Testing whether all eigenstates obey the eigenstate thermalization hypothesis

TLDR

The study investigates whether ETH holds in the strong sense that every eigenstate becomes thermal in the thermodynamic limit. They analyze few‑body operator expectation values in highly excited eigenstates of two one‑dimensional nonintegrable models via exact diagonalization, searching for outliers that deviate most from ETH. Numerical results show that even extreme outliers satisfy ETH as system size grows, and Floquet eigenstates from a periodically driven Ising model obey ETH more closely, supporting ETH in the strong sense.

Abstract

We ask whether the eigenstate thermalization hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, 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.