Yu Min = 強关联电子系統中相分离的研究 / 俞敏. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 90-91). / Text in English; abstracts in English and Chinese. / Yu Min = Qiang guan lian dian zi xi tong zhong xiang fen li de yan jiu / Yu Min. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- The Hubbard Model --- p.3 / Chapter 1.3 --- The extended Hubbard Model --- p.4 / Chapter 1.4 --- This project --- p.5 / Chapter 2 --- Methodology --- p.6 / Chapter 2.1 --- Hartree-Fock approximation --- p.6 / Chapter 2.2 --- The unrestricted Hartree-Fock method --- p.7 / Chapter 2.3 --- The restricted Hartree-Fock method --- p.10 / Chapter 2.3.1 --- "Paramagnetic phase, wave vector q = (0,0), r = 1" --- p.13 / Chapter 2.3.2 --- "Ferromagnetic phase, wave vector q = (0,0), r ≠ 1" --- p.13 / Chapter 2.3.3 --- "Wave vector g =(π，π),m ≠ 0; r = 1 antiferromagnetic phase; r≠1 ferrimagnetic phase" --- p.14 / Chapter 2.3.4 --- "Charge-density wave(CDW), wave vector q = (π, π), r≠ 1, m1≠m2" --- p.17 / Chapter 2.3.5 --- "Charge-density wave, wave vector q = (±4, ±4), r ≠1, 1,m1≠m2" --- p.19 / Chapter 2.4 --- Finite size effect in the restricted Hartree-Fock method --- p.23 / Chapter 3 --- Study of the two-dimensional Hubbard model --- p.26 / Chapter 3.1 --- Phase separation in the two-dimensional Hubbard model --- p.26 / Chapter 3.2 --- The existence of stripe phase depends on three aspects --- p.31 / Chapter 3.2.1 --- Dependence of the geometry of the lattice --- p.31 / Chapter 3.2.2 --- Dependence of the Coulomb interaction U --- p.33 / Chapter 3.2.3 --- Dependence of band filling n --- p.35 / Chapter 3.3 --- Fourier transformation of the charge distribution --- p.36 / Chapter 4 --- Study of the two-dimensional asymmetric Hubbard model --- p.40 / Chapter 4.1 --- Phase separation in the two-dimensional asymmetric Hubbard model --- p.41 / Chapter 4.2 --- The influence of t↑ on the existence of stripe phase --- p.42 / Chapter 4.3 --- Fourier transformation of the charge distribution --- p.44 / Chapter 5 --- Study of the one-dimensional Hubbard model --- p.46 / Chapter 5.1 --- The influence of U on the charge distribution --- p.46 / Chapter 5.2 --- The influence of t↑ on the charge distribution --- p.48 / Chapter 5.3 --- Conclusion --- p.50 / Chapter 6 --- Study of the extended Hubbard Model --- p.51 / Chapter 6.1 --- The influence of changing parameter V on the charge distribution --- p.52 / Chapter 6.2 --- The competing of parameter and parameter V on the charge distribution --- p.53 / Chapter 6.3 --- Conclusion --- p.59 / Chapter 7 --- Conclusions --- p.60 / Chapter A --- Program for the unrestricted Hartree-Fock method --- p.61 / Chapter B --- Program for the restricted Hartree-Fock method --- p.73

