<p>In Part I, the relationship between the topology of the Fermi surface and the entanglement entropy S is examined. Spinless fermionic systems on one and two dimensional lattices at fixed chemical potential are considered. The lattice is partitioned into sub-system of length L and environment, and the entanglement of the subsystem with the environment is calculated via the correlation matrix. S is plotted as a function of the next-nearest or next-next nearest neighbor hopping parameter, t. In 1 dimension, the entanglement entropy jumps at lifshitz transitions where the number of Fermi points changes. In 2 dimensions, a neck-collapsing transition is accompanied by a cusp in S, while the formation of electron or hole-like pockets coincides with a kink in the S as a function of the hopping parameter. The entanglement entropy as a function of subsystem length L is also examined. The leading order coefficient of the LlnL term in 2 dimensions was seen to agree well with the Widom conjecture. Of interest is the difference this coefficient and the coefficient of the term linear in L near the neck-collapsing point. The leading order term changes like |t-t_c|^1/2 whereas the first sub-leading term varies like |t-t_c|^1/3, where t_c is the critical value of the hopping parameter at the transition.</p> <p>In Part II, we study the statistics of fractionalized excitations in a bosonic model which describes strongly interacting excitons in a N-band insulator. The elementary excitations of this system are strings, in a large N limit. A string is made of a series of bosons whose flavors are correlated such that the end points of a string carries a fractionalized flavor quantum number. When the tension of a string vanishes, the end points are deconfined. We determine the statistics of the fractionalized particles described by the end points of strings. We show that either bosons or Fermions can arise depending on the microscopic coupling constants. In the presence of the cubic interaction in the Hamiltonian as the only higher order interaction term, it was shown that bosons are emergent. In the presence of the quartic interaction with a positive coupling constant, it was revealed that the elementary excitations of the system possess Fermion statistics.</p> / Master of Science (MSc)

<p>The following dissertation presents neutron scattering studies on three specific magnetic insulating oxide materials whose lattice is based on triangular structural motifs. Each of the three materials studied, LuCoGaO₄, Co₃V₂O₈ and Tb₂Ti₂O₇, displays an interesting disordered ground state that is reached by different mechanisms: site disorder, geometric frustration, and quantum fluctuations induced by a transverse magnetic field. The main focus of this work is the characterization of the resulting magnetic ground states and magnetic excitations within these systems.</p> <p>Chapters 3, 4 and 5 contain original work in the form of six research articles that have either been published or have been prepared for publication in peer-reviewed journals.</p> <p>Chapter 3 describes studies of the quasi two-dimensional triangular layered antiferromagnet LuCoGaO₄. This material is found to exhibit a spin glass ground state as a result of geometrical frustration and site disorder inherent in this system. Below the freezing temperature, this system exhibits static, two-dimensional correlations consistent with frozen short-range correlated regions in the plane of the bilayers that extend over roughly five unit cells. The dynamic correlations reveal typical spin glass behavior upon cooling. Furthermore, a resonant gapped spin-wave-like excitation is observed, that can be related to the anisotropy in the system. Such an excitation is relatively uncommon in spin glasses and has been studied for the first time in such detail.</p> <p>Chapter 4 is concerned with the study of the kagome staircase system Co₃V₂O₈. While prone to geometrical frustration due to its underlying kagome structural motif, this material is characterized by predominantly ferromagnetic interactions that lead to an unfrustrated, ferromagnetic ground state. In this chapter, departures from this conventional ground state by different disordering mechanisms are investigated. The first part focuses on the effects of site disorder by introducing quenched nonmagnetic impurities into the system. The growth of single crystals of (Co_1-xMg_x)₃V₂O₈ is reported. These crystals reveal that the ferromagnetic ground state is very sensitive to doping, and show that a low doping concentration of 19% leads to a suppression of the ferromagnetic ground state below 1.5 K. This could be understood as percolation problem on the quasi two-dimensional kagome lattice including site and bond percolation. The second part focuses on the influence of a transverse magnetic field on the ground state of Ising spins, introducing quantum fluctuations that lead to quantum phase transitions at ~6.25, 7 and 13 T. The observed quantum phase transitions are characterized by distinct changes in the magnetic structure and their associated spin excitation spectra.</p> <p>Chapter 5 presents studies on the pyrochlore antiferromagnet Tb₂Ti₂O₇, which is a proposed spin liquid candidate but whose actual ground state is still the topic of current debate. The ground state of Tb₂Ti₂O₇ was revisited by neutron scattering measurements, revealing a new phase in the low temperature low field phase diagram that can be described as a frozen antiferromagnetic spin ice that exhibits distinct elastic and inelastic scattering features.</p> / Doctor of Philosophy (PhD)

