This thesis focuses on the phase transitions, including ferro-magnetic, anti-ferromagnetic, metal to "Mott" insulator and structural transitions in perovskite and Ruddlesden-Popper ruthenates. The thesis is mainly composed of two parts. The first half presents Density Functional Theory (DFT)+Dynamical Mean Field Theory (DMFT) studies of the electronically driven phase transitions in various ruthenate materials. We study cubic perovskite BaRuO$_3$ via DFT add DMFT method using interaction parameters which were found in previous studies to be appropriate for the related materials, CaRuO$_3$ and SrRuO$_3$. The calculated variation in transition temperature between the Ba and Sr compounds is consistent with experiment, confirming the assignment of the compounds to the Hund's metal family of materials, the appropriateness of the single-site dynamical mean field approximation for these materials as well as confirming the appropriateness of the values for the interaction parameters. The results provide insights into the origin of magnetism and the role of the van Hove singularity in the physics of Hund's metals. We also study the metal-insulator transition (MIT) and magnetic transitions in Ca$_2$RuO$_4$. The Ru-O bonds lengths are found to be the most important control parameters for the metal-insulator transitions and rotations are found to be less important. The calculation successfully captures the important features of the para-magnetic (PM) "Mott" insulating state, including the orbital occupancy disproportionation and the orbitally resolved electron spectral function. It shows the advantage of single set DFT+DMFT in dealing with strongly correlated multi-orbital systems without the assumption of spin symmetry breaking. In the second half, we present a Landau free energy model that incorporates the electronic energetics, the coupling of the electronic state to local distortions and the coupling of local distortions to long-wavelength strains. The model is used to elucidate important experimental features in thermal and current-induced MIT in Ca$_2$RuO$_4$ and Ca$_3$Ru$_{2-x}$Ti$_x$O$_7$ materials. The investigation of lattice and electronic energetics and determination of parameters using DFT+DMFT methods is explained. The change in lattice energy across the metal-insulator transition is shown to be comparable to the change in electronic energy. Important consequences are a strongly first order transition, a sensitive dependence of the phase boundary on pressure and that the geometrical constraints on in-plane lattice parameter associated with epitaxial growth on a substrate typically change the lattice energetics enough to eliminate the metal-insulator transition entirely. The change in elasto-resistance across the MIT is determined. The DFT+U relaxation study shows the octahedron relaxation with respect to uniaxial strain on a and b axes are very different. This sensitive a and b axes dependence is observed in calculations on both Ca$_2$RuO$_4$ and Ca$_3$Ru$_2$O$_7$. The theory model is also generalized to investigate spatially non-homogeneous solutions. Important features of the stripe patterns at the domain boundaries of metallic and insulating phases are discussed and compared with experiments.

Shik, Hoi Yin = 自旋模型中量子相變與量子糾纏的研究 / 石海燕. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 90-96). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Shik, Hoi Yin = Zi xuan mo xing zhong liang zi xiang bian yu liang zi jiu chan de yan jiu / Shi Haiyan.

by Shui-Qin Zhou. / Publication date from spine. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 152-157). / Acknowledgments --- p.i / Abstract --- p.ii / Contents --- p.vi / Abbreviation --- p.viii / List of Figures --- p.xi / List of Tables --- p.xvi / Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Project's Significance --- p.1 / Chapter 1.2. --- Research background.....................................: --- p.1 / Chapter 1.2.1. --- Linear PNIPAM chains in aqueous solution --- p.2 / Chapter 1.2.1.1. --- Origins of the LCST --- p.2 / Chapter 1.2.1.2. --- Experimental studies --- p.4 / Chapter 1.2.2. --- PNIPAM gels --- p.9 / Chapter 1.2.2.1. --- Origins of the volume phase transition --- p.10 / Chapter 1.2.2.2. --- Experimental