[pt] Neste trabalho aplicamos o método RPA renormalizada ao modelo de Hubbard estendido para a cadeia unidimensional com preenchimento meio. Inicialmente verificamos a inúncia do termo de interação entre primeiros vizinhos, V , nas susceptibilidades de carga e longitudinal de spin e comparamos com os resultados de Hubbard puro. Para pequenas interações entre os primeiros vizinhos, a influência de V é muito pequena. À medida que V cresce, seu efeito é de diminuir a frequência dos plasmons e dificultar o aparecimento de magnons. Em seguida determinamos as susceptibilidades de spin e de carga, numericamente, para U = 3,4 e 5 com V entre 0 e próximo de U. Partindo da fase de onda de densidade de spin (SDW) e quando V cresce, o pico de plasmon na susceptibilidade de cargas em 2kF se aproxima de ômega = 0, indicando uma instabilidade para formação de uma onda de densidade de carga (CDW). Isto permite determinar a fronteira de separação entre as duas fases. De acordo com a RPA convencional, esta transformação ocorre em U = 2V mas o processo de renormalização desloca esta fronteira ligeiramente para o interior da região da fase CDW, em conformidade com outros métodos que não fazem a aproximação de campo médio. / [en] In this work we apply the Random Phase Approximation (RPA) to the Extended Hubbard Model in one dimension. Initially we investigate the effect of the first neighbor interaction term, V , on the spin and charge susceptibilities. When V is small, its influence is also very small but as it grows, it tends to lower the plasmon frequency and to inhibit the condition for the existence of magnons. We also have calculated numerically both the spin and the charge susceptibilities for U = 3,4 and 5 with V in the region (0; U). Starting from the SDW region and increasing V we found that the plasmon peak in the charge susceptibility for 2kF tends to omega = 0, indicating an instability against the formation of a CDW ground state. This allows us to determine the phase separation line between the two phases. According to the conventional RPA, this transition occurs for U = 2V but due to the renormalization process, we nd that this frontier shifts slightly to the interior of the CDW region, in agreement with methods not using the mean eld approximation.

An extended Hubbard model with large short and long-ranged Coulomb repulsions and distant transfer is numerically investigated by use of the Lanczos exact diagonalization (ED) method to study the charge order and unconditional dimerization of a chain at density rho (ρ)= 0.4. From the analysis of the spin and charge correlation functions, a picture consistent with the formation of a dimer insulating state, which is of Wigner lattice-type (WL) charge order (CO), is obtained. The next-nearest neighbour (NNN) hopping t2 enhances the intradimer correlations and weakens the interdimer correlations. Implications for the CuO2 chains in Sr14Cu24O41 are discussed.We have also introduced a Heisenberg model which parametrically depends on hole positions. If the electrostatic hole-hole repulsion is included such a model allows to evaluate all energy eigenvalues and eigenstates (for small system size) and thus enables us to evaluate thermodynamic properties as function of temperature,magnetic field, and doping. Assuming certain exchange constants we can investigate the influence of the electrostatic hole-hole repulsion on ground state properties as well as on thermal averages like the magnetization which include contributions of low-lying spin-hole configurations.

Submitted by Simone Souza (simonecgsouza@hotmail.com) on 2018-04-20T14:10:44Z No. of bitstreams: 1 DISS_2014_Raffael Chaves Juliano.pdf: 3302347 bytes, checksum: 174e8e990733d7d4d8b7abe09ac51a92 (MD5) / Approved for entry into archive by Jordan (jordanbiblio@gmail.com) on 2018-05-14T16:24:18Z (GMT) No. of bitstreams: 1 DISS_2014_Raffael Chaves Juliano.pdf: 3302347 bytes, checksum: 174e8e990733d7d4d8b7abe09ac51a92 (MD5) / Made available in DSpace on 2018-05-14T16:24:18Z (GMT). No. of bitstreams: 1 DISS_2014_Raffael Chaves Juliano.pdf: 3302347 bytes, checksum: 174e8e990733d7d4d8b7abe09ac51a92 (MD5) Previous issue date: 2014-11-28 / CAPES / Compostos de metais de transição, como o dióxido de vanadio (VO2), podem apresentar,em determinadas condições, a transição metal-isolante. No VO2, essa transição é acompanhada por uma transformação na sua estrutura cristalina, através da dimerização de átomos de vanadio presentes em sítios distintos. é dessa ligação entre dois sítios que emerge a ideia do dímero de Mott. Neste trabalho, utilizando o método da diagonalização exata, estudamos o modelo de Hubbard em sua versão estendida aplicado ao dimero de Mott, encontrando os seus autovalores e autovetores de energia. Variando os parâmetros do modelo, obtemos os resultados numéricos para os autovalores de energia do sistema. Realizamos ainda uma análise da ocupação eletrônica total e da compressibilidade de carga (densidade de estados) como função do potencial químico. No sentido de compreender melhor o sistema, estudamos o comportamento da dupla ocupação, da energia interna e do calor especifico como função da temperatura, da interação Colombiana local e não local. Além disso, diversas quantidades físicas (dupla ocupação, energia interna,calor especifico, entropia, magnetização e susceptibilidade magnética) do dímero de Mott foram calculadas analiticamente utilizando o método do ensemble canônico. / Compounds based on transition metals such as vanadium dioxide (VO2), present under certain conditions metal-insulator transitions. Regarding to VO2, this transition is accompanied by a change in its cristalline structure through dimerization of two vanadium atoms on di erent sites. Here, it is this bound state between two vanadium atoms that emerges the idea of a Mott's dimer. In this work, using exact diagonalization, we study the Hubbard model in its extended version exploring the physics of Mott's dimer. We obtain explicitly all eigenvalues and eigenvectors of this model. Varying the model parameters, we explore the energy dependence of all eigenvalues of the system. We also performed an analysis of the total electron occupation and the charge compressibility (density of states) as a function of chemical potential. In order to better understand the physical properties of a two-site Hubbard model, we study the behavior of the double occupancy, the total energy and the speci c heat as a function of temperature and the Coulomb interaction parameters. Moreover, various physical quantities (double occupancy, internal energy, speci c heat, entropy, magnetization and magnetic susceptibility) of dimer's Mott were calculated analytically using the method of the canonical ensemble.

The determination of the phase boundary between the charge density wave and the Luttinger Liquid phase for the one-dimensional Peierls extended Hubbard model is done using Stochastic Series Expansion and comparison is done with the phase boundary for the Extended Hubbard model. The result of adding an electron-phonon interaction is that the charge density wave phase weakens. par The energy autocorrelation time is reported for the Extended Hubbard Model and the Peierls Hubbard Model. For coupling near and above the critical coupling the autocorrelation time increases exponentially. par Also investigated is the presence of a spin gap and the critical value of phonon coupling with respect to two parameters, (1) the bare phonon frequency and (2) different U, at one-quarter filling.