Lee Kwok San = 二維海森堡模型的熱力學性質之數値硏究 / 李國姗. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 106-108). / Text in English; abstracts in English and Chinese. / Lee Kwok San = Er wei hai sen bao mo xing de re li xue xing zhi zhi shu zhi yan jiu / Li Guoshan. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- History of magnetism --- p.1 / Chapter 1.2 --- History of Heisenberg model --- p.2 / Chapter 1.3 --- Heisenberg model and high-Tc superconductors --- p.6 / Chapter 1.4 --- Organization of thesis --- p.8 / Chapter 2 --- Methodology --- p.10 / Chapter 2.1 --- Introduction --- p.10 / Chapter 2.2 --- Exact diagonalization --- p.11 / Chapter 2.2.1 --- Coding with only total Sz conservation --- p.11 / Chapter 2.2.2 --- Coding by using translational symmetry --- p.12 / Chapter 2.2.3 --- Coding with H acting on spin configuration --- p.17 / Chapter 2.2.4 --- Coding on finding eigenvalues and eigenvectors --- p.20 / Chapter 2.3 --- Coding on calculating dynamic properties --- p.20 / Chapter 2.3.1 --- Coding on calculating thermal properties --- p.20 / Chapter 2.3.2 --- Coding on calculating other thermal property --- p.21 / Chapter 3 --- Finite temperature calculations on unfrustrated spin systems --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- Finite temperature calculations --- p.33 / Chapter 3.2.1 --- Energy spectrum E(k) --- p.33 / Chapter 3.2.2 --- Internal energy (E) --- p.39 / Chapter 3.2.3 --- Heat capacity Cv --- p.42 / Chapter 3.2.4 --- Uniform susceptibility x --- p.45 / Chapter 3.2.5 --- Staggered magnetization mz+ --- p.47 / Chapter 3.3 --- Linear Spin Wave Theory --- p.48 / Chapter 3.3.1 --- Linear Spin Wave Theory at zero temperature --- p.48 / Chapter 3.3.2 --- Linear Spin Wave Theory at finite temperature --- p.54 / Chapter 3.4 --- Phase Transition --- p.57 / Chapter 4 --- Finite temperature calculations on frustrated systems --- p.62 / Chapter 4.1 --- Introduction --- p.62 / Chapter 4.2 --- Finite temperature calculations --- p.65 / Chapter 4.2.1 --- Energy spectrum E(k) --- p.65 / Chapter 4.2.2 --- Internal energy (E) --- p.68 / Chapter 4.2.3 --- Heat capacity Cv --- p.69 / Chapter 4.2.4 --- Uniform susceptibility x --- p.71 / Chapter 4.2.5 --- "Fourier transform of susceptibility S(qx,qy)" --- p.72 / Chapter 4.3 --- Linear Spin Wave Theory --- p.73 / Chapter 5 --- Finite Size Scaling --- p.78 / Chapter 5.1 --- Introduction --- p.78 / Chapter 5.2 --- Infinite unfrustrated system --- p.79 / Chapter 5.2.1 --- Ground state energy E0 --- p.79 / Chapter 5.2.2 --- Internal Energy (E) --- p.80 / Chapter 5.2.3 --- Staggered magnetization mz+ --- p.81 / Chapter 5.3 --- Infinite frustrated system --- p.83 / Chapter 5.3.1 --- Ground state energy E0 --- p.84 / Chapter 6 --- Comparisons between unfrustrated system and frustrated system --- p.87 / Chapter 6.1 --- Energy spectrum E(k) --- p.88 / Chapter 6.2 --- Internal energy (E) --- p.91 / Chapter 6.3 --- Heat capacity Cv --- p.92 / Chapter 6.4 --- Uniform susceptibility x --- p.93 / Chapter 7 --- Spin Lattice Relaxation l/T1 --- p.94 / Chapter 7.1 --- Introduction --- p.94 / Chapter 7.2 --- Spin temperature --- p.95 / Chapter 7.3 --- Experimental setup and its principle --- p.97 / Chapter 7.4 --- Numerical calculations --- p.102 / Chapter 8 --- Conclusion --- p.104 / Bibliography --- p.106 / Chapter A --- Method of moments --- p.109

Chan Yuk-Lin = 並行機上量子自旋模型的對角化 / 陳玉蓮. / Thesis submitted in: September 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 121-123). / Text in English; abstracts in English and Chinese. / Chan Yuk-Lin = Bing xing ji shang liang zi zi xuan mo xing de dui jiao hua / Chen Yulian. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Development of Theory of Magnetism --- p.2 / Chapter 1.3 --- Heisenberg Model --- p.5 / Chapter 1.4 --- Thesis Organization --- p.9 / Chapter 2 --- Introduction to Parallel Computing --- p.11 / Chapter 2.1 --- Architecture of Parallel Computer --- p.12 / Chapter 2.2 --- Symmetric Multiprocessors and Clusters --- p.16 / Chapter 2.2.1 --- Symmetric Multiprocessors --- p.16 / Chapter 2.2.2 --- Cluster --- p.18 / Chapter 2.2.3 --- Clusters versus SMP --- p.19 / Chapter 2.3 --- Hybrid Architectures (Cluster of SMPs) --- p.20 / Chapter 2.4 --- Hardware Platform for Parallel Computing --- p.21 / Chapter 2.4.1 --- SGI Origin 2000 (Origin) --- p.21 / Chapter 2.4.2 --- IBM RS/6000 SP (Orbit) --- p.22 / Chapter 3 --- Parallelization --- p.23 / Chapter 3.1 --- Models of Parallel Programming --- p.24 / Chapter 3.2 --- Parallel Programming Paradigm --- p.26 / Chapter 3.2.1 --- Programming for Distributed Memory Systems: MPI --- p.26 / Chapter 3.2.2 --- Programming for Shared Memory Systems: OpenMP --- p.31 / Chapter 3.2.3 --- Programming for Hybrid Systems: MPI + OpenMP --- p.39 / Chapter 4 --- Performance --- p.42 / Chapter 4.1 --- Writing a Parallel Program --- p.42 / Chapter 4.2 --- Performance Analysis --- p.43 / Chapter 