Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains

TL;DR

This paper demonstrates that applying an optimal magnetic field in quantum spin chains induces persistent ballistic entanglement spreading, significantly enhancing entanglement entropy and maintaining linear growth until saturation, even under perturbations.

Contribution

It reveals that optimal control via magnetic fields can sustain ballistic entanglement spreading in quantum spin chains, a novel approach to controlling quantum many-body dynamics.

Findings

Persistent linear growth of entanglement entropy until saturation.

Robustness of ballistic spreading under random initial state perturbations.

Optimal control enhances and sustains entanglement propagation.

Abstract

Entanglement propagation provides a key routine to understand quantum many-body dynamics in and out of equilibrium. The entanglement entropy (EE) usually approaches to a sub-saturation known as the Page value $\tilde{S}_{P} =\tilde{S} - dS$ (with $\tilde{S}$ the maximum of EE and $dS$ the Page correction) in, e.g., the random unitary evolutions. The ballistic spreading of EE usually appears in the early time and will be deviated far before the Page value is reached. In this work, we uncover that the magnetic field that maximizes the EE robustly induces persistent ballistic spreading of entanglement in quantum spin chains. The linear growth of EE is demonstrated to persist till the maximal $\tilde{S}$ (along with a flat entanglement spectrum) is reached. The robustness of ballistic spreading and the enhancement of EE under such an optimal control are demonstrated, considering particularly perturbing the initial state by random pure states (RPS's). These are argued as the results from the endomorphism of the time evolution under such an entanglement-enhancing optimal control for the RPS's.