Chromonic liquid crystals are a relatively new class of lyotropic liquid crystals. In an effort to understand this lyotropic phase better, studies on the phase behavior, defects formed in these systems and characterization of the order were performed. We studied three chromonic liquid crystal materials in nematic and biphasic regions: Sunset Yellow FCF (SSY, a food dye), a cationic perylene diimide derivative (PDI, a conducting dye) and cromolyn sodium (DSCG, a drug). For SSY chromonics in the nematic region, order parameters ( and ) were obtained by polarized Raman measurements. Using the order parameters the flow behavior was predicted and was found to be non-flow aligning. A comprehensive viscoelastic property set of SSY chromonics was obtained by studying the statics and dynamics of defects during the formation of planar aligned monodomain. Applications of PDI thin films as vapor sensors were explored; anisotropic electronic properties of oriented PDI films show good conductivity along the columns presumably arising from the overlap between the ? systems. In the biphasic region, growth and fluctuation of SSY tactoids and interesting patterns of biphasic DSCG under capillary geometry were observed; elastic properties and surface tension were estimated based on the shape of DSCG tactoids. Polymer dispersed lyotropic chromonic liquid crystals with different drop shapes and director configurations were also fabricated using various water-soluble polymers.

Le mémoire est consacré à l'étude numérique des phénomènes survenant à l'interface solide-fluide. Trois processus ont été étudiés: auto-organisation de films moléculaires sur un substrat solide, adsorption du gaz moléculaires dans un matériau nanoporeux et la cristallisation à l'interface organique/inorganique. L'étude de l'auto-organisation et des transitions de phase dans des multicouches de l'azote moléculaires adsorbées sur graphite est présentée dans le chapitre III. L'analyse est focalisée sur l'hétérogénéité spatiale du système et son influence sur le mécanisme et température de transitions ordre/désordre et la fusion des couches. Elle complète ainsi l'étude numérique du diagramme de phase de l'azote moléculaire, bien connu pour le matériau massif (3D) et les monocouches (2D) adsorbées sur un substrat. Le chapitre IV présente une étude de cinétique du mélange des gaz (méthane et méthyle-mercaptan) confiné dans les nanopores de carbone (pores en forme de fentes, de dimensions latérales finies et largeur nanométrique). L'étude porte sur la capacité de stockage de pores, la dynamique des composantes du mélange des gaz sous confinement et l'évaluation de la quantité de l'odorant nécessaire pour une détection facile en cas de fuite. Chapitre V résume les résultats de l'étude préliminaire ayant pour but la mise en place des simulations de biomineralization à l'interface organique/inorganique. Les structures secondaires de deux biomolécules, human leucine-rich peptide hLRAP et full length amelogenin, rM179 ont été prédéterminées. Les plus probables configurations ont été optimisées dans un environnement aqueux. / The present work is devoted to computer simulations of phenomena occurring at solid-fluid interfaces. Three processes have been studied in details: auto organization of molecular films at a solid substrate, adsorption of molecular gas in confined geometry and crystal formation at organic-inorganic interface. Two classical simulation methods have been used: stochastic Monte Carlo and deterministic Molecular Dynamics.The study of self-organisation and phase transitions in molecular nitrogen multilayers adsorbed on the basal plane of graphite is presented in chapter III. It focusses on the systems' spatial heterogeneity and its influence on temperatures of order-disorder and melting transitions. This study completes the numerical analysis of molecular nitrogen phase diagram, well described and understood for 3d (bulk) and 2D (monolayer film) systems.The analysis of kinetics of fluid confined in nanopores is presented in chapter IV. The working case consists of methane-methyl mercaptan mixtures confined in slit-shaped carbon nanopores. Simulations focused on both: storage capacity of carbon pores of finite size and nanometric width, and dynamics of gas mixture components under confinement. An evaluation of odorant content necessary for easy gas leak detection is presented.Chapter V gathers the results of calculations performed to set up the simulations of biomineralization at the organic-inorganic interface. The secondary structures of two amelogenins (human leucine-rich peptide, hLRAP, and full length amelogenin, rM179) have been predicted. The most probable structures have been further refined and the chain folding optimized in aqueous environment.

