量子重整化群方法中各种关联测度的性能：一个量子相变的例子研究
Performance of various correlation measures in quantum renormalization-group method: A case study of quantum phase transition
摘要：
我们利用量子重整化群（QRG）方法研究了量子相变，而在以前的大多数文献中几乎没有纠缠（并发）被证明。然而，现在众所周知，纠缠不是量子关联的唯一特征，并且已经开发了各种可计算的措施来表征复合系统中的量子关联。作为例子，详细阐述了两种情况：一维各向异性（i）XXZ模型和（ii）XY模型，以及各种量子关联度量，包括量子不协调（QD）、几何不协调（GD）、测量诱导扰动（MID）、测量诱导非定域性（MIN）和违反贝尔不等式（例如：量子不协调）。CHSH不等式）。我们证明了在两种情况下，经过几次重正化迭代后，所有这些关联测度都能有效地检测到与量子相变（QPT）相关的量子临界点。尽管如此，研究表明它们的某些动力学行为与纠缠并不完全相似，即使当纠缠度为零时，仍然存在某种量子关联，而这种关联并不被纠缠捕获。有趣的是，在整个迭代过程中，CHSH不等式永远不会被打破，这表明CHSH不等式不能揭示块-块纠缠。此外，还详细讨论了Bell破坏的非解析行为和标度行为。作为副产品，我们验证了测量引起的扰动正好等于一般X结构态的量子不协调。
英文摘要：
We have investigated quantum phase transition employing the quantum renormalization group (QRG) method while in most previous literature barely entanglement (concurrence) has been demonstrated. However, it is now well known that entanglement is not the only signature of quantum correlations and a variety of computable measures have been developed to characterize quantum correlations in the composite systems. As an illustration, two cases are elaborated: one dimensional anisotropic (i) XXZ model and (ii) XY model, with various measures of quantum correlations, including quantum discord (QD), geometric discord (GD), measure-induced disturbance (MID), measure-induced nonlocality (MIN) and violation of Bell inequalities (eg. CHSH inequality). We have proved that all these correlation measures can effectively detect the quantum critical points associated with quantum phase transitions (QPT) after several iterations of the renormalization in both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar with entanglement and even when concurrence vanishes there still exists some kind of quantum correlations which is not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iteration procedure, which indicates block-block entanglement can not revealed by the CHSH inequality. Moreover, the nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a byproduct, we verify that measure-induced disturbance is exactly equal to the quantum discord measured by σ_z for general X-structured states.
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