发表机构
University of Strasbourg; CNRS, CESQ and ISIS (UMR 7006)（斯特拉斯堡大学; 法国国家科学研究中心，CESQ与ISIS（联合研究单位7006））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明随机自由费米子模型中局部算子和演化算子的算子空间纠缠熵按 $O(\sqrt{t})$ 增长，并通过映射到排斥过程解析计算，同时探讨了其他随机类型下的不同增长行为。
AI 中文摘要
我们研究了一维数守恒自由费米子在随机空间和时间依赖演化下的算子空间纠缠熵（OSEE）的时间演化。已知在没有随机性的自由费米子系统中，\\(\emph{局部}\\) 算子的 OSEE 随时间至多 \\(\emph{对数}\\) 增长。这里我们表明，在存在随机性的情况下，涉及 Jordan-Wigner 弦的局部自旋算子的 OSEE 对所有 Rényi 指数值均按 $\mathcal O(\sqrt t)$ 增长。我们在两个模型中确立了这一点：布朗哈密顿量和砖墙匹配门电路。我们还考虑了演化算子的 OSEE，并表明它也按 $\mathcal O(\sqrt{t})$ 增长，这与没有随机性时通常预期的线性增长形成对比。我们通过将量子模型映射到对称简单排斥过程，依赖自平均假设（我们通过数值支持该假设）解析计算了两个算子的平均熵。我们还考虑了另外两种随机性：保持空间平移不变性的时间随机演化，以及淬火无序。在前一种情况下，我们发现 OSEE 也按 $\sqrt{t}$ 增长。在后一种情况下，我们发现对于哈密顿量演化，无论是带有 Jordan-Wigner 弦的局部算子还是演化算子，熵均按 $\mathcal O( \log \log t)$ 增长，而在砖墙匹配门电路中，熵在所有时刻保持有界。
英文摘要
We study the time evolution of the Operator Space Entanglement Entropy (OSEE) of one-dimensional number-conserving free fermions subject to a random space- and time-dependent evolution. It is known that, in free-fermion systems without randomness, the OSEE of \emph{local} operators grows at most \emph{logarithmically} in time. Here we show that, in the presence of randomness, the OSEE of local spin operators involving a Jordan-Wigner string grows as $\mathcal O(\sqrt t)$, for all values of the Rényi index. We establish this in two models: a Brownian Hamiltonian and a brick-wall matchgate circuit. We also consider the OSEE of the evolution operator, and we show that it also grows as $\mathcal O(\sqrt{t})$, in contrast with the linear growth generically expected without randomness. We analytically compute the average entropies of the two operators by mapping the quantum models to the symmetric simple exclusion process, relying on an assumption of self-averaging which we support numerically. We also consider two other types of randomness: random evolution in time that keeps spatial translation invariance, and quenched disorder. In the former case, we find that the OSEE also grows as $\sqrt{t}$. In the latter case, we find that the entropy grows as $\mathcal O( \log \log t)$ for Hamiltonian evolution both for local operators with a Jordan-Wigner string and for the evolution operator, whereas it remains bounded at all times in the brick-wall matchgate circuit.
