Estudamos o calor específico de um sistema formado por duas impurezas adsorvidas, sem spin, em meio fermiônico (banda de condução do metal) e que contém um buraco (elétron) tunelando entre elas. Modelamos esse sistema por dois níveis acoplados e que sofrem interação Coulombiana com a banda de condução. Através da análise das curvas de calor específico, investigamos a alteração (renormalização) da taxa de tunelamento em função da interação eletrostática entre os elétrons da banda de condução e o buraco tunelante e da separação entre as impurezas. Utilizamos o Hamiltoniano de Kondo de tunelamento para representar esse modelo e usamos o Grupo de Renormalização Numérico para diagonalizá-lo. Analisamos a influência de cada termo do Hamiltoniano na renormalização da taxa de tunelamento e verificamos que a troca de paridade das funções de onda do buraco tunelante e dos elétrons da banda desempenha papel essencial. Encontramos uma expressão que combina a distância entre as impurezas e a interação Coulombiana em um único parâmetro (a), de tal forma que sistemas diferentes mas que apresentam o mesmo a e a mesma taxa de tunelamento livre têm a mesma curva de calor específico. / We calculate the specific heat of the two-spinless impurity coupled to a fermionic bath. The model takes into account the tunneling of a hole between the impurities. The two-level system representing the impurities is coupled electrostatically with the conduction electrons. Through the specific heat curves, we analyse the renormalization of the tunneling rate as a function of the Coulomb interaction and distance between impurities. The Numerical Renormalization Group is used to diagonalize the tunneling Hamiltonian proposed by Kondo. We analyse the role of each term of the Hamiltonian in the renormalization of the bare tunneling rate and we stress the importance of the exchange parity between impurity states and conduction states. Finally, a parameter a, is found which combines the distance between impurities and Coulomb interaction in such a way that every curve is specified only by a and the bare tunneling rate.

Submitted by Geyciane Santos (geyciane_thamires@hotmail.com) on 2015-08-06T14:07:38Z No. of bitstreams: 1 Dissertação - Isabel Cristina Souza Dinóla.pdf: 562066 bytes, checksum: fb6aeda0c4854690f169abad1c217b8d (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-08-07T13:20:19Z (GMT) No. of bitstreams: 1 Dissertação - Isabel Cristina Souza Dinóla.pdf: 562066 bytes, checksum: fb6aeda0c4854690f169abad1c217b8d (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-08-07T13:24:35Z (GMT) No. of bitstreams: 1 Dissertação - Isabel Cristina Souza Dinóla.pdf: 562066 bytes, checksum: fb6aeda0c4854690f169abad1c217b8d (MD5) / Made available in DSpace on 2015-08-07T13:24:35Z (GMT). No. of bitstreams: 1 Dissertação - Isabel Cristina Souza Dinóla.pdf: 562066 bytes, checksum: fb6aeda0c4854690f169abad1c217b8d (MD5) Previous issue date: 2009-05-22 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The phase diagram of the two-dimensional super-antiferromagnetic (SAF) Ising model in the presence of a magnetic field is investigated within the framework of a real-space renormalization-group approximation. We consider nearest neighbor ferromagnetic interactions along the x(y) direction and antiferromagnetic interactions in the y(x) direction. The system presents a ordered phase at low temperatures and zero fields. The presence of a magnetic field induces a competition between the energy interactions of the SAF Hamiltonian. The resulting behavior has been a matter of controversy in the last years. We depicted the main results in the magnetic field versus temperature phase diagram. A second-order transition line separates a super-antiferromagnetic phase from a field induced ferromagnetic phase. Our study reveals that the magnetic field induces a phase transition at a single temperature value, thus, we did not find any evidence of reentrant behavior as claimed by some authors. / Utilizamos uma técnica de grupo de renormalização no espaço real para estudar o sistema super antiferromagneto (SAF) de Ising bidimensional sob a influência de um campo magnético externo. Neste modelo as interações de primeiros vizinhos na direção x são ferromagnéticas e na direção y são antiferromagnéticas. Este sistema apresenta uma fase ordenada, para baixas temperaturas e campos nulos, com uma estrutura de linhas ferromagnéticas e colunas antiferromagnéticas. A aplicação do campo magnético induz uma competição entre as energias de interação do modelo e o comportamento resultante desta competição tem sido objeto de estudo e gerado algumas controvérsias nos últimos anos. Na presença do campo magnético observa-se, além da fase SAF, a fase ferromagnética induzida pelo campo (FIC). Apresentamos neste trabalho o diagrama de fases completo do sistema SAF no plano temperatura versus campo magnético. O diagrama de fases obtido mostra uma linha de transição de segunda ordem separando a fase SAF da fase FIC. Nossos resultados contrariam resultados anteriores que preveêm um comportamento reentrante no diagrama de fases do sistema SAF.

