Scaling of geometric phases close to the quantum phase transition in the XY spin chain
Scaling of geometric phases close to the quantum phase transition in the XY spin chain
复制标题
DOI：
10.1103/physrevlett.96.077206
复制
发表时间：
2006-02-24
影响因子：
8.6
通讯作者：
Zhu, SL
中科院分区：
文献类型：
--
作者：
Zhu, SL
我们证明了XY模型中基态的几何相位在量子相变附近服从标度行为。特别是，我们发现，几何相位是非解析的和它的导数相对于磁场强度发散的临界磁场。进一步验证了几何相临界性质在模型族中的普遍性。此外，由于量子相变发生在能级交叉或避免的能级交叉处，并且这些能级结构可以被Berry曲率捕获，因此几何相变和量子相变之间建立的关系不是XY模型的特定性质，而是多体系统的非常普遍的结果。
We show that the geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that the geometric phase is nonanalytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, the universality in the critical properties of the geometric phase in a family of models is verified. In addition, since the quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by the Berry curvature, the established relation between the geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.