Local Entanglement and Quantum Phase Transition in Spin Models

In this work, 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 We show that the behavior of $E_{v}$ is dictated by the low-lying spin excitation spectra of these systems. Therefore, the anomalies of $E_{v}$ determine their critical points. It reminds us the well-known fact in optics: The three-dimensional image of one subject can be recovered from a small piece of holograph, which records 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. \textbf{References:} [1] S. Sachdev, \textit{Quantum Phase Transitions} (Cambridge University Press, Cambridge, 2000). [2] Shi-Jian Gu, Guang-Shan Tian, and Hai-Qing Lin quant-ph/0509070