Persistent Ballistic Entanglement Spreading with Optimal Control in
Quantum Spin Chains
- URL: http://arxiv.org/abs/2307.11609v1
- Date: Fri, 21 Jul 2023 14:25:22 GMT
- Title: Persistent Ballistic Entanglement Spreading with Optimal Control in
Quantum Spin Chains
- Authors: Ying Lu, Pei Shi, Xiao-Han Wang, Jie Hu, and Shi-Ju Ran
- Abstract summary: Entanglement propagation provides a key routine to understand quantum many-body dynamics in and out of equilibrium.
We uncover that the variational entanglement-enhancing'' field robustly induces a persistent ballistic spreading of entanglement in quantum spin chains.
The dependence between the velocity and interactions is explored, with $v simeq 2.76$, $4.98$, and $5.75$ for the spin chains with Ising, XY, and Heisenberg interactions, respectively.
- Score: 10.933006979719407
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 $\tilde{S} = - \log_{2}
2^{-\frac{N}{2}}=\frac{N}{2}$ with $N$ the total number of spins. The EE
satisfies $S(t) = v t$ for the time $t \leq \frac{N}{2v}$, 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
$\tilde{S}_{P} =\tilde{S} - \frac{1}{2\ln{2}}$ 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
$v \simeq 2.76$, $4.98$, 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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