Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement

TL;DR

This paper investigates how entanglement evolves in quantum many-body systems, showing that starting from product states, entanglement remains significantly below maximal levels across various models and conditions.

Contribution

It proves that in local Hamiltonian and spin-glass models, entanglement from product states does not reach maximum, contrasting with the entanglement of random states, and extends results to charge-conserving and SYK models.

Findings

Entanglement remains bounded away from maximum in local Hamiltonian systems.

In spin-glass models, average entanglement does not reach maximum.

Results extend to charge-conserving and Sachdev-Ye-Kitaev models.

Abstract

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.