On thermalization in the SYK and supersymmetric SYK models

TL;DR

This paper investigates whether the SYK and supersymmetric SYK models exhibit eigenstate thermalization, providing numerical evidence that supports ETH in these strongly chaotic quantum systems and discussing implications for gravity and quantum information.

Contribution

It offers the first numerical analysis of eigenstate thermalization in both SYK and supersymmetric SYK models, extending understanding of thermalization in these chaotic systems.

Findings

Evidence that SYK models satisfy ETH for specific operators

Supports the connection between quantum chaos and thermalization

Discusses implications for gravitational duals and quantum information

Abstract

The eigenstate thermalization hypothesis is a compelling conjecture which strives to explain the apparent thermal behavior of generic observables in closed quantum systems. Although we are far from a complete analytic understanding, quantum chaos is often seen as a strong indication that the ansatz holds true. In this paper, we address the thermalization of energy eigenstates in the Sachdev-Ye-Kitaev model, a maximally chaotic model of strongly-interacting Majorana fermions. We numerically investigate eigenstate thermalization for specific few-body operators in the original SYK model as well as its $\mathcal{N}=1$ 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.