发表机构
University of California, Berkeley; Lawrence Berkeley National Laboratory; Princeton University（加州大学伯克利分校; 劳伦斯伯克利国家实验室; 普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明强 SU(2) 对称吉布斯态中有限温度有序转变伴随纠缠转变，铁磁相纠缠增长快于顺磁相，并建立半经典理论及场论描述，经数值模拟验证。
AI 中文摘要
我们研究了具有强 SU(2) 对称性的吉布斯态中的混合态纠缠，重点关注具有铁磁相互作用的局域相互作用自旋系统。我们的主要结果是证明有限温度有序转变与纠缠转变相关联，因此强对称 Lindblad 算子的稳态可以表现出纠缠转变。虽然在顺磁相中，已知大系统两半之间的可蒸馏纠缠和对数纠缠负性随自旋数的平方根对数增长，但我们表明在铁磁相中这些量随系统尺寸以参数化更快的速度增长。为了得出这一结果，我们首先建立了这些混合态纠缠度量与在全局 SU(2) 对称变换下为单重态的状态中的自旋关联之间的关系。然后我们引入了 SU(2) 单重态热态的半经典理论。虽然全局单重态约束通常作为全半经典自旋构型的复杂函数进入该理论，但我们表明在大 S 极限下，它大幅简化为对无序相以及连续热相变附近有序相中总磁化的高斯抑制。这引导我们得到一个描述单重态扇区中自旋关联的场论。利用这一点，我们确定了低温和高温下混合态纠缠的各种探测器的行为，并使用我们半经典理论的三维晶格实现的数值蒙特卡洛模拟来支持我们的分析结果。我们还使用一维自旋-1/2系统中的精确数值计算来确认我们在顺磁相中关于混合态纠缠随关联长度和系统尺寸标度的预测。
英文摘要
We study mixed-state entanglement in Gibbs states with strong $\mathrm{SU}(2)$ symmetry, focusing on locally interacting spin systems with ferromagnetic interactions. Our main result is to show that finite-temperature ordering transitions are associated with entanglement transitions, and therefore the steady state of strongly symmetric Lindbladians can exhibit entanglement transitions. While in the paramagnetic phase it is known that the distillable entanglement and logarithmic entanglement negativity between two halves of a large system grow logarithmically with the square root of the number of spins, we show that in ferromagnetic phases these quantities grow parametrically faster with system size. To arrive at this result we first establish relations between these mixed-state entanglement measures and spin correlations in states that are singlets under global $\rm{SU}(2)$ symmetry transformations. We then introduce a semiclassical theory for $\rm{SU}(2)$ singlet thermal states. While the global singlet constraint generally enters this theory as a complicated function of the full semiclassical spin configuration, we show that in large $S$ limit it simplifies drastically to a Gaussian suppression of total magnetization in disordered phases as well as in ordered phases in the vicinity of continuous thermal phase transitions. This leads us to a field theory describing spin correlations in the singlet sector. Using this we determine the behavior of various probes of mixed-state entanglement at low and at high temperatures, supporting our analytical results using numerical Monte Carlo simulations of a three-dimensional lattice realization of our semiclassical theory. We also use exact numerics in one-dimensional spin-$1/2$ systems to confirm our predictions for the scaling of mixed-state entanglement with correlation length and system size in the paramagnetic phase.
Comments24 pages, 8 figures
