Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement

We study the entanglement dynamics of quantum many-body systems and prove the following: (I) For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy is bounded away from the maximum entropy at all times with high probability. (II) In a spin-glass model with random all-to-all interactions, starting from any product state the average entanglement entropy is bounded away from the maximum entropy at all times. 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, for the latter is nearly maximal.

Automated summary

The study reveals that for any geometrically local Hamiltonian on a lattice, the entanglement entropy is likely to be bounded away from the maximum entropy at all times with a random product state. In a spin-glass model with random all-to-all interactions, regardless of the initial state, the average entanglement entropy remains bounded away from the maximum entropy at all times. These findings highlight the difference in entanglement generation between (chaotic) Hamiltonian dynamics and random states, as the latter approaches maximum.