臺灣博碩士論文加值系統

本論文使用精確對角化（ED）以及密度矩陣重整化群（DMRG）對一維反鐵磁海森堡模型做基態性質研究。利用ED計算各向同性海森堡模型基態能量與自旋關聯，而後使用DMRG計算一維單離子單軸異向性自旋1 XXZ海森堡模型的相圖。利用Haldane相具有的對稱保護拓樸性質，經由計算利用不同晶格長度的entanglement spectrum，得到此模型的even Haldane相、odd Haldane相以及反鐵磁相，與發表於文獻中的結果一致。

In this thesis, we investigate the ground state properties of the one-dimensional antiferromagnet Heisenberg model by Exact diagonalization (ED) and Density Matrix Renormalization Group(DMRG). By the exact diagonalization, we calculate the ground state energy and spin correlation function. We employ DMRG to investigate the ground-state phase diagram of the one-dimensional uniaxial single-ion anisotropic Spin-1 XXZ Heisenberg model on different lattice sizes. By the analysis based on the property of symmetry-protected topological order, we obtain the even-Haldane phase, the odd-Haldane phase, and the anti-ferromagnetic, which are phases consistent with the published results.

誌謝 i
中文摘要 iii
英文摘要 iv
目錄 v
表目錄 vii
圖目錄 ix
第一章　緒論 1
第二章　自旋模型 4
2-1 海森堡模型 4
2-1-1 Haldane猜想 5
2-1-2 單離子單軸異向性海森堡模型 5
2-2 AKLT模型 9
第三章　數值方法 11
3-1 精確對角化 11
3-1-1 Householder方法 11
3-1-2 Lanczos 方法 13
3-2 數值重整化群 18
3-3 密度矩陣重整化群 23
3-3-1 DMRG的無限算法 24
3-3-1 DMRG的有限算法 29
第四章　研究結果 32
4-1精確對角化結果 32
4-1-1基態能量 32
4-1-2 自旋關聯函數 35
4-2 DMRG結果 40
4-2-1 基態能量 40
4-2-2 Entanglement spectrum 42
第五章　結論 49
參考文獻 51

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