Necessity of Eigenstate Thermalization

TL;DR

This paper proves that the Eigenstate Thermalization Hypothesis (ETH) is both necessary and sufficient for quantum systems to thermalize, simplifying the identification of thermal behavior to ETH verification.

Contribution

It establishes the ETH as a necessary condition for thermalization in quantum systems coupled to baths, resolving a key theoretical question.

Findings

ETH is necessary for thermalization in quantum systems.

Thermalization occurs if and only if the Hamiltonian satisfies ETH.

The result simplifies diagnosing thermal behavior in quantum systems.

Abstract

Under the Eigenstate Thermalization Hypothesis (ETH), quantum-quenched systems equilibrate towards canonical, thermal ensembles. While at first glance the ETH might seem a very strong hypothesis, we show that it is indeed not only sufficient but also necessary for thermalization. More specifically, we consider systems coupled to baths with well-defined macroscopic temperature and show that whenever all product states thermalize then the ETH must hold. Our result definitively settles the question of determining whether a quantum system has a thermal behaviour, reducing it to checking whether its Hamiltonian satisfies the ETH.