二维3态Potts量子系统的保真度与序参量

Ground-state fidelity and order parameter for quantum 3-state Potts model in 2- D

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态(i PEPS)算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于i PEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.

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 some bifurcations in the fidelity was discussed, for quantum 3-state Potts model on an infi-nite-size square lattice in 2-D.In this case, the model is known to undergo a first-order quantum phase transi-tion at the critical field.In addition, the universal order parameter and a local order parameter were constructed for quantum 3-state Potts model.The finding is applicable to any systems with symmetry breaking order, as a result of the fact that, a quantum system undergoing a phase transition is characterized in terms of spontaneous symmetry breaking captured by the universal order parameter and a local order parameter.