Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains
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Entanglement propagation provides a key routine to understand quantum many-body dynamics in and out of equilibrium. In this work, we uncover that the “variational entanglement-enhancing” field (VEEF) robustly induces a persistent ballistic spreading of entanglement in quantum spin chains. The VEEF is time dependent, and is optimally controlled to maximize the bipartite entanglement entropy (EE) of the final state. Such a linear growth persists till the EE reaches the genuine saturation S̃ = - log_2 2^-N/2=N/2 with N the total number of spins. The EE satisfies S(t) = v t for the time t ≤N/2v, with v the velocity. These results are in sharp contrast with the behaviors without VEEF, where the EE generally approaches a sub-saturation known as the Page value S̃_P =S̃ - 1/2ln2 in the long-time limit, and the entanglement growth deviates from being linear before the Page value is reached. The dependence between the velocity and interactions is explored, with v ≃ 2.76, 4.98, and 5.75 for the spin chains with Ising, XY, and Heisenberg interactions, respectively. We further show that the nonlinear growth of EE emerges with the presence of long-range interactions.
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