New equilibrium ensembles for isolated quantum systems

TL;DR

This paper introduces a new hierarchy of equilibrium ensembles for isolated quantum systems, improving the approximation to the diagonal ensemble and capturing equilibrium physics beyond traditional Gibbs states.

Contribution

It presents a novel hierarchical method to better approximate the diagonal ensemble, extending the understanding of equilibrium states in isolated quantum systems.

Findings

Hierarchical ensembles improve approximation to the diagonal ensemble

Method captures equilibrium physics beyond Gibbs ensembles

Applicable to small isolated quantum systems

Abstract

The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called "diagonal ensemble" $\rho_{DE}$. Building on the intuition provided by Jaynes' maximum entropy principle, in this paper we present a novel technique to generate progressively better approximations to $\rho_{DE}$. As an example, we write down a hierarchical set of ensembles which can be used to describe the equilibrium physics of small isolated quantum systems, going beyond the "thermal ansatz" of Gibbs ensembles.