalization hypothesis in its scaling form is satisfied in Sachdev-Ye-Kitaev models.Going substantially beyond previous treatments of eigenstate expectation values in such models, the authors present a scaling analysis and identify the situations where eigenstate thermalization holds and where it does not.

arXiv:1711.02360Physical review. B./Physical review. BSep 12, 201941 citations

On thermalization in the SYK and supersymmetric SYK models

Nicholas Hunter-Jones

Published Jun 29, 2023• 29 citations

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Abstract

DOI: 10.1007/jhep02%282018%29142

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On thermalization in the SYK and supersymmetric SYK models

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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 AdS2, 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 a putative dual theory, i.e. the AdS2 black hole.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 AdS2, 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 a putative dual theory, i.e. the AdS2 black hole.

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\mathcal{N}

= 1 supersymmetric extension and find evidence that these models satisfy ETH. We discuss the implications of ETH for a gravitational dual and the quantum information-theoretic properties of SYK it suggests.

_4

(with quartic couplings) which is maximally chaotic in the large system size limit satisfies the standard ETH scaling while SYK

_2

(with quadratic couplings), which is integrable, does not. We show that the low-energy and high-energy properties are affected drastically differently when the two Hamiltonians are mixed.