论文标题
隔离量子系统的热化中的纠缠传播
Entanglement propagation in thermalization of an isolated quantum system
论文作者
论文摘要
我们研究孤立量子多体系统的热化过程中的纠缠动力学。我们提出了一个简单的设置，用于测量数值模拟中纠缠熵（EE）的传播速度，并将其应用于1D中的可集成/非集成旋转模型 - 横向ISISING（TI）模型，Chaotic Ising（CI）模型（CI）模型，以及扩展的Chaotic Ising（ECI）模型。我们发现，在热化过程中，EE的动力学出现了两个不同的时间尺度$ t^\ ast $和$ t _ {\ rm {diff}} $：前者代表EE饱和的时间尺度，而后者则表征了EE在整个系统中的传播表征。从$ t _ {\ rm diff} $中评估纠缠的传播速度，我们发现纠缠以恒定速度传播，无论模型的集成性如何。发现纠缠的传播速度与Ti模型中准粒子激发的最大基团速度相吻合。我们还通过相互信息评估了纠缠的传播速度，并找到特征的时间尺度$ t _ {\ mathrm {mi}} $。我们表明，由$ t _ {\ mathrm {mi}} $和$ t _ {\ rm {diff}} $评估的纠缠速度符合。我们根据数值结果讨论了热化的条件，并提出在EE饱和以进行热化之前，整个系统的争夺必须发生。
We study dynamics of entanglement in the thermalization process of an isolated quantum many-body system. We propose a simple setup for measuring the propagation speed of entanglement entropy (EE) in numerical simulations and apply it to the integrable/non-integrable spin models in 1D - the transverse Ising (TI) model, the chaotic Ising (CI) model, and the extended chaotic Ising (ECI) model. We find that two distinct time-scales $t^\ast$ and $t_{\rm {diff}}$ arise in the dynamics of EE in the thermalization process: the former represents the time-scale for the saturation of EE and the latter characterizes spreading of EE over the entire system. Evaluating the propagation speed of entanglement from $t_{\rm diff}$, we find that entanglement propagates ballistically with a constant velocity irrespective of the integrability of the model. The propagation speed of entanglement is found to coincide with the maximum group velocity of quasi-particle excitations in the TI model. We also evaluate the propagation speed of entanglement by mutual information and find the characteristic time-scale $t_{\mathrm{MI}}$. We show that the propagation speeds of entanglement evaluated by $t_{\mathrm{MI}}$ and $t_{\rm {diff}}$ agree well. We discuss the condition for thermalization based on the numerical results and propose that scrambling of the entire system has to take place before saturation of EE for thermalization.
