Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems

TL;DR

This paper investigates how the initial state's structure and its relation to the Hamiltonian influence thermalization in isolated quantum many-body systems, highlighting the importance of eigenstate delocalization and energy spectrum position.

Contribution

It demonstrates the impact of initial state delocalization and spectrum position on thermalization, especially in finite systems with few-body interactions, extending understanding beyond fully extended eigenstates.

Findings

Chaotic initial states lead to thermalization with infinite temperature behavior.

Delocalization of initial states near the spectrum center promotes thermal averages.

Finite systems with few-body interactions do not have fully extended eigenstates, affecting thermalization.

Abstract

We explore the role of the initial state on the onset of thermalization in isolated quantum many-body systems after a quench. The initial state is an eigenstate of an initial Hamiltonian $\hat{H}_I$ and it evolves according to a different final Hamiltonian $\hat{H}_F$. If the initial state has a chaotic structure with respect to $\hat{H}_F$, i.e., if it fills the energy shell ergodically, thermalization is certain to occur. This happens when $\hat{H}_I$ is a full random matrix, because its states projected onto $\hat{H}_F$ are fully delocalized. The results for the observables then agree with those obtained with thermal states at infinite temperature. However, finite real systems with few-body interactions, as the ones considered here, are deprived of fully extended eigenstates, even when described by a nonintegrable Hamiltonian. We examine how the initial state delocalizes as it gets closer to the middle of the spectrum of $\hat{H}_F$, causing the observables to approach thermal averages, be the models integrable or chaotic. Our numerical studies are based on initial states with energies that cover the entire lower half of the spectrum of one-dimensional Heisenberg spin-1/2 systems.