Eigenstate Thermalization in the Two-Site SYK and SYK Chain Models

TL;DR

This paper investigates the Eigenstate Thermalization Hypothesis in finite-size SYK models, demonstrating that they can rapidly thermalize via ETH, contrasting previous findings of subthermal behavior in entanglement entropy.

Contribution

It provides the first detailed ETH analysis of the two-site SYK and SYK chain models using exact diagonalization, showing they satisfy ETH conditions.

Findings

Single realizations approximately satisfy ETH

Ensemble averages strictly satisfy ETH

Models can rapidly thermalize via light modes

Abstract

A recent study of R\'enyi entanglement entropy in the SYK chain of Majorana fermions suggested that the model does not rapidly thermalize, despite being maximally chaotic. In this work, I examine the Eigenstate Thermalization Hypothesis (ETH) for both the SYK chain and the two-site SYK models using exact diagonalization. I show that single realizations of both models approximately satisfy ETH conditions, while ensemble averages strictly satisfy ETH. Therefore, I conclude that the finite-size SYK chain and two-site SYK models can rapidly thermalize with respect to generic few-body operators through the ETH mechanism. This suggests that the subthermal behavior observed in previous studies of R\'enyi entanglement entropy does not manifest in finite-size systems, and that these systems can thermalize rapidly via their light modes. It also indicates that the proposed gravitational dual may undergo rapid thermalization.