局域扰动量子动力学中的多区纠缠
Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
摘要：
我们研究了多区域两体纠缠熵在局域混沌量子动力学下的演化。我们发现，多区纠缠可以显着修改的单区纠缠的增长，其效果在很大程度上被忽略了在现有的文献。我们发展了一个新的理论框架，称为纠缠特征形式主义，将所有的多区域纠缠系统地组织为一个无符号的多体态。我们进一步提出了一种双参数矩阵乘积态（MPS）方法来有效地捕获指数级多区域纠缠特征。利用这些工具，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。通过比较纠缠切割运动的动力学约束，我们能够在一个统一的纠缠特征哈密顿量中识别不同的量子动力学模型。在量子动力学模型的基础上，我们发现多区效应可以主导单区纠缠的增长，并且只有在Haar随机电路中多区效应才消失。我们利用纠缠特征哈密顿量计算了算符平均的无序相关器，并从结果中提取了蝴蝶速度。我们发现，以前的纠缠速度和蝴蝶速度之间的束缚仍然成立，即使在多区纠缠的影响。这些发展可以使更有效的数值模拟和更系统的理论理解量子多体系统中的多区域纠缠动力学。
英文摘要：
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.
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