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Liu, Yang = 軌道簡并性對強關聯系統的磁性的研究 / 劉陽. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 49-51). / Abstracts in English and Chinese. / Liu, Yang = Gui dao jian bing xing dui qiang guan lian xi tong de ci xing de yan jiu / Liu Yang. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Phenomena of Magnetism --- p.1 / Chapter 1.1.1 --- Magnetic susceptibility and classification of magnetic phases --- p.2 / Chapter 1.1.2 --- Paramagnetism and Diamagnetism --- p.3 / Chapter 1.1.3 --- "Ferromagnetism, antiferromagnetism, and ferrimagnetism" --- p.3 / Chapter 1.2 --- Models describing the magnetic system --- p.5 / Chapter 1.2.1 --- The quantum mechanical origin of the interaction between magnetic moments --- p.5 / Chapter 1.2.2 --- Heisenberg model --- p.6 / Chapter 1.2.3 --- Hubbard model --- p.7 / Chapter 1.2.4 --- Background of ferromagnetism in Hubbard model --- p.8 / Chapter 1.3 --- Two-orbital Hubbard model --- p.9 / Chapter 2 --- Low energy effective theory and perturbation method --- p.14 / Chapter 2.1 --- Perturbation by diagrams --- p.14 / Chapter 2.2 --- Illustration of the basic idea: from Hubbard model to Heisenberg model --- p.15 / Chapter 2.2.1 --- Low energy space and intermediate basis --- p.16 / Chapter 2.2.2 --- Diagrams presenting the effective coupling --- p.17 / Chapter 2.2.3 --- Operator form --- p.18 / Chapter 2.3 --- Effective Hamiltonian of quarter filled two-orbital Hubbard model in the large-U limit --- p.19 / Chapter 2.3.1 --- Low energy space and intermediate basis --- p.19 / Chapter 2.3.2 --- Diagrams presenting the effective coupling --- p.20 / Chapter 2.3.3 --- Operator form --- p.23 / Chapter 2.4 --- Two-site problem of two-orbital Hubbard model --- p.25 / Chapter 2.4.1 --- Exact solution --- p.25 / Chapter 3 --- ED method and Numerical results --- p.29 / Chapter 3.1 --- ED method --- p.29 / Chapter 3.1.1 --- Construction of Hilbert space of the many-body model --- p.30 / Chapter 3.1.2 --- Lanczos iterative algorithm --- p.30 / Chapter 3.2 --- Spin structure factor --- p.31 / Chapter 3.2.1 --- Spin structure factor changes with various filling --- p.32 / Chapter 3.2.2 --- Spin structure factor changes with various J --- p.34 / Chapter 3.2.3 --- Spin structure factor changes with various U' --- p.34 / Chapter 3.3 --- Ground state spin magnetization --- p.36 / Chapter 4 --- Quantum phase transition in 1D Half-filled Asymmetric Hubbard model --- p.38 / Chapter 4.1 --- Introduction --- p.38 / Chapter 4.2 --- Spin stiffness --- p.41 / Chapter 4.3 --- Numerical result --- p.43 / Chapter 4.4 --- Summary --- p.46 / Chapter 5 --- Summary --- p.48 / Bibliography --- p.49 / Chapter A --- Conditions of spin and orbital rotational invariant --- p.52 / Chapter A.l --- condition of spin rotational invariant --- p.52 / Chapter A.2 --- conditions of orbital rotational invariant --- p.54 / Chapter B --- Detailed calculation of effective Hamiltonian of two-orbital Hubbard model --- p.57 / Chapter C --- Perturbation of the quartic equation --- p.89

In order to explore a quantum version of a discrete nonlinear Schrödinger equation (DNLS), we quantize one nonlinear Schrödinger model, which is used to study different physical systems, e.g. coupled Bose-Einstein condensates. We will focus on small systems, like Dimer and Trimer.In our efforts to solve this quantum problem, we develop a Mathematica routine that implements the Number State Method and solves the corresponding Schrödinger equation. We calculate analytically and numerically the energy spectrum of the Dimer and Trimer systems. Those eigenenergies depend on the parameter set Q=Q1, Q2, Q3, Q4, Q5 and by adjusting this set Q, we can obtain the desired results and examine their effects. After the quantization of the extended DNLS we obtain a quantum DNLS, also known as an extended Bose-Hubbard (BH) model. The aim of this Master's thesis is to study the differences and similarities between the classical DNLS and the extended BH model, and what happens when we approach from the quantum regime to the classical one. Taking into account that the Hamiltonian has an important conserved quantity, the number operator, enables the total Hamiltonian to be block-diagonalized. This can be accomplished by taking advantage of additional symmetries, such as translational symmetry, which will simplify the analysis of the Hamiltonian matrix. In our results we discuss several effects that break the lattice symmetry, as the intersection between symmetric and antisymmetric states. We also compare our results with those obtained in previous works for the classical model, and we find some similarities, e.g. the transition of the highest-energy state from a one-site solution to a two-site solution depending on which Q parameters we vary, but also differences, as the appearance of a three-site solution, in a Trimer system.

by Lee Kai Cheung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references. / Acknowledgements --- p.II / Abstract --- p.III / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Theory --- p.7 / Chapter Chapter 3 --- Application of the Connected-Moments Expansion to the S=l/2 Heisenberg Antiferromagnet Paper I --- p.16 / Chapter Chapter 4 --- Application of the Connected-Moments Expansion to the Half-filled Hubbard Model Paper II --- p.18 / Chapter Chapter 5 --- Conclusion --- p.20 / Appendix I --- p.21 / Appendix II --- p.29 / References --- p.37

