臺灣博碩士論文加值系統

量子自旋系統一直是凝體物理中熱門的研究課題，除了在磁性的表現上有豐富的相變行為外，它也跟超導和超流體及超固體有關。本論文以精確對角化法計算一維量子自旋系統的熱力學性質，除了驗證解析理論的預測之外，並且試圖與實驗的數據比較。我們將以反鐵磁海森堡模型為中心，考慮各向異向的反鐵磁海森堡模型，交錯反鐵磁海森堡模型，以及自旋-晶格作用造成之Spin-Peierls相變。另外，我們也研究了有限溫度Lanczos法在量子自旋系統的應用。

The field of quantum spin systems offers a wonderful playground for both theorists and experimentalists to investigate a variety of exotic phases. This system is related to the phenomenon such as superconductivity, superfluidity and supersolid. In this work we will study the thermodynamic properties of the one-dimensional quantum spin systems with the exact diagonalization method. We will verify some of the predictions by Bethe ansatz and other theoretical analyses. We will try to fit the experimental data including specific heat and magnetic susceptibility to get the physical parameters for our quantum spin models. We will take isotropic Heisenberg anti-ferromagnetic chain as the starting model. Then we extend it to include anisotropic spin interaction, alternating anti-ferromagnetic interaction, next-nearest neighbor interaction. Finally we will include the spin-lattice interaction in order to simulate the spin-Peierls transition observed in CuGeO3 material. In addition, we will present some attempts of applying the finite-temperature Lanczos method in the quantum spin systems.

誌謝 i
中文摘要 ii
英文摘要 iii
目錄 iv
圖目錄 v

第１章 序論 1
第２章 模型與方法 8
２-１ 量子自旋模型 8
２-２ Householder對角化法 12
２-３ Lanczos對角化法 15
２-４ 有限溫度性質 18
２-５ 有限溫度Lanczos方法 ( Finite Temperature Lanczos , FTLZ ) 20
第３章 反鐵磁海森堡鏈的熱力學性質 24
３-１ γ＝1 isotropic Δs＝0 25
３-２ γ≠1 anisotropic Δs≠0 29
第４章 交錯海森堡鏈的數值分析結果 33
４-１ 簡介 33
４-２ 交錯鏈的熱力學性質 36
４-３ 低磁場特性 41
４-４ 高磁場特性 44
第５章 CuGeO3的Spin-Peierls 相變 47
５-１ CuGeO3的次近鄰交互作用J' 47
５-２ CuGeO3的Spin-Peierls相變 52
第６章 結論 57
參考文獻 59
作者簡歷 61

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