{
  "id": "2307.11609",
  "version": "v1",
  "published": "2023-07-21T14:25:22.000Z",
  "updated": "2023-07-21T14:25:22.000Z",
  "title": "Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains",
  "authors": [
    "Ying Lu",
    "Pei Shi",
    "Xiao-Han Wang",
    "Jie Hu",
    "Shi-Ju Ran"
  ],
  "comment": "5 pages, 4 figures",
  "categories": [
    "quant-ph",
    "cond-mat.str-el",
    "cs.LG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-21T14:25:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum spin chains",
      "persistent ballistic entanglement spreading",
      "optimal control",
      "understand quantum many-body dynamics",
      "page value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}