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 midspectrum 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 midspectrum eigenstates.
Highlights
Ergodicity and equilibration in the quantum realm remain imperfectly understood, and the characterization of quantum ergodicity is an active research front
One view is that quantum ergodicity corresponds to eigenstates of manybody systems being effectively random
We present a study of this discrepancy, uncovering the ways in which midspectrum eigenstates deviate from random states
Summary
Ergodicity and equilibration in the quantum realm remain imperfectly understood, and the characterization of quantum ergodicity is an active research front. We focus on spin-1/2 chains with L sites with all symmetries broken, so that the Hilbert space is D = 2L, and consider the entanglement between two subsystems (A, B) of equal size In this case, the random states have an average EE wellapproximated by the Page formula [38,39], SPage = log DA −. The departure from the Page value for comb partitions is due to a correlated Hilbert space blockade, such that certain types of configurations in the Hilbert space are blocked from appearing in the midspectrum eigenstates. The departure from the Page value falls off much more slowly, possibly even saturating
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