Thermalization without eigenstate thermalization

TL;DR

This paper demonstrates that in certain quantum many-body systems, thermalization can occur without the eigenstate thermalization hypothesis (ETH) being satisfied, challenging the traditional understanding of thermalization mechanisms.

Contribution

It provides a proof of thermalization in a nearly integrable Sachdev-Ye-Kitaev model without requiring ETH, showing ETH is not necessary for thermalization.

Findings

Thermalization occurs in the model when the subsystem size exceeds the square root of the system size.

Almost all eigenstates violate the ETH in this setting.

Thermalization is achieved from a random product state despite ETH violations.

Abstract

In an isolated quantum many-body system undergoing unitary evolution, we study the thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to explain thermalization. Consider a nearly integrable Sachdev-Ye-Kitaev model obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. When the subsystem size is larger than the square root of but is still a vanishing fraction of the system size, we prove thermalization if the system is initialized in a random product state, while almost all eigenstates violate the ETH. In this sense, the ETH is not a necessary condition for thermalization.