Thesis advisor: Ying Ran / Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.

L'extrême variété d'architecture moléculaire et de morphologie cristalline du polyéthylène (PE) pennet l'obtention d'une gamme de matériaux aux propriétés très diverses. Des mélanges et assemblages de différents PE ont été réalisés afin de mieux cerner la compatibilité entre les matériaux et I'influence sur les propriétés mécaniques résultantes. Dans cette étude, deux copolymèrcs métallocènes polyéthylènes ultra basse densité (UL) et linéaire basse densité (LL), et un polyéthylène haute densité (HD) issu de la polymérisation Ziegler-Natta ont été utilisés. Les mélanges binaires réalisés par extrusion ont été caractérisés à l'aide de nombreuses techniques expérimentales complémentaires : la rhéologie dynamique afin d'évaluer la miscibilité à l'état fondu, l'analyse thermique pour déterminer le comportement à la fusion et les cinétiques de cristallisation, la microscopie AFM et la diffusion des rayons X pour l'étude morphologique à différents niveaux d'échelle. La séparation de phase semble être un phénomène prédominant pour les espèces étudiées, avec une faible solubilité mutuelle. Il s'avère toutefois qu'une phase semi-cristalline à gradient de composition se développe à l'interface des domaines ségrégés, Du fait de la distribution assez large des unités comonomères au sein de ces matériaux, les chaînes structurellement "cousines" constituent un facteur favorable de miscibilité et de co-cristallisation partielles. L'incidence de cette organisation structurale sur l'efficacité du soudage d'assemblages bicouches a été évaluée par des tests mécaniques. / The extremely large variety of molecular architecture and crystal morphology of polyethylene (PE) materials results in a wide range of properties of these materials. Different types of PE were blended and assembled in the aim to understand their compatibility and the resulting mechanical properties. ln this study, two ethylene-octene copolymers, i.e. an ultra low density polyethylene (UL) and a linear IOl\" density polyethylene (LL) from the metallocene catalysis, and a high density polyethylene (HD) obtained by Ziegler-Natta polymerization, were used. Binary blends were processed by extrusion and characterized by several complementary techniques:dvnamic melt rheology in the aim to study the miscibility in the melt, thermal analysis to determine the melting behavior and the crystallization kinetics, MFA microscopy and X-ray diffusion for the morphology investigation at various scale levels. The phase separation seems to apply to every blend of this study, with a low mutual solubility. However. a semi-crystalline phase with a composition gradient has been shown to occur at the intertàce of the unlike phases. Due to the quite broad distribution of the co-units in the se materials, the presence of structurally similar chains in the components creates an opportunity for partial miscibility and co-crystallization. The incidence of this structural organisation on the efficiency of welding of bilayer assemblies was assessed by mechanical testing.

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Le combustible des réacteurs à eau sous pression (REP) est confiné par une première barrière appelée gaine combustible constituée d'alliages de zirconium. A ce jour, la plupart des gaines combustibles sont fabriquées en Zircaloy-4. En service, les tubes de gainages absorbent une fraction de l'hydrogène dégagée par la réaction de corrosion du métal. De nombreuses études ont démontré le caractère fragilisant des hydrures vis à-vis des propriétés mécaniques des tubes de gainage. Afin de garantir leur intégrité lors du maintien en service mais également une fois hors service (phases de transport et d'entreposage), il est nécessaire de pouvoir prédire le comportement des alliages de zirconium hydrurés en fonction de l'environnement dans lequel ils se trouvent (changements brusques de température, application d'une contrainte ... ). A ce jour il n'existe pas de modèle de précipitation permettant de rendre compte de la microstructure observée en présence d'une contrainte externe. Dans l'objectif de pallier au moins partiellement ce manque, une étude de caractérisation des hydrures a été menée en utilisant les techniques de la Microscopie Electronique en Transmission (MET). Elle a conduit à l'identification d'une nouvelle phase d'hydrure appelée <. A l'issue du travail de caractérisation, une modélisation de la précipitation de cet hydrure à l'échelle mésoscopique a été menée en utilisant un modèle de champ de phases développé au cours de ce travail. / Ln pile, zirconium alloys in contact with the primary medium are submitted to hydrogen absorption that has significant consequences on their thermodynamic, mechanical and corrosion behaviors. Therefore, hydrogen in solid solution or hydrides precipitation can affect Zirconium alloys behaviors during service but also in long term storage and in accidental conditions. For both fundamentals aspects and safety reasons it is important te understand the precipitation process and to predict the influence various parameters like temperature, stresses, cooling rates and microstructure may have. Numerical modeling at the mesoscopic scale is an appealing approach to describe the precipitation and the "phase field" method appears to be particularly weil suited. The achievement of a realistic mesoscopic modeling should take into account an accurate kinetic, thermodynamic and structural data base in order to properly describe hydride nucleation, growth and coalescence as weil as hydride interaction with externat stresses. Such a data base relies on experimental data that are not always available; this is the reason why an accu rate structural characterization was performed. Therefore transmission electron microscopy observations were carried out on Zircaloy 4 specimens with various H contents. From this study, a new hydride phase called <, coherent with the matrix, was identified.

