[论文解读] Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law

Thomas Botzung, Sebastian Diehl+1 more|arXiv (Cornell University)|Jan 1, 2021

Neural Networks and Reservoir Computing被引用 1

一句话总结

本文研究了在工程化退相干作用下，量子自旋链中由耗散稳定化的纠缠演化与单位幺正动力学竞争所引发的纠缠相变。随着单位幺与耗散作用比例的增加，系统表现出从对数增长纠缠到面积律的相变，该相变可通过单个量子轨迹中的状态依赖可观测量及纠缠熵分布检测到，但在平均化的 Lindblad 动力学中则不存在。

ABSTRACT

Recent theoretical work has shown that the competition between coherent unitary dynamics and stochastic measurements, performed by the environment, along wavefunction trajectories can give rise to transitions in the entanglement scaling. In this work, complementary to these previous studies, we analyze a situation where the role of Hamiltonian and dissipative dynamics is reversed. We consider an engineered dissipation, which stabilizes an entangled phase of a quantum spin$-1/2$ chain, while competing single-particle or interacting Hamiltonian dynamics induce a disentangled phase. Focusing on the single-particle unitary dynamics, we find that the system undergoes an entanglement transition from a logarithmic growth to an area law when the competition ratio between the unitary evolution and the non-unitary dynamics increases. We evidence that the transition manifests itself in state-dependent observables at a finite competition ratio for Hamiltonian and measurement dynamics. On the other hand, it is absent in trajectory-averaged steady-state dynamics, governed by a Lindblad master equation: although purely dissipative dynamics stabilizes an entangled state, for any non-vanishing Hamiltonian contribution the system ends up irremediably in a disordered phase. In addition, a single trajectory analysis reveals that the distribution of the entanglement entropy constitutes an efficient indicator of the transition. Complementarily, we explore the competition of the dissipation with coherent dynamics generated by an interacting Hamiltonian, and demonstrate that the entanglement transition also occurs in this second model. Our results suggest that this type of transition takes place for a broader class of Hamiltonians, underlining its robustness in monitored open quantum many-body systems.

研究动机与目标

• 研究工程化退相干在量子自旋链中诱导纠缠相变的作用。
• 探索非幺正耗散动力学与相干单位幺演化在驱动纠缠标度中的竞争机制。
• 确定当哈密顿量被相互作用动力学取代时，纠缠相变是否仍然存在。
• 对比基于轨迹的动力学与系综平均的 Lindblad 主方程行为。
• 识别相变的稳健指标，如纠缠熵分布与状态依赖可观测量。

提出的方法

• 分析在工程化退相干与单位幺演化作用下的自旋-1/2链的量子轨迹（QTs）。
• 采用单粒子与相互作用哈密顿量来驱动退相干，与耗散稳定化作用竞争。
• 利用状态依赖可观测量在有限竞争比下检测相变。
• 通过单条轨迹分析研究纠缠熵分布作为相变指标。
• 将单条量子轨迹的结果与由 Lindblad 主方程推导的稳态行为进行比较。
• 应用数值与解析方法研究受监测开放量子多体系统中的纠缠标度与相变。

实验结果

研究问题

• RQ1 当工程化退相干与单位幺动力学在自旋链中竞争时，是否诱导了从对数律到面积律的纠缠标度相变？
• RQ2 此类相变是否可在单条量子轨迹中检测到，且在轨迹平均的 Lindblad 描述中是否不存在？
• RQ3 该相变在不同轨迹中纠缠熵的分布中如何表现？
• RQ4 当单位幺动力学被相互作用哈密顿量取代时，相变是否仍然存在？
• RQ5 相变的关键指标是什么，它们在轨迹特异性与系综平均可观测量之间有何差异？

主要发现

• 随着单位幺与耗散动力学比例的增加，系统表现出从对数纠缠增长到面积律的相变。
• 在有限竞争比下，通过单条量子轨迹中的状态依赖可观测量可检测到该相变。
• 在由 Lindblad 主方程控制的轨迹平均稳态中，该相变不存在，其中任何非零哈密顿量项均会使系统驱动至无序相。
• 轨迹间纠缠熵的分布是相变的高效指标。
• 当单位幺动力学被相互作用哈密顿量取代时，纠缠相变依然存在，表明其在不同哈密顿量类中具有广泛鲁棒性。
• 结果表明，此类相变在受监测的开放量子多体系统中具有普遍性，不局限于特定哈密顿量形式。