Many novel materials, such as the vanadates MgV 2O5, the cuprates SrCu 2O3, conducting polymers and organic salts which involve longer-range Coulomb interactions, can be modeled by the extended Hubbard model. In this thesis, we applied the strong-coupling perturbation theory to study a generalized extended Hubbard model characterized by the inter-chain electron hopping t' and the inter-chain nearest-neighbor interaction V' as well as the on-site interaction U, the intra-chain nearest-neighbor interaction V and the intra-chain electron hopping t at strong coupling limit for quarter and half band fillings. / The early strong coupling perturbation expansion was only up to the fourth order in t/U and t/V expansion, which is good for the large values of interaction, U/t > 10. However, for real physical systems, the reasonable range of U/t should be from 4 to 10. In order to investigate the physical systems more accurately, we worked out a perturbation expansion up to the sixth order, hence obtained an effective Hamiltonian in t/U, t/V, t/V', t'/U, t'/V and t'/V' expansion for the extended Hubbard model in half and quarter band filings. The effective Hamiltonian obtained only contains the spin-spin correlation terms. For the half-filled band, we calculated the four spin-spin correlation terms and applied the first and second nearest-neighbor correlation of the linear Heisenberg model obtained by Hulthen and Takahashi and the third nearest-neighbor correlation obtained by Kazumitsu Sakai's group to calculate the ground state energy for the 1-D extended Hubbard chain with the realistic Coulomb interactions, U/t ranges from 4 to 14 and V/t ranges from 0 to 2 respectively. For the quarter-filled case, we worked out the effective Hamiltonian for the 1-D and the 2-D cases and calculated the spin-spin correlation functions by the spin-wave theory. We calculated the ground state energy with the same ranges of the on-site interaction input in the half-filled case and the V/t ranges from 1.5 to 4.0 for the 1-D, the quasi 2-D (t > t', t'/V ∼ t/V) and the isotropic 2-D (t = t', V = V') case respectively. In order to check the validity of the perturbation expansion, we proceeded numerical calculations of the ground state energy by exact diagonalization for the same values of U, V, t, V' and t' for both the half-filled and the quarter-filled cases. / Lee Wing Fai = 強耦合擴展 Hubbard模型之微擾計算 / 李榮輝. / "August 2005." / Adviser: Lin Hai Qing. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0323. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 157-160). / 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, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / School code: 1307. / Lee Wing Fai = Qiang ou he kuo zhan Hubbard mo xing zhi wei rao ji suan / Li Ronghui.

Lau Wai Chuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 93-94). / Lau Wai Chuen. / Contents --- p.ii / List of Figures --- p.iv / List of Tables --- p.vi / Abstract --- p.ix / Acknowledgement --- p.x / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Superconductivity --- p.1 / Chapter 1.2 --- The Hubbard model and the Extended Hubbard model --- p.3 / Chapter 1.3 --- Gap Equation --- p.6 / Chapter 1.3.1 --- One-dimensional solutions --- p.11 / Chapter 1.3.2 --- Two-dimensional solutions --- p.12 / Chapter Chapter 2. --- Solving BCS equation --- p.15 / Chapter 2.1 --- Zero value of the denominator of the BCS equations --- p.15 / Chapter 2.2 --- Discontinuity of the BCS equations --- p.16 / Chapter Chapter 3. --- Results of BCS equations for finite size clusters --- p.34 / Chapter 3.1 --- Method used to solve BCS equations --- p.34 / Chapter 3.2 --- Results for the one dimensional and two dimensional lattices --- p.34 / Chapter 3.2.1 --- Extended S-wave solution --- p.35 / Chapter 3.2.2 --- P-wave and D-wave solutions --- p.36 / Chapter Chapter 4. --- Results of BCS equations compare with exact solutions --- p.69 / Chapter 4.1 --- "An exact solution of D-wave, Ne=2" --- p.69 / Chapter 4.2 --- Comparison of the ground state energy with the results calculated by exact diagonalization --- p.73 / Chapter Chapter 5. --- The Phase Diagram of the superconducting state --- p.78 / Chapter Chapter 6. --- Conclusion --- p.91 / Bibliography --- p.93

Huang Zhongbing. / "4 November, 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 123-131). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Systems with competing orders are of great interest in condensed matter physics. When two phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states. In the first part of the thesis, we study the attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis. The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments. We drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors. In the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems. We then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange. For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’ states. For S=1/2, this lattice nematic takes the form of a valence bond solid. With J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO. We discuss implications for the honeycomb lattice Hubbard model.

Systems with competing orders are of great interest in condensed matter physics. When two phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states. In the first part of the thesis, we study the attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis. The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments. We drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors. In the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems. We then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange. For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’ states. For S=1/2, this lattice nematic takes the form of a valence bond solid. With J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO. We discuss implications for the honeycomb lattice Hubbard model.