當絶熱地改變哈密頓量的參數時，波函數會獲得一個幾何相位，既 Berry相。它可以表示為參數空間內一個局域的規範場，叫作 Berry曲率。Berry曲率在凝聚態物理的許多領域的研究中起著至關重要的作用，例如量子霍爾效應以及拓撲絶緣體。因此它已成為固體的最基本的性質之一。在量子霍爾效應中，霍爾電導可以表示為 Berry曲率在布里淵區上的積分。這個積分是一個量子化的 Chern數，並且反映了系統的拓撲結構。然而由於時間反演對稱性，拓撲絶緣體的霍爾電導等於零。因此對時間反演不變絶緣體的 Berry曲率的直接以及非破壞性的測量已經成為凝聚態物理中的重要問題。 / 在這篇論文中，我們提出標準的非線性光譜學可以用來探測時間反演不變絶緣體的性質，而且非線性光譜學的實驗比直流實驗更可控。通過計算，我們發現當遠紅外光和 THz光入射到樣品上時，系統的三階光學響應不為零，這與輸運實驗的結果相比形成了鮮明的對比。更重要的是響應函數正比於能帶的非阿貝爾 Berry曲率。這個結果提供了直接測量時間反演不變系統的 Berry曲率的可能性。 / 對具有(近似的 )空間旋轉對稱性的時間反演不變絶緣體，我們發現三階光學響應與等能球面的 Berry曲率通量直接相關。由於 Berry曲率通量給出了能帶簡併點處的奇異單子的拓撲電荷，因此人們可以利用這種方法直接測量能帶的拓撲結構。作為一個例子，這個方法被應用於 III-V族化合物半導體的八帶模型，並給出了一個拓撲電荷為 3的非線性響應。 / Berry phase, a geometric phase acquired by a wave function by adiabatically varying the parameters of the Hamiltonian, can be expressed in terms of a local gauge field in parameter space, called Berry curvature. The Berry curvature plays an essential role in many fields of condensed matter physics, such as the quantum Hall eect and in the study of Topological insulators (TI) and hence it has become one of the most fundamental properties of solids. In Quantum Hall eect, the Hall conductance can be expressed as an integral of the Berry curvature over the Brillouin zone, which is a quantized Chern number and reflects the topology of the system. However in TI, the Hall conductance is equal to zero as a result of the time-reversal (TR) symmetry. Thus, the direct and nondestructive measurement of the Berry curvature of a TR invariant insulator is an important issue in condensed matter physics. / In this thesis, we show that the standard nonlinear optical spectroscopy, being more experimentally controllable than DC experiments, can be used to detect the bulk properties of TR invariant insulators. Through a general calculation, we nd that, when optical and terahertz light fields are employed, the third order optical eect is nonzero compared with the transport method. And the susceptibility is exactly proportional to the non-Abelian Berry curva-ture of the energy band, which provides the possibility of determining Berry curvature directly. / For the TR invariant insulator with (approximate) rotational symmetry, the third order optical susceptibility is related to the the Berry curvature flux through the iso-energy sphere, which gives the topological charge of the monopole at the degeneracy point. Hence it enables one to measure the topo¬logical property of the energy band explicitly. As an example, the method is applied to the eight-band model of III-V compound semiconductors and gives a quantized susceptibility with topological charge equal to 3. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Yang, Fan = 時間反演不變絶緣體的Berry曲率的非線性光學測量 / 楊帆. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 77-[80]). / Abstracts also in Chinese. / Yang, Fan = Shi jian fan yan bu bian jue yuan ti de Berry qu lu de fei xian xing guang xue ce liang / Yang Fan. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction of Berry phase --- p.1 / Chapter 1.1.1 --- Basic concepts of the Berry phase and Berry curvature --- p.2 / Chapter 1.1.2 --- Degeneracy and monopole --- p.5 / Chapter 1.1.3 --- Berry phase in Bloch bands --- p.7 / Chapter 1.1.4 --- Non-Abelian Berry curvature --- p.8 / Chapter 1.2 --- Quantum Hall effect and topological insulator --- p.10 / Chapter 1.2.1 --- Anomalous velocity and Quantum Hall effect --- p.11 / Chapter 1.2.2 --- Topological insulator --- p.14 / Chapter 1.3 --- Introduction of nonlinear optics --- p.16 / Chapter 1.3.1 --- Nonlinear optical susceptibilities --- p.16 / Chapter 1.3.2 --- Density matrix formalism --- p.19 / Chapter 1.3.3 --- Diagrammatic analysis of nonlinear optical processes --- p.21 / Chapter 1.4 --- Polarization operator of band electrons --- p.24 / Chapter 1.5 --- Outline of this thesis --- p.26 / Chapter 2 --- Third-order Optical Response of a General Insulator --- p.28 / Chapter 2.1 --- Introduction --- p.28 / Chapter 2.2 --- Microscopic mechanism --- p.30 / Chapter 2.3 --- Third-order nonlinear susceptibility --- p.31 / Chapter 2.3.1 --- A general model --- p.31 / Chapter 2.3.2 --- Perturbative calculation I --- p.35 / Chapter 2.3.3 --- Perturbative calculation II --- p.40 / Chapter 2.3.4 --- Total response --- p.43 / Chapter 2.4 --- Diagrammatic calculation of the third-order response --- p.45 / Chapter 2.5 --- Application to topological insulators --- p.56 / Chapter 2.6 --- Summary --- p.59 / Chapter 3 --- Nonlinear Optical Measurement of Topological Charge --- p.61 / Chapter 3.1 --- Introduction --- p.61 / Chapter 3.2 --- Third-order response with resonant interband transitions --- p.62 / Chapter 3.3 --- Third-order response and topological charge in a rotationally symmetric insulator --- p.66 / Chapter 3.4 --- Quantized susceptibility of III-V compound semiconductors --- p.70 / Chapter 3.5 --- Summary --- p.74 / Chapter 4 --- Summary and Conclusions --- p.75 / Bibliography --- p.77 / Chapter A --- Calculation of equation (2.32) --- p.81 / Chapter B --- Proof of formula (3.20) --- p.89 / Chapter C --- Third-order response with multiple conduction and valence bands --- p.92

