XY模型几何量子关联临界行为与路径关系研究

Study on Relationship between the Critical Behavior and Path of Geometric Measure of Quantum Discord in XY Model

分别在三临界点和Ising临界点附近研究了外磁场中XY模型基态几何量子关联(GMQD)的临界行为。结果表明,GMQD在三临界点附近的行为和趋于该点的路径参数α有关。当α<2时,GMQD及其一阶导数在三临界点附近呈现振荡行为;当α2时,振荡行为消失,GMQD的一阶导数在三临界点附近只出现一个极大值。这说明GMQD不能准确表征系统的多临界点,它所表征的是系统的准临界点。在Ising临界点,不论路径参数α取什么值,GMQD及其一阶导数出现极值,且可以准确地表征该临界点。研究结果对利用几何量子关联刻画量子相变现象提供一定的理论参考。

We investigate the geometric measure of quantum discord（GMQD） of the ground state in a one-dimensional transverse XY spin chain in the vicinity of quantum critical points. The critical behavior are investigated both at the multi and Ising critical points. Our results show that the behavior of GMQD at muti-critical point has close relation with the paths that approaching the point.For [α〈2], the GMQD and its first derivation show oscillation behavior. For [α≥2], the first derivation of GMQD appears a solo maximal value. This indicates that the GMQD can＇t describe exactly the muti-critical point of the XY model. However, the critical behavior of GMQD at the Ising point has no relation with the path which describe exactly the critical point. Our results can provide reference to the investigation of relationships between GMQD and quantum phase transitions.