Local entanglement and quantum phase transition in spin models

In this paper, we study quantum phase transitions in both the one- and two-dimensional XXZ models with either spin S = 1/ 2 or S = 1 by a local entanglement E-v. We show that the behaviour of E-v is dictated by the low-lying spin excitation spectra of these systems. Therefore, the anomalies of E-v imply their critical points. This recalls the well-known fact in optics: the three-dimensional image of one subject can be recovered from a small piece of holograph, which records the interference pattern of the reflected light beams from it. Similarly, we find that the local entanglement, which is rooted in the quantum superposition principle, provides us with a deep insight into the long-range spin correlations in these quantum spin systems.