Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis

TL;DR

This paper investigates whether all eigenstates in certain quantum many-body systems satisfy the Eigenstate Thermalization Hypothesis (ETH), providing numerical evidence that even outliers tend to obey ETH as system size grows, especially under periodic driving.

Contribution

The study offers the first numerical evidence that all eigenstates, including outliers, obey ETH in large nonintegrable quantum systems, and shows that periodic driving enhances thermalization.

Findings

Outliers tend to obey ETH as system size increases.

Periodic driving improves adherence to ETH.

Numerical evidence supports ETH in a strong sense.

Abstract

We ask whether the Eigenstate Thermalization Hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, {\it every} eigenstate is thermal. We examine expectation values of few-body operators in highly-excited many-body eigenstates and search for `outliers', the eigenstates that deviate the most from ETH. We use exact diagonalization of two one-dimensional nonintegrable models: a quantum Ising chain with transverse and longitudinal fields, and hard-core bosons at half-filling with nearest- and next-nearest-neighbor hopping and interaction. We show that even the most extreme outliers appear to obey ETH as the system size increases, and thus provide numerical evidences that support ETH in this strong sense. Finally, periodically driving the Ising Hamiltonian, we show that the eigenstates of the corresponding Floquet operator obey ETH even more closely. We attribute this better thermalization to removing the constraint of conservation of the total energy.