论文标题
纠缠过渡作为准粒子和量子热化的探针
Entanglement transitions as a probe of quasiparticles and quantum thermalization
论文作者
论文摘要
我们引入了基于混合态纠缠的量子热化诊断。具体而言，鉴于三方系统$ abc $的纯净状态，我们研究了纠缠负性在$ a $ a和$ b $之间的缩放。对于自热系统的代表性状态，无论是征量状态的征征或征收状态的状态，当在有限的临界值跨子系统体积分数调谐时，负态性表明从区域法缩放到体积法缩放的急剧过渡。相比之下，对于具有准颗粒的系统，它表现出量表的比例，而与子系统分数无关。对于多体局部系统，相同的数量显示了本征征的区域法缩放，以及长期进化产品状态的体积范围缩放，而与子系统分数无关。我们提供了数值观察和分析论证的结合，以支持我们的猜想。在此过程中，我们证明并利用了“连续性结合”的否定性：我们根据希尔伯特·史克米特（Hilbert-Schmidt）的差异来束缚两个密度矩阵的负面差异。
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.