Espectros de foto-emissão são calculados com um modelo simples para a adsorção química em superfícies metálicas. Neste modelo já discutido por outros autores, o metal é representado por uma banda de condução semipreenchida e o íon adsorvido por dois níveis: um nível profundo, inicialmente ocupado pelo fotoelétron e o segundo, um nível ressonante, um orbital do átomo adsorvido o qual, atraído pelo potencial do buraco profundo, é deslocado para abaixo da energia de Fermi. O cálculo, baseado nas técnicas de grupo de renormalização desenvolvidas por Wilson para resolver o problema Kondo, considera pela primeira vez a interação eletrostática entre o buraco profundo e os estados de condução. Os resultados mostram que esta interação reduz efetivamente o acoplamento entre o nível ressonante e a banda de condução, e, portanto, modifica qualitativamente os espectros de foto-emissão. / X-Ray Photoemission spectra (XPS) are calculated for a simple model for chemisorptions on metallic surfaces. In the spineless model, already discussed by other authors, the metal is represented by a half-filled conduction band and the adsorbed ion by two levels, one representative of a deep core state initially occupied by the photoelectron and the second, a resonant level, of an initially empty adsorbate orbital which, attracted by the core hole potential, is dragged below the Fermi energy. The calculation based on the renormalization group techniques devised by Wilson to analyze the Rondo problem, accounts for the first time for the electrostatic interaction between the core hole and the conduction states. The results show that this interaction effectively narrows the coupling between the resonant level and the conduction band and hence changes qualitatively the photoemission spectra.

Ces travaux de thèse se sont concentrés sur le développement, l'implémentation et l'application de différents types de méthodes quantiques prenant la corrélation électronique en compte, dans le but de fournir des outils performants pour la description de systèmes moléculaires à l'état fondamental et excité. La méthode dite DMRG (Density Matrix Renormalization Group) a été étudiée et un logiciel correspondant a été développé en FORTRAN. Cette méthode permet de limiter le nombre d'états électroniques à prendre en compte, ce qui fait gagner du temps de calcul, tout en assurant une précision des résultats du même ordre que celle fournie par les toutes meilleures méthodes post-Hartree-Fock actuelles. Dans la deuxième partie de cette thèse, nous avons utilisé une autre méthode : la DFT (Density Functional Theory). Une étude théorique a été effectuée sur deux fonctionnelles à séparation de portée (HISS-A et -B) afin d'évaluer dans quelle mesure ces fonctionnelles, développées au départ pour l'étude des systèmes métalliques, pouvaient être appliquées à la description de l'état fondamental et excité de systèmes moléculaires hautement conjugués. Nous avons également utilisé la DFT afin de modéliser et rationaliser le comportement photo-physique d'un composé moléculaire présentant une émission dite " duale ". Nous avons pu ainsi caractériser le comportement complexe de la molécule à l'état excité et expliquer les résultats surprenants qui avaient été observés, en particulier au niveau des spectres d'émission UV et d'excitation de fluorescence. Le phénomène d'émission duale observé a ainsi pu être lié à la présence d'un degré de liberté conformationnel important de la molécule. / In the last few years, a lot of energy has been put forward in the area of quantum chemistry to develop new methods, or to improve existing methods, that are able to describe very precisely the electronic structure of molecular systems. In this manuscript, a precise overview of such a method (namely the Density Matrix Renormalization Group, DMRG method) is given. A software able to carry out DMRG calculations has indeed been developed from scratch in the laboratory during this thesis. This method can be seen as a post-Hartree-Fock method, in which only the electronic states that are relevant for the correct description of the molecule are kept. In this way, the computational cost remains acceptable, and the results are in line with those given by "exact" methods such as full-CI. Density Functional Theory (DFT) has also been investigated in this work. DFT and TD-DFT calculations have indeed also been carried out. The performances of two middle-range-separated functionals, namely HISS-A and HISS-B, to describe electronic transitions in conjugated molecules have been probed in a theory vs. theory study. Those functionals, which had been first developed for the study of metals, show to be adequate for the correct description of electronic excitations of chromophores and of push-pull molecules. Optical properties of a dual emittor have also been studied using TD-DFT. The dual emission of this molecule has been shown to stem from the presence of two distinct emissive states, respectively of Intramolecular Charge Transfer (ICT) and locally excited (LE) nature. TD-DFT has allowed us to link those two emissive states to two different conformations of the molecule.

The objective of this thesis is to reach theoretical understanding of the unusual relationship between charge-ordering and superconductivity in correlated-electron systems. The competition between these broken symmetries and magnetism in the cuprate high temperature superconductors has been extensively discussed, but exists also in many other correlated-electron superconductors, including quasi-two-dimensional organic charge-transfer solids. It has been suggested that the same attractive interaction is responsible for both charge-order and superconductivity. We propose that the specific interaction is the tendency in correlated-electron systems to form spin-singlet bonds, which is strongly enhanced at the commensurate carrier density p of ½ a charge carrier per site, characteristic of all superconducting charge-transfer solids. To probe superconductivity driven by electron correlations, a necessary condition is that electron-electron interactions enhance superconducting pair-pair correlations, relative to the non-interacting limit. We have performed state of the art numerical calculations on the two-dimensional Hubbard model on different triangular lattices, as well as other lattices corresponding to K-BEDT-TTF based organic charge transfer solids, for the complete range of carrier densities per site p (0 ≤ p ≤ 1). We have shown that pair-pair correlation for each cluster is enhanced by electron-electron interaction only for p ≃ 0.5, far away from the density range thought to be important for superconductivity. Although initial focus is on charge-transfer solids, the results of the research will impact the field of correlated electrons as a whole. We believe our calculations will provide fundamental and fresh insight to the theory of superconductivity in strongly correlated systems.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21571号 / 理博第4478号 / 新制||理||1642(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 菅沼 秀夫, 教授 永江 知文, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

