Made available in DSpace on 2014-06-12T18:03:16Z (GMT). No. of bitstreams: 2 arquivo4146_1.pdf: 1109274 bytes, checksum: df5758c186c54ed0c194843a67e9ad8c (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2008 / Faculdade de Amparo à Ciência e Tecnologia do Estado de Pernambuco / Nesta dissertação estudamos o modelo de Hubbard estendido na cadeia AB2. O hamiltoniano do modelo contém um termo cinético, parametrizado por t, e dois termos de repulsão coulombiana,U (intra-sítio) eV (inter-sítio). Considerando uma simetria de troca local peculiar desta cadeia, bem como simetrias globais do hamiltoniano de Hubbard, utilizamos o método numérico do grupo de renormalização da matriz densidade com condições de contorno abertas e número de estados máximo, M =200, focalizando nossos esforços na determinação do estado fundamental do sistema. Obtivemos o diagrama de fases produzido pela competição entre U e V em condições de semi-preenchimento de banda, um elétron por sítio. Confrontamos nossos resultados, obtidos para um sistema de vinte e quatro células, com aqueles obtidos pelo método de diagonalização exata para um sistema com seis células. Foram identificadas três regiões relevantes: para V . U/4 encontramos uma fase ferrimagnética, que é uma continuação da fase encontrada em V = 0, a qual se enquadra no conhecido teorema de Lieb; para V & U/4, foram caracterizadas regiões de separação de fases com a coexistência de uma região isolante (paramagnética) e metálica (ferromagnética), e uma fase reminiscente daquela encontrada para U = 0. A caracterização das regiões foi realizada através da medida dos perfis de carga e de spin, bem como pelo estudo da energia em função dos parâmetros do modelo

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.

This project presents regional velocity measurements for the eastern portion of the St. Elias Mountains, including the entire glaciated area of Kluane National Park, derived from speckle tracking of Radarsat-2 imagery acquired in winter 2011 and 2012. This technique uses a cross-correlation approach to determine the displacement of the ‘speckle’ pattern of radar phase returns between two repeat-pass images. Further reconstruction of past velocities is performed on a selection of key glaciers using feature tracking of Landsat-5 imagery, allowing for the investigation of variability in glacier motion on interannual and decadal time scales. The results of the analysis showed that there is a strong velocity gradient across the region reflecting high accumulation rates on the Pacific-facing slope of the mountain range. These glaciers may have velocities an order of magnitude greater than glaciers of a similar size on the landward slope. Interannual variability was high, both in relation to surge events, of which a number were identified, and variation of other unknown controls on glacier motion. A long-term trend of velocity decrease was observed on the Kaskawulsh Glacier when comparing the results of this analysis to work carried out in the 1960s, the pattern of which is broadly congruent to measurements of surface elevation change over a similar period.

No description available.

Orientador: Vivian Vanessa França / Coorientador: Érica Regina Filetti Nascimento / Banca: Rodrigo Fernando Costa Marques / Banca: Sérgio Ricardo Muniz / Resumo: Nesse trabalho propomos o desenvolvimento de redes neurais artificiais capazes de fornecer a energia do estado fundamental do modelo de Hubbard para nanoestruturas fermiônicas interagentes e homogêneas. Uma vez otimizado o funcional via rede neural, este pode ser usado como input em cálculos de funcionais da densidade para sistemas heterogêneos. O modelo neural obtido mostrou um desempenho excelente, com desvios menores que ∼ 0,2%, recuperando todos os regimes de densidade, magnetização e uma vasta extensão de regimes de interação, quando comparado com resultados numéricos exatos. Comparado à funcionais analíticos, o modelo neural é mais preciso em todos os regimes de parâmetros, especialmente no regime de fraca interação, onde o funcional analítico mais recente apresenta um grande desvio: ∼ 7%, contra ∼ 0,1% para o nosso modelo neural. Aplicado em aproximações de densidade local para cálculos de DFT para cadeias finitas e com heterogeneidades, como impurezas localizadas e potenciais confinantes, nosso modelo neural se mostrou uma alternativa confiável e usando apenas uma fração dos recursos computacionais de outros tratamentos numéricos. / Abstract: In this work we propose an artificial neural network model to the ground-state energy of fermionic interacting particles in homogeneous chains described by the Hubbard model. Once the neural network functional is optimized, it can be used as input in density functional calculations for inhomogeneous systems. The neural network model obtained, showed excellent performance, deviating by less than ∼ 0.2%, recovering all regimes of density and magnetization and for a vast range of interactions when compared to exact numerical results. Compared to analytical functionals, the neural network is more accurate in all regimes of parameters, especially at the weakly interacting regime, where the most recent analytical parametrization fails the most: ∼ 7%, while only ∼ 0.1% for our neural network model. When applied in local density approximations for density functionals calculations for finite chains with inhomogeneities, such as localized impurities and confining potentials, our neural model has proven to be a reliable alternative, while using only a fraction of the computational resources from other numerical treatments. / Mestre

