Entanglement Dynamics from Random Product States at Long Times

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.

Automated summary

This study demonstrates that the entanglement entropy of randomly generated states in the long-time evolution of quantum many-body systems does not approach the Page curve, whether in geometrically local Hamiltonians or spin-glass models.