Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-08-15T14:25:56Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Francisco Manoel Bezerra e Rocha.pdf: 738392 bytes, checksum: a00ec5827bbe61c7fe8f36e3b2be9973 (MD5) / Made available in DSpace on 2014-08-15T14:25:56Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Francisco Manoel Bezerra e Rocha.pdf: 738392 bytes, checksum: a00ec5827bbe61c7fe8f36e3b2be9973 (MD5) Previous issue date: 2012-06-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We apply the perturbative eld-theoretical renormalization group (RG) implemented within an approach which considers the calculation for the e ective couplings up to one loop and the computation of the self-energy up to two loops of the single-impurity Anderson model with particle-hole symmetry. To this end, we follow Feynman's diagrammatic method applied to the model and we begin our analysis by calculating the so-called vertex corrections up to one loop. The e ect of correlations on the single-particle excitations is viewed most clearly by means of the computation of the self-energy and its closely-related quantity: the quasiparticle weight. Moreover, to determine the nature of the ground state of the model, we also perform the RG calculation of the so-called uniform spin susceptibility. Then we apply the RG technique, adapting it conveniently to our problem at hand. The next step consists of deriving analytically and solving numerically the coupled di erential RG ow equations for the e ective couplings, the quasiparticle weight and the uniform spin susceptibility. We show that our results agree qualitatively with other analytical works available in the literature, such as, e.g., the functional RG. To benchmark our method, we compare our results with Wilson's numerical RG data. This latter method provides highly accurate numerical results for the quantities analyzed here and, for this reason, it will be an important check for our analytical method. Since the eldtheoretical RG turns out to be a exible technique and also simpler to be implemented at higher orders if compared to some versions of the functional RG method, we argue here that the present methodology could potentially o er a possible alternative to other analytic RG methods to describe eletronic correlations within the single-impurity Anderson model. / Nesta dissertação, aplicamos o método do grupo de renormalização (GR) perturbativo construído a partir de uma abordagem mista que mescla um cálculo até um loop para os acoplamentos efetivos e um cálculo até dois loops para a auto-energia do modelo de Anderson de uma impureza com simetria partícula-buraco. Para isso, utilizamos o método diagramático de Feynman aplicado ao modelo e iniciamos nossa análise calculando todos os chamados diagramas de correção ao vértice até um loop. Os efeitos de correlação nas excitações de uma partícula são vistos mais claramente por meio do cálculo da auto-energia e de uma quantidade física diretamente relacionada que é o peso da quasipartícula. Além disso, para determinarmos a natureza do estado fundamental desse modelo, efetuamos também o cálculo de GR da chamada susceptibilidade uniforme de spin. Desenvolveremos, em seguida, a técnica do GR, adaptando-a convenientemente ao nosso problema de interesse. O próximo passo consistiu em derivar analiticamente e então resolver numericamente as equações diferenciais acopladas para os acoplamentos efetivos, o peso da quasipartículas e a susceptibilidade uniforme de spin. Mostramos que os nossos resultados concordam qualitativamente com outros trabalhos analíticos disponíveis na literatura como, por exemplo, o método do grupo de renormalizalização funcional. Procuramos também comparar nossos resultados com o chamado método do GR numérico de Wilson. Esse é o último método fornece resultados numéricos altamente precisos para as grandezas aqui calculadas em nosso modelo, de modo que essa técnica serviria como uma referência-padrão para nossa abordagem analítica. Nesse sentido, como o método do GR de teoria de campos se revela uma técnica flexível e mais simples de ser utilizada em cálculos perturbativos de ordens superiores se comparada com algumas implementações do método do grupo de renormalização funcional, vamos argumentar que a presente metodologia do GR pode oferecer uma abordagem analítica alternativa para descrever as correlações eletrônicas contidas no modelo de Anderson de uma impureza

La motivation principale de cette thèse a été de déterminer les avantages et les inconvénients de l'utilisation de la spectroscopie de photoémission résolue en angle dans le domaine des rayons X mous.<br />L'étude d'un système bien connu, Ag(001) nous permet de discuter plusieurs questions telles que le rôle de la quantité de mouvement du photon, la pertinence de l'approximation d'électron libre à l'état final, et le rôle des phonons. La polarisation de la lumière incidente a aussi été exploitée. En choisissant un tel système, nous avons aussi voulu comparer les résultats expérimentaux avec des spectres calculés de photoémission résolue en angle dans cette gamme d'énergie.<br />Le comportement à basse température atypique des composés de Cérium est généralement imputé à l'effet Kondo. Des résultats originaux ont été obtenus en étudiant la bande de valence de trois composés monocristallins iso-structuraux de Cérium, CeCu2Ge2, CeNi2Ge2 et CeCo2Ge2. La position du seuil d'absorption M5 du Cérium dans la bande d'énergie des rayons X mous est exploitée pour isoler la contribution 4f à ces spectres. De plus, l'utilisation de photons incidents d'énergie relativement élevée permet de minimiser les effets de surface. Les spectres de photoémission présentés dans cette thèse incluent des études de dépendance en température, des spectres à la résonance, des spectres résolus en angle ou bien intégrés angulairement. Les premiers sont en accord avec le modèle d'impureté unique d'Anderson, alors que les derniers suggèrent qu'il est important de prendre en compte le réseau cristallin.

