This thesis considers various strongly correlated quantum phases in solid state and cold atom spin systems. In the first part we focus on phases emerging in multi-orbital materials. We study even-parity spin-triplet superconductivity originating from Hund's coupling between t2g orbitals and investigate the effect of spin-orbit interaction on spin-triplet and spin-singlet pairing. Various aspects of the pairing state are discussed against the backdrop of the spin-triplet superconductor Sr2RuO4. Motivated by the remarkable phenomena observed in the bilayer compound Sr3Ru2O7, which point to the formation of an electronic nematic phase in the presence of critical fluctuations, we investigate how such a broken symmetry state emerges from electronic interactions. Since the broken x-y symmetry is revealed experimentally by applying a small in-plane magnetic field component, we examine nematic phases in a bilayer system and the role of the in-plane magnetic field using a phenomenological approach. In addition, we propose a microscopic mechanism for nematic phase formation specific to Sr3Ru2O7. The model is based on a realistic multi-orbital band structure and local and nearest neighbour interactions. Considering all t2g-orbital derived bands on an equal footing, we find a nematic quantum critical point and a nearby meta-nematic transition in the phase diagram. This finding harbours important implications for the phenomena observed in Sr3Ru2O7. The second part is devoted to the study of the anisotropic bilinear biquadratic spin-1 Heisenberg model, where the existence of an unusual direct phase transition between a spin-nematic phase and a dimerized valence bond solid phase in the quasi-1D limit was conjectured based on Quantum Monte Carlo simulations. We establish the quasi-1D phase diagram using a large-N Schwinger boson approach and show that the phase transition is largely conventional except possibly at two particular points. We further discuss how to realize and to detect such phases in an optical lattice.

This thesis considers various strongly correlated quantum phases in solid state and cold atom spin systems. In the first part we focus on phases emerging in multi-orbital materials. We study even-parity spin-triplet superconductivity originating from Hund's coupling between t2g orbitals and investigate the effect of spin-orbit interaction on spin-triplet and spin-singlet pairing. Various aspects of the pairing state are discussed against the backdrop of the spin-triplet superconductor Sr2RuO4. Motivated by the remarkable phenomena observed in the bilayer compound Sr3Ru2O7, which point to the formation of an electronic nematic phase in the presence of critical fluctuations, we investigate how such a broken symmetry state emerges from electronic interactions. Since the broken x-y symmetry is revealed experimentally by applying a small in-plane magnetic field component, we examine nematic phases in a bilayer system and the role of the in-plane magnetic field using a phenomenological approach. In addition, we propose a microscopic mechanism for nematic phase formation specific to Sr3Ru2O7. The model is based on a realistic multi-orbital band structure and local and nearest neighbour interactions. Considering all t2g-orbital derived bands on an equal footing, we find a nematic quantum critical point and a nearby meta-nematic transition in the phase diagram. This finding harbours important implications for the phenomena observed in Sr3Ru2O7. The second part is devoted to the study of the anisotropic bilinear biquadratic spin-1 Heisenberg model, where the existence of an unusual direct phase transition between a spin-nematic phase and a dimerized valence bond solid phase in the quasi-1D limit was conjectured based on Quantum Monte Carlo simulations. We establish the quasi-1D phase diagram using a large-N Schwinger boson approach and show that the phase transition is largely conventional except possibly at two particular points. We further discuss how to realize and to detect such phases in an optical lattice.

