Abstract
We study the entanglement dynamics of quantum many-body systems at long times and prove the following: (I) For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy almost never approaches the Page curve. (II) In a spin-glass model with random all-to-all interactions, starting from any product state the average entanglement entropy does not approach the Page curve. We also extend these results to any unitary evolution with charge conservation and to the Sachdev-Ye-Kitaev model. Our results highlight the difference between the entanglement generated by (chaotic) Hamiltonian dynamics and that of random states.
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