Transition metal oxides adopt a wide variety of crystal structures and display a diverse range of physical phenomena from Mott insulating states to electron-nematics to unconventional superconductivity. Detailed understanding of these states and how they may be manipulated by structural modifications requires both precise structural knowledge and in-depth physical property measurements using as many techniques over as wide a range of phase space as possible. In the work described in this thesis a range of transition metal oxides were studied using high-resolution powder neutron diffraction and detailed low-temperature physical property measurements. The quaternary barium orthotellurates Ba₂NiTeO₆, Ba₂CuTeO₆ and Ba₂ZnTeO₆ belong to an almost unstudied family of materials. The development of procedures for synthesizing large single crystals has facilitated the investigation of interesting new anisotropic magnetic states in the Cu and Ni systems and the existence of a possible structural phase transition in the Zn-based compound. YMnO₃ is a multiferroic with improper ferrielectricity. The study of the high-temperature structural phases described in this thesis has led to the identification both of the transition path to the ferrielectric state and the identification of an isostructural phase transition within the ferrielectric phase. BiFe₀.₇Mn₀.₃O₃ is also a multiferroic material but with proper ferroelectricity. The investigation of the structural phases of this compound have provided confirmation of the high-temperature phases with the reassignment of the symmetry of the highest-temperature phase which is intriguingly different to that of the unsubstituted material. Finally, an investigation of the electronic structures of the high conductivity delafossites PdCoO₂ and PdCrO₂ using micro-cantilever torque magnetometry measurements of quantum oscillations is described. This has resolved the warping of the Fermi surface of PdCoO₂ and given insights into the complicated Fermi surface of the itinerant antiferromagnet PdCrO₂.

Nous avons étudié le transfert de chaleur et de matière au cours de l'histoire de la Terre primitive à de multiples échelles en utilisant des modèles numériques. Deux systèmes différents sont abordés. Tout d’abord, nous nous concentrons sur les premiers stades de la formation du noyau terrestre lorsque le fer se sépare des silicates et descend vers l'intérieur de la planète. Au cours de la différenciation, des interactions chimiques et thermiques se produisent entre les gouttes de fer dispersées dans des silicates fondus formant un océan de magma. Nous étudions le transport chimique des éléments traces à l'intérieur et autour des gouttes. Nous tirons quelques relations fonctionnelles dépendante du régime dynamique d'écoulement et montrons que le système tend à être en équilibre chimique extrêmement rapidement par rapport à l'échelle de temps de la descente de la goutte de fer. Peu de temps après la fin de l'accrétion de la Terre, la fusion extensive de son intérieur profond ainsi que la formation d'un océan de magma en surface a lieu. Comme le rayonnement de la chaleur dans l'espace est très efficace, les silicates fondus superficiels cristallisent très rapidement. L'histoire thermique de la couche liquide enterrée, appelée océan de magma basal (OMB), se déroule sur une longue période de temps et il est proposé que ses restes soient aujourd'hui observables sous forme de poches partiellement fondues au dessus de frontière noyau-manteau. Nous déterminons les paramètres régissant un système convectif dans lequel se produit une transition solide/liquide. Les lois d'échelle ainsi obtenues ont été appliquées à l'OMB et indiquent que la différence de température qui peut être maintenue dans les couches limites supérieure et inférieure de l'OMB est infime. Par conséquent, la température du noyau suit la température de liquidus à la base du manteau et ainsi la vitesse de refroidissement de l'OMB doit être la même que celle du noyau de la Terre. / We have studied the heat and mass transfer during the early Earth history at multiple scales and for multiple systems by means of numerical computing. Two different systems are approached. Firstly, we focus on the early stages of the Earth core formation when iron segregates from silicates and descends toward the interior of the planet. During the differentiation there are chemical and thermal interactions between dispersed iron blobs and surrounding molten silicates. We study the chemical transport of trace elements within and around the drops. We derive functional relations between critical parameters and show that the system tends to be in chemical equilibrium.During the accretion process of the Earth, extensive melting of its deep interior as well as formation of shallow magma oceans occurred.As heat radiation into space happens with high efficiency, surface molten silicates crystallize very rapidly, in about 10 My. The thermal history of the buried liquid layer, called the basal magma ocean (BMO), proceeds over a long time and it is proposed that its remnants are nowadays observable as partial melts in the core-mantle boundary region.We develop numerical models of the thermal history of the crystallizing basal magma ocean that enable to study coupling between the mantle and the core in the presence of the BMO. We derive parametrized relations for this convective system that undergoes solidification/melting. Obtained scaling equations applied to the BMO indicate that the temperature difference that can be maintained across the top and bottom boundaries of the BMO is minute. Hence, the temperature of the core follows the temperature of liquidus at the bottom of the mantle and thus the rate of the BMO cooling must be the same as that of the Earth's core.

