Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles

TL;DR

This paper investigates why mid-spectrum eigenstates in chaotic many-body systems deviate from random state predictions, revealing that spatial correlations and orthogonality to edge states cause systematic entanglement entropy deviations.

Contribution

It identifies specific structural reasons, such as spatial correlations and orthogonality effects, that cause deviations from randomness in mid-spectrum eigenstates.

Findings

Mid-spectrum eigenstates show systematic deviations from random state entanglement entropy.

Spatial correlations contribute to non-random entanglement features.

Orthogonality to edge states imposes structure on mid-spectrum eigenstates.

Abstract

Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization hypothesis and volume-law scaling of entanglement. We point out that systematic departures from complete randomness are generically present in mid-spectrum eigenstates, and focus on the departure of the entanglement entropy from the random-state prediction. We show that the departure is (partly) due to spatial correlations and due to orthogonality to the eigenstates at the spectral edge, which imposes structure on the mid-spectrum eigenstates.