Stron eigenstate thermalization hypothesis

TL;DR

This paper generalizes the eigenstate thermalization hypothesis (ETH), showing that individual eigenstates can represent microcanonical ensembles for local and certain non-local operators, with a derivation for perturbed integrable models.

Contribution

It extends ETH to include some non-local operators and provides a derivation for systems with a small Gaussian perturbation.

Findings

Eigenstates can represent microcanonical ensembles for local operators.

ETH can be generalized to include certain non-local operators.

Derivation provided for perturbed integrable many-body systems.

Abstract

We present a generalization of the ETH conjecture. Using this generalization we are able to derive the fact that an arbitrary eigenstate of a general many body system may be used to represent microcanonical ensemble in any many body experiment that involves only local operators and projectors onto eigenstates of the system Hamiltonian. In particular we extend the ETH to include some non-local operators. We present a derivation of this conjecture in the case of a many body model whose Hamiltonian is composed of two parts: an integrable Hamiltonian and a small but finite Gaussian perturbation.