Zhu W, Huang Zhoushen, He Yin-Chen, Wen Xueda
Institute of Natural Science, Westlake Institute of Advanced Study and School of Science, Westlake University, Hangzhou 310024, China.
Argonne National Laboratory, Lemont, Illinois 60439, USA.
Phys Rev Lett. 2020 Mar 13;124(10):100605. doi: 10.1103/PhysRevLett.124.100605.
A powerful perspective in understanding nonequilibrium quantum dynamics is through the time evolution of its entanglement content. Yet apart from a few guiding principles for the entanglement entropy, to date, much less is known about the refined characteristics of entanglement propagation. Here, we unveil signatures of the entanglement evolving and information propagating out of equilibrium, from the view of the entanglement Hamiltonian. We investigate quantum quench dynamics of prototypical Bose-Hubbard model using state-of-the-art numerical technique combined with conformal field theory. Before reaching equilibrium, it is found that a current operator emerges in the entanglement Hamiltonian, implying that entanglement spreading is carried by particle flow. In the long-time limit the subsystem enters a steady phase, evidenced by the dynamic convergence of the entanglement Hamiltonian to the expectation of a thermal ensemble. Importantly, the entanglement temperature in steady state is spatially independent, which provides an intuitive trait of equilibrium. These findings not only provide crucial information on how equilibrium statistical mechanics emerges in many-body dynamics, but also add a tool to exploring quantum dynamics from the perspective of the entanglement Hamiltonian.
理解非平衡量子动力学的一个有力视角是通过其纠缠内容的时间演化。然而，除了关于纠缠熵的一些指导原则外，迄今为止，对于纠缠传播的精细特征知之甚少。在这里，我们从纠缠哈密顿量的角度揭示了纠缠演化和信息在非平衡态下传播的特征。我们使用最先进的数值技术结合共形场论来研究典型的玻色 - 哈伯德模型的量子猝灭动力学。在达到平衡之前，发现在纠缠哈密顿量中出现了一个流算符，这意味着纠缠的传播是由粒子流携带的。在长时间极限下，子系统进入一个稳定阶段，这由纠缠哈密顿量向热系综期望值的动态收敛所证明。重要的是，稳态下的纠缠温度在空间上是独立的，这提供了平衡的一个直观特征。这些发现不仅提供了关于平衡统计力学如何在多体动力学中出现的关键信息，而且还增加了一种从纠缠哈密顿量的角度探索量子动力学的工具。
