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

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 midspectrum eigenstates, and focus on the departure of the entanglement entropy from the randomstate 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 midspectrum eigenstates.

Automated summary

Eigenstates of local many-body interacting systems far from spectral edges are believed to be ergodic and close to randomness, aligning with the eigenstate thermalization hypothesis and entanglement volume-law scaling. However, systematic departures from complete randomness are typically present in mid-spectrum eigenstates, partly due to spatial correlations and orthogonality to eigenstates at the spectral edge, which introduce structure to these mid-spectrum states.