Wong Hon Man = 量子力學中之幾何相位 / 黃漢文. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 75-78). / Text in English; abstracts in English and Chinese. / Wong Hon Man = Liang zi li xue zhong zhi ji he xiang wei / Huang Hanwen. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Geometric Phase in Orthogonal States --- p.2 / Chapter 1.2 --- Projective Phase --- p.3 / Chapter 1.3 --- Bose-Einstein Condensate --- p.3 / Chapter 1.4 --- Arrangement of the Thesis --- p.3 / Chapter 2 --- Review of Geometric Phase --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Berry's Phase --- p.6 / Chapter 2.3 --- Aharonov-Anadan Phase --- p.9 / Chapter 2.4 --- Pancharatnam Phase --- p.10 / Chapter 2.5 --- Example of a Two-State System --- p.13 / Chapter 2.6 --- Remark on Phase Factor --- p.15 / Chapter 3 --- Review of Geometric Phase near Orthogonal States --- p.16 / Chapter 3.1 --- π Phase Change --- p.17 / Chapter 3.2 --- Off-diagonal Geometric Phase --- p.18 / Chapter 4 --- Projective Phase --- p.21 / Chapter 4.1 --- Projective Measurement --- p.21 / Chapter 4.2 --- Definition in Differential Geometry --- p.22 / Chapter 4.3 --- Gauge Transformation --- p.24 / Chapter 4.4 --- Two-state System and Monopole --- p.26 / Chapter 5 --- π Phase Change --- p.30 / Chapter 5.1 --- Projective Phase near Orthogonal States --- p.30 / Chapter 5.2 --- Two-state system --- p.32 / Chapter 5.3 --- Three-state systems --- p.33 / Chapter 5.4 --- Topological restriction for Spin-1 System --- p.36 / Chapter 5.5 --- Remark on Continuity of Curves --- p.37 / Chapter 6 --- Topological Number Associated with Projective Phase --- p.38 / Chapter 6.1 --- Curves Separated by Zero Dot Products --- p.38 / Chapter 6.2 --- Definition of Phase without 2π arbitrary phase --- p.41 / Chapter 6.3 --- 1st Chern Number Associated with Closed Loops --- p.42 / Chapter 6.4 --- Example with a Spin-m System --- p.43 / Chapter 6.5 --- πphase change --- p.45 / Chapter 6.6 --- Variation of Projection States and Curves --- p.46 / Chapter 7 --- Off-diagonal geometric phase --- p.50 / Chapter 7.1 --- Experiment to Measure Projective Phase --- p.52 / Chapter 8 --- Summary on Geometric Phase near Orthogonal States --- p.53 / Chapter 9 --- Review of Bose-Einstein Condensate --- p.55 / Chapter 9.1 --- Gross-Pitaevskii Equation --- p.55 / Chapter 9.2 --- One-Dimensional GP equation --- p.57 / Chapter 9.3 --- Elementary Excitations --- p.57 / Chapter 10 --- Geometric Phase in Bose-Einstein Condensate --- p.59 / Chapter 10.1 --- Two-state Geometric Phase --- p.59 / Chapter 10.2 --- Geometric Phase in Perturabation --- p.60 / Chapter 10.3 --- Numerical Results --- p.63 / Chapter 10.4 --- Discussions --- p.64 / Chapter A --- Monopole --- p.69 / Chapter B --- Definition of Fibre Bundle --- p.71 / Chapter C --- Evaluation of Bargmann invariant by Pancharatnam Phase Formula --- p.73 / Bibliography --- p.75

Thèse de doctorat : Sciences physiques et de l'ingénieur. Lasers, matières, nanosciences : Bordeaux 1 : 2009. / Titre provenant de l'écran-titre.