Thermalization of isolated quantum many-body system and the role of entanglement

TL;DR

This paper explores how entanglement in isolated quantum many-body systems contributes to thermalization, demonstrating that entangled energy eigenstates produce thermal averages consistent with statistical mechanics.

Contribution

It provides a theoretical demonstration that entangled energy eigenstates lead to thermalization, linking quantum entanglement with statistical mechanics in many-body systems.

Findings

Entangled energy eigenstates yield thermal averages.

Observable expectation values match microcanonical and canonical averages.

Entanglement plays a key role in quantum thermalization.

Abstract

Thermalization of an isolated quantum system has been a nontrivial problem since the early days of quantum mechanics. In generic isolated quantum systems, nonequilibrium dynamics is expected to result in thermalization, indicating the emergence of statistical mechanics from quantum dynamics. However, what feature of a many-body quantum system facilitates quantum thermalization is still not well understood. Recent experimental advancements have shown that entanglement may act as a thermalizing agent, not universally but particularly. Here, we theoretically show that the thermal averages of an observable in an isolated many-body quantum system with a large number of degrees of freedom emerge from the entangled energy eigenstates of the system. In particular, we show that the expectation values of an observable in entangled energy eigenstates and its marginals are equivalent to the microcanonical and canonical averages of the observable.