横场中具有周期性各向异性的一维XY模型的量子相变
发布时间：2019-06-12 07:20
【摘要】：通过解析和数值计算的方法研究了横场中具有周期性各向异性的一维XY自旋模型的量子相变和量子纠缠.主要讨论了周期为二的情况,即各向异性参数交替地取比值为α的两个值.结果表明,与横场中均匀XY模型相比,α=-1所对应的模型在参数空间的相图存在着明显的不同.原来的Ising相变仍然存在,没有了沿x和y方向的各向异性铁磁(FM_x,FM_y)相,即各向异性相变消失,出现了一个新的相,并且该相内沿x和y方向的长程关联函数相等且大于零,我们称新相为各向同性铁磁(FM_(xx))相.这是由于系统新的对称性所导致的.解析结果还说明系统在FM_(xx)相中的单粒子能谱有两个零点,是一个无能隙的相.最后,利用冯·诺依曼熵数值地研究了系统在新相内各点的量子纠缠,发现该相内每一点的冯·诺依曼熵的标度行为与均匀XY模型在各向异性相变处的相似,即S_L～1/33襙2L+Const.
[Abstract]:The quantum phase transition and quantum entanglement of one-dimensional XY spin model with periodic anisotropy in transverse field are studied by analytical and numerical methods. In this paper, we mainly discuss the case where the period is two, that is, the anisotropy parameter alternately takes two values of the ratio 伪. The results show that the phase diagram of the model corresponding to 伪 =-1 is obviously different from that of the uniform XY model in the transverse field. The original Ising phase transition still exists, without the anisotropy ferromagnetic (FM_x,FM_y) phase along the x and y directions, that is, the anisotropy phase transition disappears and a new phase appears, and the long-range correlation function along the x and y directions in the phase is equal and greater than zero. We call the new phase isotropic ferromagnetic (FM_ (xx) phase). This is caused by the new symmetry of the system. The analytical results also show that the single particle energy spectrum of the system in FM_ (xx) phase has two zeros, which is a phase with incompetent gap. Finally, the quantum entanglement of the system at each point in the new phase is studied by using von Neiman entropy. It is found that the scaling behavior of the von Neiman entropy of each point in the phase is similar to that of the uniform XY model at the anisotropy phase transition, that is, S_L~1/33 鈮，
本文编号：2497841
[Abstract]:The quantum phase transition and quantum entanglement of one-dimensional XY spin model with periodic anisotropy in transverse field are studied by analytical and numerical methods. In this paper, we mainly discuss the case where the period is two, that is, the anisotropy parameter alternately takes two values of the ratio 伪. The results show that the phase diagram of the model corresponding to 伪 =-1 is obviously different from that of the uniform XY model in the transverse field. The original Ising phase transition still exists, without the anisotropy ferromagnetic (FM_x,FM_y) phase along the x and y directions, that is, the anisotropy phase transition disappears and a new phase appears, and the long-range correlation function along the x and y directions in the phase is equal and greater than zero. We call the new phase isotropic ferromagnetic (FM_ (xx) phase). This is caused by the new symmetry of the system. The analytical results also show that the single particle energy spectrum of the system in FM_ (xx) phase has two zeros, which is a phase with incompetent gap. Finally, the quantum entanglement of the system at each point in the new phase is studied by using von Neiman entropy. It is found that the scaling behavior of the von Neiman entropy of each point in the phase is similar to that of the uniform XY model at the anisotropy phase transition, that is, S_L~1/33 鈮，
本文编号：2497841
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