在本計畫中，我們在自旋為1且各向異性的一維量子自旋系統中，利用密度矩陣重整化群(Density Matrix Renormalization Group)計算出不同的基態之間的相似度(fidelity)和基態的糾纏熵(entanglement entropy)。研究基態相似度的二次導數在臨界點附近的行為，使得最近提出來的有限尺度關係(finite scaling relation)在數值上得到進一步的確認。不但如此，從我們計算的數據中，透過有限尺度分析，得到臨界點和對應的臨界指數與文獻中所得數值相當吻合。因此，對於利用相似度來鑑定量子相變，我們的工作提供了一個數值上的支持。 By means of the density matrix renormalization group technique, the scaling relation of the fidelity susceptibility proposed recently is verified for the spin-one XXZ spin chain with an on-site anisotropic term. Moreover, from the results of both the fidelity susceptibility and the entanglement entropy, the critical points and some of the corresponding critical exponents are determined through a proper finite-size scaling analysis, and these values agree with the findings in the literature. Thus our work provides a numerical support of the use of the fidelity in detecting quantum phase transitions.