studies --- p.11 / Chapter 1.2.3. --- Surfactant effects --- p.13 / Chapter 1.3. --- The objective of the project --- p.15 / Chapter 1.4. --- Experimental difficulties --- p.17 / Chapter 2. --- Basic Theory --- p.20 / Chapter 2.1. --- Laser light scattering (LLS) --- p.20 / Chapter 2.2. --- Polymer chains in solution --- p.23 / Chapter 2.3. --- Swollen polymer gels --- p.27 / Chapter 3. --- Results and Discussion --- p.32 / Chapter 3.1. --- Linear PNIPAM chains --- p.32 / Chapter 3.1.1. --- D = kDM-αD for PNIPAM in THF and water --- p.32 / Chapter 3.1.2. --- Coil-to-globule transition of single PNIPAM chains in water --- p.46 / Chapter 3.1.3. --- Additional chain-conformation broadening of the line-width distribution in dynamic LLS --- p.64 / Chapter 3.1.4. --- Internal motions of long linear PNIPAM chains --- p.72 / Chapter 3.1.5. --- Structural model of spherical water/AOT/n-hexane microemulsion --- p.80 / Chapter 3.2. --- Spherical PNIPAM microgels --- p.94 / Chapter 3.2.1. --- Volume phase transition of PNIPAM microgels --- p.94 / Chapter 3.2.2. --- Internal motions of short PNIPAM subchains inside the gel networks --- p.107 / Chapter 3.2.3. --- Surfactant effects on the volume phase transition --- p.113 / Chapter 3.2.4. --- Swelling and drying kinetics of a very thin PNIPAM gel film --- p.129 / Chapter 4. --- Conclusions --- p.141 / Chapter 5. --- Experimental --- p.145 / Chapter 5.1 --- Sample preparation --- p.145 / Chapter 5.2 --- Physical measurement --- p.149 / Chapter 6. --- References --- p.152

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Physics. / M̲i̲c̲ṟo̲f̲i̲c̲ẖe̲ c̲o̲p̲y̲ a̲v̲a̲i̲ḻa̲ḇḻe̲ i̲ṉ A̲ṟc̲ẖi̲v̲e̲s̲ a̲ṉḏ S̲c̲i̲e̲ṉc̲e̲. / Vita. / Bibliography : leaf 134. / Ph.D.

Deng Shusa = 费米系統中的量子纠缠 : 在一维哈伯德模型中的研究 / 邓蜀萨. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 85-90). / Text in English; abstracts in English and Chinese. / Deng Shusa = Feimi xi tong zhong de liang zi jiu chan : zai yi wei Habode mo xing zhong de yan jiu / Deng Shusa. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Introduction to our study on quantum entanglement --- p.2 / Chapter 1.3 --- Introduction to Quantum Entanglement --- p.3 / Chapter 1.4 --- Introduction to Quantum Phase Transition --- p.7 / Chapter 1.5 --- Introduction to Extended Hubbard Model --- p.9 / Chapter 1.6 --- Arrangement of thesis writing --- p.14 / Chapter 2 --- Measurements of Entanglement --- p.15 / Chapter 2.1 --- Von neumann entropy --- p.16 / Chapter 2.2 --- Concurrence --- p.20 / Chapter 2.3 --- Negativity --- p.22 / Chapter 2.4 --- Other measurements --- p.24 / Chapter 3 --- Fermionic concurrence --- p.26 / Chapter 3.1 --- The model and formulism --- p.27 / Chapter 3.2 --- Extended Hubbard dimer with two electrons --- p.31 / Chapter 3.3 --- Dimer under a nonuniform field --- p.38 / Chapter 3.4 --- Large system for site=6 --- p.41 / Chapter 3.5 --- Negativity --- p.44 / Chapter 4 --- Block Entanglement --- p.48 / Chapter 4.1 --- The model and formulism --- p.50 / Chapter 4.2 --- Three-dimensional Phase diagram --- p.55 / Chapter 4.3 --- Entanglement change with block size and parameter --- p.62 / Chapter 4.4 --- Entanglement change with size and parameter --- p.66 / Chapter 4.5 --- Scaling behavior for block block entanglement --- p.70 / Chapter 4.6 --- Further discussion --- p.73 / Chapter 5 --- Conclusion --- p.82 / Bibliography --- p.85

Yu, Wing Chi = 多體系統中的量子相變動力學 / 余詠芝. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 94-99). / Abstracts in English and Chinese. / Yu, Wing Chi = Duo ti xi tong zhong de liang zi xiang bian dong li xue / Yu Yongzhi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Quantum phase transitions --- p.1 / Chapter 1.2 --- Schemes detecting QPTs --- p.3 / Chapter 1.2.1 --- Traditional schemes --- p.3 / Chapter 1.2.2 --- Quantum Entanglement --- p.4 / Chapter 1.2.3 --- Quantum fidelity --- p.4 / Chapter 1.2.4 --- Loschmidt echoes --- p.5 / Chapter 1.2.5 --- Quench dynamics --- p.6 / Chapter 1.3 --- Motivation --- p.7 / Chapter 2 --- Theoretical framework --- p.9 / Chapter 2.1 --- Quantum Zeno effect --- p.9 / Chapter 2.2 --- Mathematical formulation --- p.11 / Chapter 2.3 --- Remarks --- p.14 / Chapter 3 --- Analysis on the One-dimensional Transverse-field