Critical behavior of geometric measure of quantum discord when approaching the critical points via different paths

摘要

We investigate the critical behavior of geometric measure of quantum discord (GMQD) in a one-dimensional transverse XY spin chain. The critical and the scaling behavior of the ground state GMQD are investigated both at the multi-critical and Ising critical points. Our results show that the behavior of GMQD at muti-critical point (MCP) has close relation with the path, which is determined by the parameter alpha, that approaching the MCP. For alpha 2, the GMQD and its first derivation show oscillation behavior. For alpha = 2, no oscillation behavior is observed. This indicates that the GMQD can not describe exactly the multi-critical point of the XY model. However, at the Ising critical point, the path parameter has no influence on the critical behavior. The GMQD (first derivation of GMQD) shows peaks (dips) and indicates exactly the position of Ising critical point. The results also show that the path parameter influences much to the scaling behavior near the MCP, but less to that of Ising critical point. Our results may provide reference to the exploration of relationships between GMQD and quantum phase transitions.