Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis

Understand

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.