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

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.