We introduce a diagnostic for quantum thermalization based on mixed-state entanglement. Specifically, given a pure state on a tripartite system $ABC$, we study the scaling of entanglement negativity between $A$ and $B$. For representative states of self-thermalizing systems, either eigenstates or states obtained by a long-time evolution of product states, negativity shows a sharp transition from an area-law scaling to a volume-law scaling when the subsystem volume fraction is tuned across a finite critical value. In contrast, for a system with quasiparticles, it exhibits a volume-law scaling irrespective of the subsystem fraction. For many-body localized systems, the same quantity shows an area-law scaling for eigenstates, and volume-law scaling for long-time-evolved product states, irrespective of the subsystem fraction. We provide a combination of numerical observations and analytical arguments in support of our conjecture. Along the way, we prove and utilize a “continuity bound” for negativity: we bound the difference in negativity for two density matrices in terms of the Hilbert-Schmidt norm of their difference.

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纠缠跃迁作为准粒子和量子热化的探针

我们介绍基于混合态纠缠的量子热化诊断。具体来说，给定三方系统上的纯状态$\mathrm{一种}乙C$，我们研究了纠缠负性之间的定标 $\mathrm{一种}$ 和 $乙$。对于自热系统的代表性状态，无论是本征状态还是通过产品状态的长期演化而获得的状态，当子系统体积分数在一个范围内调整时，负性显示出从面积定律到体积定律的急剧转变。有限临界值。相反，对于具有准粒子的系统，无论子系统分数如何，都表现出体积律定标。对于多体本地化系统，无论子系统分数如何，相同的数量都会显示本征态的面积定律缩放比例，以及长期演化的产品状态的体积定律缩放比例。我们将数值观察和分析论证相结合，以支持我们的猜想。在这一过程中，我们证明并利用“连续性界限”来实现负性：