Les propriétés d'électrons en deux dimensions (2D) soulèvent des questions fondamentales qui ont été largement explorées au moyen des techniques théoriques de la matière condensée. L'extension de modèles classiques tel le modèle de Hubbard en 2D, en incluant par exemple plusieurs bandes électroniques, ore la possibilité d'accéder à des phénomèmes plus complexes, comme l'interaction du transport électronique et du magnétisme observé dans les composés de fermions lourds. Ces modèles sont en lien direct avec la question de couches minces couplées, les hétérostructures, qui sont depuis peu l'objet d'intenses recherches et orent la possibilité d'intéressantes applications. Dans ce contexte, nous étudions numériquement diérents syst èmes au moyen de la méthode du Monte Carlo Quantique du Déterminant. Tout d'abord, l'eet de la corrélation électronique dans un isolant de bande est évaluée, montrant en particulier l'absence d'une phase métallique intermédiaire. Un deuxième système est composé de deux bandes électroniques couplées, dans lequel l'eet de la largeur de bande de la partie corrélée est exploré de façon systématique. Finalement, nous étudions une interface métal-isolant, qui présente une phase intermédiaire surprenante lorsque le couplage à l'interface est ajusté. / The properties of electrons in two dimensions (2D) raise fundamental questions that have been extensively explored by condensed matter theory. Extending standard frameworks such as the 2D Hubbard model by accounting for more than one electronic band oers the opportunity to access more complex phenomena, such as the interplay between transport and magnetism found in heavy-fermions materials. Such models are directly connected to the problem of coupled layers in complex materials known as heterostructures, which have been widely studied and synthesized in recent years, and are expected to lead to important applications. In that context, we study numerically several systems, by mean of the Determinant Quantum Monte Carlo Method (DQMC). We rst analyze the eect of electronic correlation in a band insulator, showing in particular the absence of an intermediate metallic phase. A second system consists of two coupled bands that modelize a heavy fermion model, in which the role of the bandwidth of the correlated band is systematically investigated. Finally, we consider the case of a metal-insulator interface, unveiling an intriguing intermediate phase as the interfacial coupling is tuned.

Neste trabalho realizo uma adaptação do método de Ma, Dasgupta e Hu para o estudo e caracterização das transições de fase quânticas, induzidas por um campo transverso, em cadeias XY de spins 1/2, unidimensionais e aperiódicas, no espírito da adaptação correspondente para cadeias XXZ. O presente trabalho determina de forma analítica uma série de expoentes críticos associados às transições ferro-paramagnéticas do sistema, e dá pistas quanto à natureza das estruturas presentes no estado fundamental. Os resultados são então testados pelo emprego da técnica de férmions livres, da análise de nite size scaling e, no limite de Ising, de resultados extraídos do mapeamento do problema em uma caminhada aleatória. / We employ an adaptation of the Ma, Dasgupta, Hu method in order to analyze the quantum phase transition, induced by a transversal magnetic eld, at spin-1/2 aperiodic XY chains, in analogy to the corresponding adaptation for XXZ chains. We derive analytical expressions for some cri tical exponents related with the ferro-paramagnetic transitions, and shed light onto the nature of the ground state structures. The main results obtained by this approach were tested by the free-fermion method, nite-size scaling analyses and, at the Ising limit of the model, by using results derived from a mapping to a random-walk problem.