Ising model --- p.17 / Chapter 3.1 --- The model --- p.17 / Chapter 3.2 --- Diagonalization of the Hamiltonian --- p.20 / Chapter 3.2.1 --- Jordan-Wigner transformation --- p.20 / Chapter 3.2.2 --- Fourier Transformation --- p.24 / Chapter 3.2.3 --- Bogoliubov transformation --- p.26 / Chapter 3.3 --- Quantum Zeno dynamics in the model --- p.28 / Chapter 3.3.1 --- Analytical calculation of the Zeno susceptibility --- p.28 / Chapter 3.3.2 --- Validity of the analytical result --- p.31 / Chapter 3.3.3 --- Scaling behavior of the Zeno susceptibility --- p.33 / Chapter 3.3.4 --- Zeno susceptibility around the critical point --- p.35 / Chapter 3.4 --- Conclusion and experimental outlook --- p.38 / Chapter 4 --- Analysis on the Lipkin-Meshkov-Glick Model --- p.40 / Chapter 4.1 --- The model --- p.41 / Chapter 4.2 --- Diagonalization of the Hamiltonian --- p.46 / Chapter 4.2.1 --- Holstein-Primakoff transformation --- p.46 / Chapter 4.2.2 --- Bogoliubov transformation --- p.49 / Chapter 4.3 --- Quantum Zeno dynamics in the model --- p.51 / Chapter 4.3.1 --- Analytical form of the Zeno susceptibility and its scaling behavior --- p.51 / Chapter 4.3.2 --- Validity of the analytical result --- p.54 / Chapter 4.3.3 --- Numerical analysis of the Zeno susceptibility --- p.55 / Chapter 4.4 --- Conclusion --- p.60 / Chapter 5 --- Analysis on the Kitaev model on a honeycomb lattice --- p.61 / Chapter 5.1 --- The model --- p.61 / Chapter 5.2 --- Diagonalization of the Hamiltonian --- p.63 / Chapter 5.2.1 --- Jordan-Wigner transformation for two-dimensional systems --- p.64 / Chapter 5.2.2 --- Majorana fermion representation --- p.68 / Chapter 5.2.3 --- Fermions on the 之-bonds --- p.71 / Chapter 5.2.4 --- Bogoliubov transformation --- p.73 / Chapter 5.3 --- Energy spectrum --- p.75 / Chapter 5.4 --- Quantum Zeno dynamics in the model --- p.77 / Chapter 5.4.1 --- Coupling along the Jx = Jy line --- p.77 / Chapter 5.4.2 --- Coupling along the line with constant Jz --- p.83 / Chapter 5.5 --- Conclusion --- p.90 / Chapter 6 --- Conclusion and outlook --- p.91 / Bibliography --- p.94 / Chapter A --- Perturbative form of the Loschimdt Echo --- p.100 / Chapter B --- Hellmann-Feynman theorem --- p.107 / Chapter C --- Commutation relations in the Jordan-Wigner transformation --- p.108

In chapter 1, we give an introduction to QPT, and take one-dimensional XXZ model as an example to illustrate the QPT therein. Through this simple example, we would show that when the tunable parameter is varied, the system evolves into different phases, across two quantum QPT points. The distinct phases exhibit very different behaviors. Also a schematic phase diagram is appended. / In chapter 2, we are engaged in research on ordered phases. Originating in the work of Landau and Ginzburg on second-order phase transition, the spontaneous symmetry breaking induces nonzero expectation of field operator, e.g., magnetization M in the Ising model, and then we say long range order (LRO) exists in the system. LRO plays a key role in determining the ordered-disorder transition. Thereby, we investigate two-dimensional 120° orbital-only model to present how to extract the information of LRO in a pedagogical manner, by applying the reflection positivity method introduced by Dyson, Lieb, and Simon. We rigorously establish the existence of an anti-ferromagnetic like transverse orbital long-range order in the so called two-dimensional 120° model at zero temperature. Next we consider possible pairings in the family of FeAs-based ReO1--xFxFeAs (Re=La, Nd, Ce, Pr, etc.) high-temperature superconductors. We build some identities based on a two-orbital model, and obtained some constraints on a few possible pairings. We also establish the sufficient conditions for the coexistence of two superconducting orders, and we propose the most favorable pairings around half filling according to physical consideration. / In chapter 3, we present a quantum solvation process with solvent of fermion character based on the one-dimensional asymmetric t-J-Jz model. The model is experimental realizable in optical lattices and exhibits rich physics. In this work, we show that there exist two types of phase separations, one is driven by potential energy while the other