标题： 局部杂化量子动力学中的多区域纠缠 显示英文标题

标题： Multi-Region Entanglement in Locally Scrambled Quantum Dynamics

摘要： 我们研究了多区域双部分纠缠熵在局部混杂量子动力学下的演化。 我们表明，多区域纠缠可以显著修改单区域纠缠的增长，这种影响在现有文献中被很大程度地忽略了。 我们开发了一个新的理论框架，称为纠缠特征形式，以系统地组织所有多区域纠缠作为无符号的多体状态。 我们进一步提出了一种两参数矩阵乘积态（MPS）假设，以高效地捕捉指数级多区域纠缠特征。 使用这些工具，我们能够联合研究多区域纠缠动力学，并在MPS参数空间中表示演化过程。 通过比较纠缠切口运动的动力学约束，我们能够在统一的纠缠特征哈密顿量中识别不同的量子动力学模型。 根据量子动力学模型，我们发现多区域效应可以主导单区域纠缠的增长，并且仅在Haar随机电路中消失。 我们基于纠缠特征哈密顿量计算了算符平均的非时序相关函数，并从结果中提取了蝴蝶速度。 我们证明了之前关于纠缠速度和蝴蝶速度之间的猜想界限即使在多区域纠缠的影响下仍然成立。 这些进展可能使更高效的数值模拟和对量子多体系统中多区域纠缠动力学更系统的理论理解成为可能。 显示英文摘要

摘要： We study the evolution of multi-region bipartite entanglement entropy under locally scrambled quantum dynamics. We show that the multi-region entanglement can significantly modify the growth of single-region entanglement, whose effect has been largely overlooked in the existing literature. We developed a novel theoretical framework, called the entanglement feature formalism, to organize all the multi-region entanglement systematically as a sign-free many-body state. We further propose a two-parameter matrix product state (MPS) ansatz to efficiently capture the exponentially many multi-region entanglement features. Using these tools, we are able to study the multi-region entanglement dynamics jointly and represent the evolution in the MPS parameter space. By comparing the dynamical constraints on the motion of entanglement cuts, we are able to identify different quantum dynamics models in a unifying entanglement feature Hamiltonian. Depending on the quantum dynamics model, we find that multi-region effects can dominate the single region entanglement growth and only vanish for Haar random circuits. We calculate the operator-averaged out-of-time-order correlator based on the entanglement feature Hamiltonian and extract the butterfly velocity from the result. We show that the previously conjectured bound between the entanglement velocity and the butterfly velocity holds true even under the influence of multi-region entanglement. These developments could enable more efficient numerical simulations and more systematic theoretical understandings of the multi-region entanglement dynamics in quantum many-body systems.