The past two decades have witnessed a surge of interest in borrowing tools from quantum information theory to investigate quantum phase transitions (QPTs). The best-known examples are entanglement measures whose nonanalyticities at critical points were tied to QPTs in a plethora of physical models. Here, focusing on the $XXZ$ model, we show how QPTs can be revealed through the quantum steering ellipsoid (QSE), which is a geometric tool capable of characterizing both the strength and type of quantum correlations between two subsystems of a compound system. We find that the QSE associated with the $XXZ$ model changes in shape with the QPTs; that is, it is a needle in the ferromagnetic phase, an oblate spheroid in the gapless phase, and a prolate spheroid in the antiferromagnetic phase. This finding offers an example demonstrating the intriguing possibility of unveiling QPTs in a geometrically visible fashion. Some connections between our results and previous ones are discussed.

中文翻译：

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通过量子转向椭球可视化 XXZ 模型中的量子相变

在过去的二十年里，人们对借用量子信息理论的工具来研究量子相变 (QPT) 的兴趣激增。最著名的例子是纠缠度量，其关键点的非分析性与大量物理模型中的 QPT 相关。在这里，重点$XXZ$在模型中，我们展示了如何通过量子转向椭球 (QSE) 揭示 QPT，这是一种几何工具，能够表征复合系统的两个子系统之间的量子相关性的强度和类型。我们发现 QSE 与$XXZ$模型随 QPT 的形状变化；即铁磁相为针状，无间隙相为扁球体，反铁磁相为扁长球体。这一发现提供了一个例子，展示了以几何可见的方式揭示 QPT 的有趣可能性。讨论了我们的结果与以前的结果之间的一些联系。