La cosmologie moderne amène à étudier la théorie quantique des champs en espace-temps courbe. Les champs scalaires légers, notamment, génèrent un mécanisme simple pour l'inflation et les fluctuations primordiales. Cependant, les calculs de boucles de ces modèles contiennent des divergences infrarouges et séculaires qui requièrent des techniques de resommation. Dans ce but, on implémente le groupe de renormalisation non perturbatif pour des champs scalaires en espace-temps de De Sitter. Dans un premier temps, on applique l'Approximation de Potentiel Local (APL). On démontre que les effets infrarouges sont responsables d'une restauration de la symétrie, et qu'une masse est générée en accord avec l'approche stochastique. On étudie ensuite la limite d'espace-temps plat de notre formalisme en prenant la courbure $H\to 0$, ce qui reproduit un certain nombre de résultats connus. Enfin, on s'intéresse à l'expansion dérivative, qui va au-delà de l'APL. Son implémentation semble trop complexe dans le cas général d'un espace-temps courbe, mais les symétries de De Sitter permettent de trouver une représentation simple. On définit une prescription pour tous les ordres de l'expansion, puis on implémente le flot du terme de premier ordre dans le cas simple où la dépendance en champ est négligée / The nonperturbative renormalization group for quantum field theory in de Sitter space.The study of cosmology draws us to the topic of quantum fields in curved space-time. In particular, light scalar fields offer a simple mechanism for inflation and primordial fluctuations. When computing loop corrections to these models however, infrared and secular divergences appear which call for resummation techniques. To this end, we implement the nonperturbative renormalization group for quantum scalar fields on a fixed de Sitter background. First, the Local Potential Approximation (LPA) is applied. We show that there is always symmetry restoration due to infrared effects, and that mass is generated in agreement with the stochastic approach. Next, we study the flat space limit of our formalism by taking the curvature $H\to0$, and we check that it reproduces a number of known results. Finally, we discuss the derivative expansion, which goes beyond the LPA. Its implementation seems too complex in general curved space-times, but de Sitter symmetries allow for a simpler representation. We define a prescription for all orders of the expansion, and discuss the flow of the first order term in the simple case where we neglect the field dependency (LPA')

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18062号 / 理博第3940号 / 新制||理||1568(附属図書館) / 30920 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 石田 憲二, 准教授 藤本 聡 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20895号 / 理博第4347号 / 新制||理||1624(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々 真一, 教授 川上 則雄, 教授 早川 尚男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This thesis presents renormalization group (RG) analyses of two strongly correlated condensed matter systems. In the first part, the phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnetic model on a spatially anisotropic triangular lattice is discussed. This model, together with a Dzyaloshinskii-Moriya (DM) interaction, describes the magnetic properties of the layered Mott insulator Cs$_{2}$CuCl$_{4}$. Employing a real-space RG approach, it is found, in agreement with a previous similar study, that a fragile collinear antiferromagnetic (CAF) state can be stabilized at sufficiently strong anisotropies. The presented RG analysis only indicates the presence of the CAF and spiral states in the phase diagram, with no extended quantum-disordered state at strong anisotropies. Specifically, it reveals a fine-tuning of couplings that entails the persistence of ferromagnetic correlations between second-nearest chains over large length scales even in the CAF phase. This has important implications on how numerical studies on finite-size systems should be interpreted, and reconciles the presence of the CAF state with the observation of only ferromagnetic correlations in numerical studies. The effect of a weak DM interaction within this RG approach is examined. It is concluded that Cs$_{2}$CuCl$_{4}$ is well within the stability region of the spiral ordering. In the second part, the fate of a neck-narrowing Lifshitz transition in two-dimensions and in the presence of weak interactions is studied. Such a transition is a topological quantum phase transition, with no change in symmetry. At the critical point of this transition, the density of states at the Fermi energy is logarithmically divergent and a van Hove singularity appears. It is found that, at the critical point, the Wilsonian effective action is intrinsically non-local. This non-locality is attributed to integrating out an emergent soft degree of freedom. Away from the critical point, a local perturbative RG description is presented, and it is shown that weak attractive interactions grow as $\log^2L$ ($L$ is the physical length). However, this local description is restricted to a finite momentum range that shrinks as the critical point is approached. / Thesis / Candidate in Philosophy