Neste trabalho estudamos as transições de fases cinéticas e o comportamento crítico da produção de entropia em modelos de spins com interação entre primeiros vizinhos e sujeitos a duas dinâmicas de Glauber, as quais simulam dois banhos térmicos a diferentes temperaturas. Para tanto, é admitido que o sistema corresponde a um processo markoviano contínuo no tempo o qual obedece a uma equação mestra. Dessa forma, o sistema atinge naturalmente estados estacionários, que podem ser de equilíbrio ou de não-equilíbrio. O primeiro corresponde exatamente ao modelo de Ising, que ocorre quando o sistema se encontra em contato com apenas um dos reservatórios. Dessa forma, há uma transição de fase na temperatura de Curie e o balanceamento detalhado é seguramente satisfeito. No segundo caso, os dois banhos térmicos são responsáveis por uma corrente de probabilidade que só existe visto que a reversibilidade microscópica não é mais verificada. Como conseqüência, nesse regime de não-equilíbrio o sistema apresenta uma produção de entropia não nula. Para avaliarmos os diagramas de fase e a produção de entropia utilizamos as aproximações de pares e as simulações de Monte Carlo. Além disso, admitimos que a teoria de escala finita pode ser aplicada no modelo. Esses métodos foram capazes de preverem as transições de fases sofridas pelo sistema. Os expoentes e os pontos críticos foram estimados através dos resultados numéricos. Para a magnetização e a susceptibilidade obtemos = 0,124(1) e = 1,76(1), o que nos permite concluir que o nosso modelo pertence à mesma classe de Ising. Esse resultado refere-se ao princípio da universalidade do ponto crítico, que é verificado devido o nosso modelo apresentar a mesma simetria de inversão que a do modelo de Ising. Além disso, as aproximações de pares também mostraram uma singularidade na derivada da produção de entropia no ponto crítico. E as simulações de Monte Carlo nos permitem sugerir que tal comportamento é uma divergência logarítmica cujo expoente crítico associado vale 1. / We study kinetic phase transitions and the critical behavior of the entropy production in spin models with nearest neighbor interactions subject to two Glauber dynamics, which simulate two thermal baths at different temperatures. In this way, it is assumed that the system corresponds to a continuous time Markov process which obeys the master equation. Thus, the system naturally reaches steady states, which can be equilibrium or nonequilibrium. The former corresponds exactly to the Ising model, which occurs since the system is in contact with only one of the reservoirs. In this case, there is a phase transition at the Curie temperature and the detailed balance surely holds. In the second case, the two thermal baths create a non trivial probability current only when microscopic reversibility is not verified. As a consequence, there is a positive entropy production in a non-equilibrium steady state. Pair approximations and Monte Carlo simulations are employed to evaluate the phase diagrams and the entropy production. Furthermore, we assume that the finite-size scaling theory can be applied to the model. These methods were able to predict the phase transitions undergone by the system. The exponents and the critical points were estimated by the numerical results. Our best estimates of critical exponents to the magnetization and susceptibility are = 0,124 (1) and = 1,76 (1), which allows us to conclude that our model belongs to the same class of Ising. This result refers to the principle of universality of the critical point, which is checked because our model has the same inversion symmetry of the Ising model. Moreover, the pair approximation also showed a singularity in the derivative of the entropy production at the critical point. And Monte Carlo simulations allow us to suggest that the divergence at the critical point is of the logarithmic type whose critical exponent is 1

Neste trabalho estudamos um modelo estocástico com simetria Ising e dois estados absorventes em três dimensões com uma rede cúbica e em duas dimensões através de uma rede triangular. O estudo levou em conta cálculos de aproximação de campo médio e simulações de Monte Carlo. Os resultados mostraram que o modelo tem transição de segunda ordem de uma fase paramagnética para uma fase ferromagnética, uma transição da fase ferromagnética para uma fase absorvente, também de segunda ordem, e ainda uma transição de primeira ordem da fase paramagnética para a fase absorvente. No espaço de parâmetros as três linhas de transição se encontram no diagrama de fases em um ponto onde o modelo se comporta como o modelo do votante. / In this work we studied a stochastic model with ising symmetry and two simmetric absorbing configurations in a three-dimensional cubic lattice and in two dimensions using a triangular lattice. The study took into account simple mean-field approximations and Monte Carlo simulations. The results showed that the model has a second-order transition from a paramagnetic phase to a ferromagnetic phase and second-order transition from ferromagnetic phase to the absorbing one. A first-order phase transition from the paramagnetic phase to the absorbing phase is observed too. In the phase diagram the two second-order transition lines aproaches to the point where the model behaves like the voter model.