运用无限纠缠投影对态(iPEPS)表示的张量网络(TN)算法,任意选取初态对二维无限正方格子XYX量子模型进行数值模拟演化,从而得到两个不同的具有简并对称破缺的基态波函数。在二维XYX量子模型中,既可以运用普适序参量的性质,又可以运用约化密度矩阵保真度的分叉行为,来确定这个系统由自发对称性破缺引起的量子相变的临界点及量子相变的类型。即基于iPEPS算法,从普适序参量和约化密度矩阵保真度的角度,来刻画二维XYX量子多体系统的相变,其为典型的Ising普适类的二级相变。因而,运用iPEPS算法通过普适序参量和约化密度矩阵保真度,可以确定一个量子系统经历的量子相变,这为研究热力学极限下的强关联电子量子系统的量子相变和量子临界现象提供了一种更有效的强大的工具。

This mini review article aims to introduce how to characterize phase transitions in quantum many-body systems. By computing the ground-state wave function in the context of the tensor network algorithm based on the infinite projected entangled pair state representation (iPEPS), an intriguing connection between quantum phase transition and bifurcations in the reduced fidelity, universal order parameter were discussed, for quantum XYX model in an external magnetic field on an infinite-size square lattice in 2-D. In this case, XYX model is known to undergo a second-order quantum phase transition. The finding is applicable to any systems with symmetry breaking order.