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Orientador: Eduardo Miranda / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física "Gleb Wataghin" / Made available in DSpace on 2018-09-24T13:52:11Z (GMT). No. of bitstreams: 1 HerazoWarnes_JesusMaria_D.pdf: 4836710 bytes, checksum: 5b7290f1db20bc31b153f3e7202fff39 (MD5) Previous issue date: 2011 / Resumo: A questão da natureza das transições de fases de sistemas de redes de bósons tem se tornado cada vez mais urgente à vista da capacidade de carregamento de átomos ultrafrios em redes ópticas. Nesta tese, tentamos avançar este conhecimento através do estudo de 3 modelos básicos de redes de bósons interagentes. Inicialmente, determinamos o diagrama de fases c as propriedades físicas do modelo bosônico de impureza única de Anderson. Este modelo é interessante tanto em si mesmo quanto por causa de sua relação com outras abordagens teóricas tais como a teoria dinâmica de campo médio bosônica. Usamos como estratégia a inclusão de um pequeno campo externo acoplado ao parâmetro de ordem superfluido, que quebra a simetria global de calibre do modelo. Desta forma, foi possível estudar a transição de condensação de Base-Einstein através do critério de quebra espontânea de simetria global de calibre. Outras quantidades como a ocupação da impureza, o desvio padrão da ocupação e a susceptibilidade com respeito ao campo externo também foram calculadas, caracterizando a transição de fase do modelo. Alguns desses resultados foram comparados com aqueles já obtidos na literatura através do grupo de renormalização numérico. Encontramos bom acordo entre os dois métodos. O segundo estudo realizado nesta tese refere-se ao comportamento crítico do modelo de Bose-Hubbard desordenado através da chamada teoria de campo médio estocástica. O objeto central dessa teoria de campo médio é a distribuição de parâmetros de ordem P(?). Estudos numéricos estabelecem que perto da linha crítica que separa as fases superfluida e vidro de Base do modelo, essa distribuição exibe uma grande região com comportamento de lei de potência P(?) ~ ? ^-(1+ß_c), onde ß_c < 1. Usando esse comportamento como tentativa, obtivemos analiticamente tanto a fronteira de fases quanto o valor do expoente crítico da lei de potência ß_c , encontrando um razoável acordo com os resultados numéricos e avançando o entendimento da natureza da transição de fase específica ao modelo desordenado. Finalmente, o modelo de Bose-Hubbard desordenado para partículas de spin-1 foi estudado dentro da teoria de campo médio estocástica. As distribuições de probabilidade de várias quantidades físicas como o parâmetro de ordem superfluido, o desvio padrão da ocupação por sítio, a fração do condensado, o quadrado do operador de spin, bem como seus valores médios, foram determinados para as três fases do modelo, a saber, o superfluido polar, o isolante de Mott e o vidro de Bose. Uma completa caracterização das propriedades físicas dessas fases e das transições de fase entre elas foi estabelecida / Abstract: The question of the nature of phase transitions of systems of lattice bosons has become increasingly more pressing in view of the capability of loading ultracold atoms in opticallattices. In this thesis we try to advance this understanding through the study of 3 basic models of interacting lattice bosons. Initially, we determined the phase diagram and physical properties of the bosonic singleimpurity Anderson model. This model is interesting both in its own right and because of its relation to other theoretical approaches such as the bosonic dynamical field theory method. We used as strategy the inclusion of a small external field coupled to the superfluid order parameter, which breaks the global gauge symmetry of the model. Thus, it was possible to study the Base-Einstein condensation transition through the criterion of the onset of spontaneous broken global gauge symmetry. Other quantities such as the occupation of the impurity, the standard deviation of the occupation and the susceptibility with respect to the external! Field were calculated characterizing the phase transition in the model. Some of the results were compared with those already reported in the literature, obtained with tic numerical renormalization group. We found good agreement between the two methods. The second study carried out in this thesis concerned the critical behavior of the disordered