by kinetic energy. In between, solvation process occurs. Analytically, we are able to obtain some rigorous results to understand the underlying physics. Numerically, we perform exact diagonalization and density matrix renormalization group calculations, accompanied by detailed finite size analysis. / In chapter 4, we explore several characterizations of QPT points. As distinguished from the methods in condensed-matter physics, we give much attention to understand QPT from the quantum information (QI) point of view. The perspective makes a new bridge between these two fields. It no only can facilitate the understanding of condensed-matter physics, but also provide the prominent playground for the quantum information theory. They are fidelity susceptibility and reduced fidelity susceptibility. We establish a general relation between fidelity and structure factor of the driving term in a Hamiltonian through fidelity susceptibility and show that the evaluation of fidelity in terms of susceptibility is facilitated by using well developed techniques such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium. Furthermore, we show that the reduced fidelity susceptibility in the family of one-dimensional XY model obeys scaling law in the vicinity of quantum critical points both analytically and numerically. The logarithmic divergence behavior suggests that the reduced fidelity susceptibility can act as an indicator of quantum phase transition. / Quantum Phase Transition (QPT) describes the non-analytic behaviors of the ground-state properties in a many-body system by varying a physical parameter at absolute zero temperature - such as magnetic field or pressure, driven by quantum fluctuations. Such quantum phase transitions can be first-order phase transition or continuous. The phase transition is usually accompanied by a qualitative change in the nature of the correlations in the ground state, and describing this change shall clearly be one of our major interests. We address this issue from three prospects in a few strong correlated many-body systems in this thesis, i.e., identifying the ordered phases, studying the properties of different phases, characterizing the QPT points. / The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions (QPTs), driven by experimental advance on the cuprate superconductors, the heavy fermion materials, organic conductors, Quantum Hall effect, Fe-As based superconductors and other related compounds. It is clear that strong electronic interactions play a crucial role in the systems of current interest, and simple paradigms for the behavior of such systems near quantum critical points remain unclear. Furthermore, the rapid progress in Feshbach resonance and optical lattice provides a flexible platform to study QPT. / You, Wenlong = 強關聯多體體系中的量子相變 / 尤文龍. / Adviser: Hai Qing Lin. / Source: Dissertation Abstracts International, Volume: 70-09, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 104-115). / 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. / Abstracts in English and Chinese. / School code: 1307. / You, Wenlong = Qiang guan lian duo ti ti xi zhong de liang zi xiang bian / You Wenlong.

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Leung, Ching Yee = LMG模型中的保真度對數和絶熱要求 / 梁靜儀. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 53-58). / Abstracts in English and Chinese. / Leung, Ching Yee = LMG mo xing zhong de bao zhen du dui shu he jue re yao qiu / Liang Jingyi. / Chapter 1 --- Quantum phase transition and fidelity --- p.1 / Chapter 1.1 --- What is a quantum phase transition --- p.1 / Chapter 1.2 --- Use of fidelity in describing QPT --- p.3 / Chapter 1.3 --- Quantum fidelity versus classical fidelity --- p.5 / Chapter 1.4 --- Motivation of the project --- p.8 / Chapter 2 --- Introduction to LMG model --- p.11 / Chapter 2.1 --- The LMG model --- p.11 / Chapter 2.2 --- General ground-state solution of LMG model --- p.13 / Chapter 2.3 --- Analytical solution of ground-state fidelity of LMG model --- p.16 / Chapter 2.4 --- Numerical diagonalization of the Hamiltonian --- p.23 / Chapter 3 --- Scaling dependence of logarithmic fidelity in the LMG model --- p.26 / Chapter 3.1 --- Symmetry-broken phase --- p.26 / Chapter 3.2 --- Polarized