Beaucoup de personnes voient la chimie comme un sujet abstrait et difficile parce qu’elle concerne l’´étude d’éléments invisibles à l’oeil nu. Mais, en y réfléchissant, la chimie est partout ! Des processus chimiques se déroulent tout autour de nous et aussi en nous tous les jours : dans le corps humain où les protéines jouent un grand rôle, dans les bouteilles de shampoing, dans le dentifrice, dans le ciment utilisé pour bâtir les maisons... Cela ne devrait donc être une surprise pour personne qu’autant d’efforts soient employés dans l'étude des processus chimiques.Qu’elles sont ces espèces invisibles avec lesquelles la chimie fonctionne ? Je pense pouvoir affirmer avec peu de doutes que vous avez tous entendu parler des atomes et des molécules (qui sont un assemblage d’atomes). Atomes et molécules ne sont pas toujours des espèces neutres, c’est-`a-dire, elles peuvent porter une charge électrique (dans ce cas, les atomes sont appelés desions). Cette transformation d’une espèce chargée à une espèce neutre peut se dérouler lorsque la particule est plongée dans un solvant (comme l’eau).C’est le cas par exemple lorsque l’on met du sel dans l’eau et que des ions sont formés. Les exemples de particules qui deviennent chargées dans unsolvant sont nombreux: protéines, virus, polyélectrolytes ... Mais pourquoi cette charge électrique est elle si importante ? Comme pour les aimants, où lepôle positif attire le négatif, les espèces vont commencer à interagir selon leur charge. Parmi d’autres facteurs, tel que la forme de la particule, le rôle joué par les charges dans les processus chimiques est primordial. La physico-chimie se concentre sur la compréhension du comportement de telles petites particules (appelées particules colloïdales) lorsqu’elles sont immergées dans une solution. Néanmoins, à cette échelle, l’étude expérimentale des dispersions colloïdales n’est pas triviale. Dans ce contexte, les simulations informatiques se trouvent être très utile. Elles ont pour but, par l’emploi de modèles physiques et mathématiques, d’essayer de reproduire les résultats obtenus expérimentalement et d’accéder à des valeurs qu’aucunes autres techniques ne peuvent procurer. Elles sont donc complémentaires aux expériences. Cette thèse traite de simulations moléculaires, réalisées `a l’aide de l’algorithme de Metropolis, de particules minérales en forme de disques. Dans un premier projet, l’évolution du nombre de charges sur une particule en fonction de la concentration en sel est étudiée. Dans un second temps, l’influence de la charge portée par les particules sur la formation des phases de gels et de cristaux liquides est examinée. Un des résultats les plus marquant est la découverte de nouvelles phases de cristaux liquides qui pourraient permettre le développement de nouveaux matériaux. Enfin, la croissance de nanoparticules et leurs interactions sont étudiées dans des conditions similaires à celles rencontrées dans les pâtes de ciment. [résumé simplifié] / A considerable amount of mineral particles are found to have a plate-like shape. The work in this thesis concerns theoretical investigations, using a Monte Carlo method, of the properties of such particles in aqueous solutions. The objectives were first to create a model that could capture the essential physics of clay suspensions and also to understand the role of thermodynamics in certain chemical processes. For all investigations, the results are related to experimental studies. The acid-base behavior of clays have been studied, using the primitive model, and an excellent agreement between simulated and experimental results was found. The formation of gel phases as a function of the charge anisotropy have also been investigated. Liquid-gel and sol-gel transitions are found to occur for high and moderate charge anisotropy, respectively. These transitions were also found to be size and salt dependent. In absence of charge anisotropy, a liquid-glass transition is reported. The formation of smectic and columnar liquid crystals phases with plate-like particles has been found to be favored by a strong charge anisotropy, in opposition to what was observed for nematic phases. New liquid-crystal phases were also reported. The stability and growth of nanoplatelets is discussed. It was found that the internal Coulombic repulsion could be the cause of the limited growth of C-S-H platelets. The influence of thermodynamics on the agregation mode of such platelets was also investigated / De flesta ser nog kemi som ett abstrakt och komplicerat ämne mestadels föratt det behandlar byggstenar så små att de inte kan ses med blotta ögat. Menom man tänker på det så finns kemi överallt ! Kemiska processer sker runtomoch inuti oss oavbrutet : i våra kroppar där proteiners kemi spelar en stor roll,i produkter som schampo och tandkräm, i cement som används för att byggavåra hus etc. Det borde därför inte komma som någon stor överraskning attenormt mycket resurser läggs på att förstå olika kemiska processer.Så vad är då dessa osynliga beständsdelar som kemi handlar om? Jag trormig våga påstå att alla någon gång hört talas om atomer och molekyler(varav de senare utgörs av en grupp sammanlänkade atomer). Atomer ochmolekyler är inte alltid neutrala, d.v.s., dom kan bära en elektrisk laddning.Övergången från en neutral till en elektriskt laddad enhet kan exempelvis skenär atomer eller molekyler kommer i kontakt med ett lösningsmedel, vilketär fallet när ett salt löses upp i vatten och blir till fria joner. Fler exempelpå molekyler som blir laddade i vatten är proteiner, virus, polyelektrolyteretc. Liksom magneters positiva och negativa poler attraherar varandra, kommerden erhållna elektriska laddningen i molekyler spela en viktig roll förhur dessa interagerar. Bland många andra faktorer såsom tex partikelgeometrin,spelar laddningen en primär roll i kemiska processer. Fysikaliskkemi fokuserar på att förstå de processer som äger rum när så kallade kolloidalapartiklar interagerar i en lösning under olika förhållanden. Att utföraexperiment med partiklar i storleksordningen 1-1000 nanometer är inte trivialt.Här kommer beräkningskemin in som en kraftfullt komplement. Genomatt använda matematiska och fysikaliska modeller, så eftersträvar man attsimulera de experimentellt erhållna resultaten och samtidigt förstå de underliggandemekanismerna och drivkrafterna på en nivå som ej är möjlig pånågot annat sätt.Den här avhandlingen behandlar Monte Carlo-simuleringar av diskformademineralpartiklar. I första projektet undersöktes hur antalet laddningar på diskformad mineralpartikel varierar som funktion av pH i en saltlösning avolika koncentrationer. Därefter studerades hur denna laddningsfördelningpåverkar bildandet av geler och flytande kristallina faser. Genom dennastudie upptäcktes nya termodynamiskt stabila faser vilket kan leda till utvecklandetav nya material. Slutligen så studerades tillväxten av diskformadenanopartiklar och deras interaktioner under förhållande jämförbara med deförekommande i en cementblandning [populärvetenskaplig sammanfattning på svenska]

A considerable amount of mineral particles are found to have a plate-like shape. The work in this thesis concerns theoretical investigations, using a Monte Carlo method, of the properties of such particles in aqueous solutions. The objectives were first to create a model that could capture the essential physics of clay suspensions and also to understand the role of thermodynamics in certain chemical processes. For all investigations, the results are related to experimental studies. The acid-base behavior of clays have been studied, using the primitive model, and an excellent agreement between simulated and experimental results was found. The formation of gel phases as a function of the charge anisotropy have also been investigated. Liquid-gel and sol-gel transitions are found to occur for high and moderate charge anisotropy, respectively. These transitions were also found to be size and salt dependent. In absence of charge anisotropy, a liquid-glass transition is reported. The formation of smectic and columnar liquid crystals phases with plate-like particles has been found to be favored by a strong charge anisotropy, in opposition to what was observed for nematic phases. New liquid-crystal phases were also reported. The stability and growth of nanoplatelets is discussed. It was found that the internal Coulombic repulsion could be the cause of the limited growth of C-S-H platelets. The influence of thermodynamics on the agregation mode of such platelets was also investigated