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.
