Atypicality of Most Few-Body Observables

TL;DR

This paper challenges the typicality argument underlying the eigenstate thermalization hypothesis (ETH), showing that most few-body observables do not follow ETH when the energy shell width decreases polynomially with system size.

Contribution

It demonstrates that the typicality argument for ETH does not hold for most few-body observables under certain conditions, revealing limitations of ETH in these cases.

Findings

Most few-body observables violate ETH when energy shell width decreases polynomially.

Typicality argument does not apply to these observables in such regimes.

ETH may not universally explain thermalization in all quantum systems.

Abstract

The eigenstate thermalization hypothesis (ETH), which dictates that all diagonal matrix elements within a small energy shell be almost equal, is a major candidate to explain thermalization in isolated quantum systems. According to the typicality argument, the maximum variations of such matrix elements should decrease exponentially with increasing the size of the system, which implies the ETH. We show, however, that the typicality argument does not apply to most few-body observables for few-body Hamiltonians when the width of the energy shell decreases at most polynomially with increasing the size of the system.