Alternatives to Eigenstate Thermalization

TL;DR

This paper examines alternatives to the eigenstate thermalization hypothesis (ETH) in quantum many-body systems, analyzing their validity and exploring conditions under which thermalization occurs without ETH.

Contribution

It demonstrates that von Neumann's quantum ergodic theorem depends on an assumption equivalent to ETH and investigates thermalization in integrable systems with specific initial states.

Findings

Von Neumann's theorem relies on an assumption equivalent to ETH.

Thermal behavior can occur in integrable systems with certain initial states.

Examples show initial states that obeyed ETH before quench can lead to thermalization.

Abstract

An isolated quantum many-body system in an initial pure state will come to thermal equilibrium if it satisfies the eigenstate thermalization hypothesis (ETH). We consider alternatives to ETH that have been proposed. We first show that von Neumann's quantum ergodic theorem relies on an assumption that is essentially equivalent to ETH. We also investigate whether, following a sudden quench, special classes of pure states can lead to thermal behavior in systems that do not obey ETH, namely, integrable systems. We find examples of this, but only for initial states that obeyed ETH before the quench.