4.3 --- Synchronization and Communication --- p.47 / Chapter 4.3.1 --- Communication modes --- p.47 / Chapter 5 --- Exact Diagonalization --- p.50 / Chapter 5.1 --- Symmetry Invariance --- p.52 / Chapter 5.2 --- Lanczos Method --- p.53 / Chapter 5.2.1 --- Basic Lanczos Algorithm --- p.54 / Chapter 5.2.2 --- Modified Lanczos Method --- p.56 / Chapter 5.3 --- Dynamic Memory Allocation --- p.58 / Chapter 6 --- Parallelization of Exact Diagonalization --- p.62 / Chapter 6.1 --- Parallelization of Lanczos Method --- p.62 / Chapter 6.2 --- Hamiltonian Matrix Decomposition --- p.66 / Chapter 6.2.1 --- Row-Wise Block Decomposition --- p.67 / Chapter 6.2.2 --- Column-Wise Block Decomposition --- p.69 / Chapter 7 --- Results and Discussion --- p.71 / Chapter 7.1 --- Lattice structure --- p.71 / Chapter 7.2 --- Definition of Timing --- p.72 / Chapter 7.3 --- Rowwise vs Columnwise --- p.73 / Chapter 7.4 --- SGI Origin 2000(0rigin) --- p.77 / Chapter 7.4.1 --- Timing Results --- p.77 / Chapter 7.4.2 --- Performance --- p.79 / Chapter 7.5 --- IBM RS/6000 SP(Orbit) --- p.82 / Chapter 7.5.1 --- MPI vs Hybrid --- p.82 / Chapter 7.5.2 --- Timing and Performance --- p.84 / Chapter 7.6 --- Timing on Origin vs Orbit --- p.89 / Chapter 8 --- Conclusion --- p.91 / Chapter A --- Basic MPI Concepts --- p.95 / Chapter A.1 --- Message Passing Interface --- p.95 / Chapter A.2 --- MPI Routine Format --- p.96 / Chapter A.3 --- Start writing a MPI program --- p.96 / Chapter A.3.1 --- The First MPI Program --- p.97 / Chapter A.3.2 --- Sample MPI Program #1 --- p.100 / Chapter A.3.3 --- Sample MPI Program #2 --- p.106 / Chapter B --- Compiling and Running Parallel Jobs in IBM SP --- p.111 / Chapter B.1 --- Compilation --- p.111 / Chapter B.1.1 --- Compiler Options --- p.112 / Chapter B.2 --- Running Jobs --- p.114 / Chapter B.2.1 --- Loadleveler --- p.114 / Chapter B.2.2 --- Serial Job Script --- p.114 / Chapter B.2.3 --- Parallel Job Script : MPI Program --- p.115 / Chapter B.2.4 --- Parallel Job Script: OpenMP Program --- p.117 / Chapter B.2.5 --- Parallel Job Script: Hybrid MPI/OpenMP Program . . --- p.118 / Chapter B.2.6 --- LoadLeveler Commands --- p.120 / Bibliography --- p.123

In the chapter 3, we study ferromagnetic fluctuations on two types of bilayer triangular lattices by the single-band Hubbard model. We start from the tight-binding model to obtain energy spectrum, the density of sates, and the spin susceptibility. With finite Coulomb interaction turned on, we apply the random phase approximation and use the determinant quantum Monte Carlo method to study spin susceptibility for the two bilayer triangular lattices and make comparisons of their magnetic properties. The effects of the interlayer coupling is also examined in detail. / In the chapter 4, we addresses the issue of the ferromagnetism in graphene-based samples. To study magnetic correlations in graphene, we systematically carry out quantum Monte Carlo simulations of the Hubbard model on a honeycomb lattice. In the filling region below the Van Hove singularity, the system shows a short-range ferromagnetic correlation, which is slightly strengthened by the on-site Coulomb interaction and markedly by the next-nearest-neighbor hopping integral. The ferromagnetic properties depend on the electron filling strongly, which may be manipulated by the electric gate. Due to its resultant high controllability of ferromagnetism, graphene-based samples may facilitate the new development of many applications. / In the chapter 5, we examined theoretically the magnetism of impurity adatoms in graphene by quantum Monte Carlo simulation technique based on Hirsch-Fye algorithm. When tuning the Fermi energy of graphene by gate voltage with available experiments, the values of occupancy and local moment for impurity can be changed. Furthermore, with medium and large hybridizations between impurity and graphene atoms, the local moment can be switched on and off by Kondo effects. We also use maximum entropy method to study the spectral density from Green's function for impurity, and we find very unconventional behaviors which are absolutely different from the cases in the normal metal. These signatures of spectral density enlarge the possibility for controlling the impurity magnetism by gate voltage. / In this research thesis, we mainly study three strongly correlated systems: Hubbard model in bilayer triangular lattice which corresponds to the real material of NaxCoO2 · yH 2O, strong-interaction electrons in graphene system and Anderson impurity in graphene. Our numerical method is determinant quantum Monte Carlo method which will be introduced in the chapter 2. / Hu, Feiming = 阻錯系統的量子門特卡洛研究 / 胡飛鳴. / Adviser: Lin Hai-Qing. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 107-126). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Hu, Feiming = Zu cuo xi tong de liang zi Mente Kaluo yan jiu / Hu Feiming.