Eigenstate Thermalization Hypothesis

TL;DR

The paper reviews the Eigenstate Thermalization Hypothesis (ETH), explaining how individual quantum energy eigenstates mimic statistical ensembles, and discusses its theoretical foundations, applications, experimental tests, and cases of breakdown.

Contribution

It provides an accessible overview of ETH, connecting quantum chaos, random matrix theory, and statistical mechanics, highlighting recent experimental and theoretical developments.

Findings

ETH explains thermalization in isolated quantum systems

Numerous experiments support ETH in various physical systems

Research explores conditions where ETH fails, revealing new phenomena

Abstract

The emergence of statistical mechanics for isolated classical systems comes about through chaotic dynamics and ergodicity. Here we review how similar questions can be answered in quantum systems. The crucial point is that individual energy eigenstates behave in many ways like a statistical ensemble. A more detailed statement of this is named the Eigenstate Thermalization Hypothesis (ETH). The reasons for why it works in so many cases are rooted in the early work of Wigner on random matrix theory and our understanding of quantum chaos. The ETH has now been studied extensively by both analytic and numerical means, and applied to a number of physical situations ranging from black hole physics to condensed matter systems. It has recently become the focus of a number of experiments in highly isolated systems. Current theoretical work also focuses on where the ETH breaks down leading to new interesting phenomena. This review of the ETH takes a somewhat intuitive approach as to why it works and how this informs our understanding of many body quantum states.