We introduce a method which based on Bell inequalities, to study quantum phase transitions. By using the non-linear programming, we compare two different kinds of Bell inequalities, the original Bell inequality and Clauser-Horne-Shimony-Holt (CHSH) inequality. And we find that the original Bell inequality is more accurate in detecting the Bell non-locality. By defining the maximal violation of Bell inequalities, we calculate two kinds of transitions, the one is magnetic transition in the spin-\(\frac {1}{2}\) XX model and the other is topological transition in the Kitaev honeycomb model. The critical points are detected successfully. Compared with traditional methods, our method requires no prior knowledge of order parameters and it is base-free.

我们介绍一种基于贝尔不等式的方法，以研究量子相变。通过使用非线性编程，我们比较了两种不同的Bell不等式，即原始Bell不等式和Clauser-Horne-Shimony-Holt（CHSH）不等式。并且我们发现原始的Bell不等式在检测Bell非局部性方面更为准确。通过定义最大的Bell不等式违反，我们计算出两种转变，一种是自旋XX模型中的磁跃迁\（\ frac {1} {2} \），另一种是Kitaev蜂窝模型中的拓扑转变。关键点已成功检测到。与传统方法相比，我们的方法不需要先验订单参数知识，而且不需要任何基础知识。