横场中非束缚类准周期伊辛链的赝临界点

Quantum pseudocritical point in the unbounded quasiperiodic transverse field Ising chain

本文系统地研究了有限尺寸下非束缚类准周期量子伊辛链在横场中的赝临界点的行为.首先,通过计算平均磁矩和协作参量,发现这两个量的导数随着横场的变化都会出现两个清晰的峰.这与束缚类伊辛链和无序伊辛链的结果明显不同.其次,研究了横场中赝临界点的概率分布情况,发现概率分布并不是高斯型的.这也与无序的结果不同.最后,分析了赝临界点产生的原因,发现赝临界点是由非束缚类准周期伊辛链中的集团结构造成的.

We study the quantum pseudocritical points in the unbounded quasiperiodic transverse field Ising chain of finite-size systematically. Firstly, we study the derivatives of averaged magnetic moment and the averaged concurrence with transverse fields. Both of them show two visible peaks, with are nearly not raised when the length of chain is increased. Moreover, the places where the peaks occur in the transverse field are obviously different from that of the quantum phase transition point in the thermodynamic limit. These results are very different from those of the bounded quasiperiodic transverse field Ising chain and the disordered transverse field Ising chain. Then, we analyze the origin of the two visible peaks. For that we study the derivative of magnetic moment for each spin with transverse field. For all spins, the single magnetic moment only show one peak. However, the places where the peaks occur are not random. The peaks always occur in two regions. Thus, the derivatives of averaged magnetic moment reveal two peaks. Furthermore, we study the probability distribution of the pseudocritical points through finding out the peaks of the single magnetic moment in 1000 samples. The distribution is not Guassian. This result is obviously different from that of the disordered case. Besides, the pseudocritical points nearly do not occur at the quantum phase transition point. Finally, we analyze the origin of the pseudocritical points. For that we study the relationship between the spin places and the corresponding places of pseudocritical points. It is found that the pseudocritical points are caused by the two groups that exist in the nearest neighboring interactions of the unbounded quasiperiodic structure. When a spin is in one group, this group will decide the probable place of the pseudocritical point. Through this study, we find that although the quantum phase transition behaviors of the unbounded quasiperiodic transverse field Ising chain and the disordered transverse field Ising chain belong to the same universal class in the thermodynamic limit, the thermodynamic behaviors of the two Ising chains are very different as in finite sizes. The differences are caused by the special structure in the unbounded quasiperiodic system.