phase --- p.29 / Chapter 3.3 --- Scaling behavior of logarithmic fidelity around the critical point --- p.30 / Chapter 4 --- Quench dynamics --- p.35 / Chapter 4.1 --- Introduction to quench dynamics --- p.35 / Chapter 4.2 --- Quantum adiabatic theorem --- p.35 / Chapter 4.3 --- Ground-state quench dynamics --- p.37 / Chapter 4.4 --- Motivation --- p.38 / Chapter 4.5 --- "Adiabaticity, residue energy and fidelity" --- p.39 / Chapter 4.6 --- Adiabatic requirement --- p.40 / Chapter 5 --- LMG model in quench dynamics --- p.42 / Chapter 5.1 --- Numerical analysis method --- p.42 / Chapter 5.2 --- Loss of adiabaticity --- p.44 / Chapter 5.3 --- The adiabatic requirement in the symmetry-broken phase --- p.45 / Chapter 5.4 --- The adiabatic requirement in the polarized phase --- p.46 / Chapter 5.5 --- In the critical region --- p.47 / Chapter 6 --- Summary --- p.50 / Chapter 6.1 --- Scaling dependence of logarithmic fidelity --- p.50 / Chapter 6.2 --- Scaling dependence of duration time in quench dynamics --- p.52 / Bibliography --- p.53

Kwok, Ho Man = 多體系統中的量子臨界現象與保真度 / 郭灝民. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 106-109). / Abstracts in English and Chinese. / Kwok, Ho Man = Duo ti xi tong zhong de liang zi lin jie xian xiang yu bao zhen du / Guo Haomin. / Chapter 1 --- Overview of Quantum Phase transitions --- p.1 / Chapter 1.1 --- Classification of QPTs --- p.2 / Chapter 1.2 --- Teaching model: The quantum Ising model --- p.4 / Chapter 1.3 --- Critical exponents and universality classes --- p.6 / Chapter 1.4 --- A new tool to the QPT: Fidelity --- p.8 / Chapter 1.5 --- Fidelity susceptibility --- p.12 / Chapter 1.6 --- Motivation of this report --- p.16 / Chapter 2 --- Analysis of the One Dimensional Quantum XY model --- p.17 / Chapter 2.1 --- Introduction to the model Hamiltonian --- p.17 / Chapter 2.2 --- Diagonalizing the Hamiltonian --- p.18 / Chapter 2.2.1 --- Jordan-Wigner transformation --- p.18 / Chapter 2.2.2 --- Bogoliubov transformation --- p.22 / Chapter 2.3 --- Ground state properties --- p.24 / Chapter 2.4 --- Calculating the fidelity susceptibility --- p.25 / Chapter 2.5 --- Fidelity susceptibility in Quantum Ising model --- p.31 / Chapter 2.6 --- Numerical comparison --- p.36 / Chapter 3 --- The Lipkin-Meshkov-Glick model --- p.40 / Chapter 3.1 --- Literature Review --- p.40 / Chapter 3.1.1 --- Scaling Behaviour --- p.41 / Chapter 3.1.2 --- Quantum Phase Transition --- p.42 / Chapter 3.1.3 --- Mathematical formalism --- p.44 / Chapter 3.1.4 --- Conserved quantities --- p.46 / Chapter 3.2 --- Energy spectrum for isotropic case --- p.47 / Chapter 3.3 --- Energy spectrum for anisotropic case --- p.49 / Chapter 3.3.1 --- The Holstein-Primakoff mapping --- p.49 / Chapter 3.3.2 --- Bogoliubov transformation for Boson systems --- p.53 / Chapter 3.4 --- Fidelity susceptibility in the isotropic case --- p.55 / Chapter 3.4.1 --- h> h0 --- p.56 / Chapter 3.4.2 --- h0 > h> h1 --- p.57 / Chapter 3.4.3 --- h1 > h > h2 --- p.57 / Chapter 3.5 --- Fidelity susceptibility in the anisotropic case --- p.60 / Chapter 3.5.1 --- "h > 1, driving by γ - xF(γ)" --- p.60 / Chapter 3.5.2 --- "h > 1, driving by h - xF(h)" --- p.62 / Chapter 3.5.3 --- "h < 1, driving by γ - xF(γ)" --- p.63 / Chapter 3.5.4 --- "h < 1, driving by h - xF(h)" --- p.64 / Chapter 3.6 --- Discussion and numerical analysis --- p.65 / Chapter 3.7 --- A possible resolution to the isotropic case: Partial-state fidelity and its susceptibility --- p.71 / Chapter 3.7.1 --- Review of the formalism --- p.72 / Chapter 3.7.2 --- Continuous level crossing and fidelity in the isotropic model --- p.74 / Chapter 3.7.3 --- Partial-state fidelity susceptibility --- p.77 / Chapter 4 --- Numerical Approach to Fidelity Susceptibility --- p.81 / Chapter 4.1 --- The Scaling Ansatz and Critical exponents --- p.81 / Chapter 4.2 --- Examples --- p.83 / Chapter 4.2.1 --- One Dimensional Quantum Ising model --- p.83 / Chapter 4.2.2 --- LMG model --- p.86 / Chapter 4.2.3 --- Two Dimensional Quantum Ising model --- p.90 / Chapter 4.2.4 --- Two Dimensional XXZ model --- p.93 / Chapter 4.2.5 --- One Dimensional Heisenberg model --- p.96 / Chapter 4.3 --- Discussion --- p.100 / Chapter 5 --- Summary --- p.105 / Bibliography --- p.106