Bose-Hubbard model within the so-called stochastic mean-field theory. The central object of this mean-field theory is the distribution of order parameters P(?). Numerical studies establish that near the critical line separating the superfluid and Bose glass phases of this model, this distribution shows a wide region of power-law behavior P(?) ~ ? ^-(1+ß_c), where ß_c < 1. Using this behavior as an Ansatz, we obtained analytically both the phase boundary and the value of the critical power-law exponent ß_c, finding a reasonably good agreement with the numerical results and thus shedding new light on the nature of this phase transition specific to disordered model. Finally, the disordered Bose-Hubbard model for spin-1 particles was studied within the stochastic mean-field theory. The probability distributions of various physical quantities, such as the superfluid order parameter, the standard deviation of the occupation per site, the condensate fraction, the square of the spin operator, as well as their average values, were determined for the three phases of the model, namely, the polar superfluid, the Mott insulating and the Bose glass phases. A complete characterization of the physical properties of these phases and the phase transitions between them was then established / Doutorado / Física da Matéria Condensada / Doutor em Ciências

In the first two chapters we presented the basics of density functional theory and semiempirical LSD+U approximation, which was implemented in the full-potential local-orbital (FPLO) minimal-basis calculation scheme. In the third chapter we tested the implemented version of LSDA+U on 3d transitional metal monoxides. Essential improvement of the spectroscopic properties was obtained. A simple model describing the value and direction of the magnetic moment of a transition metal ion was presented. The model visualizes the interplay of the spin-orbit coupling and crystal field splitting. In the fourth chapter we calculated the electronic spectrum of the single Zn impurity in CuO2 plane considered as a vacancy in Cu 3d states. The analytic solution for the states of different symmetry was obtained. Depending on the strength of perturbation induced by the impurity on the neighboring Cu ions, the states are either resonant or localized. The critical values of the perturbation were computed. In the fifth chapter we presented the calculations for three novel vanadates: MgVO3, Sb2O2VO3 and VOMoO4. The tight-binding parameters and the exchange integrals were computed. The magnesium and antimony vanadates appeared to be spin-½ one-dimensional systems, the latter having much stronger one-dimensional character and being probably the best realization of inorganic spin-Peierls system. The molybdenum vanadate was found to be two-dimensional spin-½ system. The Mo 4d orbitals play an important role in the electronic transfer.

In the first two chapters we presented the basics of density functional theory and semiempirical LSD+U approximation, which was implemented in the full-potential local-orbital (FPLO) minimal-basis calculation scheme. In the third chapter we tested the implemented version of LSDA+U on 3d transitional metal monoxides. Essential improvement of the spectroscopic properties was obtained. A simple model describing the value and direction of the magnetic moment of a transition metal ion was presented. The model visualizes the interplay of the spin-orbit coupling and crystal field splitting. In the fourth chapter we calculated the electronic spectrum of the single Zn impurity in CuO2 plane considered as a vacancy in Cu 3d states. The analytic solution for the states of different symmetry was obtained. Depending on the strength of perturbation induced by the impurity on the neighboring Cu ions, the states are either resonant or localized. The critical values of the perturbation were computed. In the fifth chapter we presented the calculations for three novel vanadates: MgVO3, Sb2O2VO3 and VOMoO4. The tight-binding parameters and the exchange integrals were computed. The magnesium and antimony vanadates appeared to be spin-½ one-dimensional systems, the latter having much stronger one-dimensional character and being probably the best realization of inorganic spin-Peierls system. The molybdenum vanadate was found to be two-dimensional spin-½ system. The Mo 4d orbitals play an important role in the electronic transfer.