We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length lampta_2 on disorder and interaction strength is investigated. Our results demonstrate that the recently proposed enhancement of lampta_2 as compared to the results for single particles is entirely due to the finite size of the systems considered. This is shown for a Hubbard-like onsite interaction and also a long-range interaction.

We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder 1 c ss U= 2. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

We study two interacting particles in a random potential chain by a transfer matrix method which allows a correct handling of the symmetry of the two- particle wave function, but introduces an artificial ¨bag¨ interaction. The dependence of the two-particle localization length lambta 2on disorder, interaction strength and range is investigated. Our results demonstrate that the recently proposed enhancement of lambta 2 as compared to the results for single particles is vanishingly small for a Hubbard interaction. For longer-range interactions, we observe a small enhancement but with a different disorder dependence than proposed previously.

This thesis focuses on developing new approaches to solving the ground state properties of quantum many-body Hamiltonians, and the goal is to develop a systematic approach which properly balances efficiency and accuracy. Two new formalisms are proposed in this thesis: the Variational Discrete Action Theory (VDAT) and the Off-Shell Effective Energy Theory (OET). The VDAT exploits the advantages of both variational wavefunctions and many-body Green's functions for solving quantum Hamiltonians. VDAT consists of two central components: the Sequential Product Density matrix (SPD) and the Discrete Action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer N, and N controls the balance of accuracy and cost; monotonically converging to the exact solution for N → ∞. The Discrete Action emerges by treating the each projector in the SPD as an effective discrete time evolution. We generalize the path integral to our discrete formalism, which converts a dynamic correlation function to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism, which results in analogous but distinct mathematical structures due to the non-abelian nature of the SPD, yielding discrete versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We apply VDAT to two canonical models of interacting electrons: the Anderson impurity model (AIM) and the Hubbard model. We prove that the SPD can be exactly evaluated in the AIM, and demonstrate that N=3 provides a robust description of the exact results with a relatively negligible cost. For the Hubbard model, we introduce the local self-consistent approximation (LSA), which is the analogue of the dynamical mean-field theory, and prove that LSA exactly evaluates VDAT for d=∞. Furthermore, VDAT within the LSA at N=2 exactly recovers the Gutzwiller approximation (GA), and therefore N>2 provides a new class of theories which balance efficiency and accuracy. For the d=∞ Hubbard model, we evaluate N=2-4 and show that N=3 provides a truly minimal yet precise description of Mott physics with a cost similar to the GA. VDAT provides a flexible scheme for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework. VDAT will have broad applications in condensed matter and materials physics. In the second part of the thesis, we propose a different formalism, off-shell effective energy theory (OET), which combines the variational principle and effective energy theory, providing a ground state description of a quantum many-body Hamiltonian. The OET is based on a partitioning of the Hamiltonian and a corresponding density matrix ansatz constructed from an off-shell extension of the equilibrium density matrix; and there are dual realizations based on a given partitioning. To approximate OET, we introduce the central point expansion (CPE), which is an expansion of the density matrix ansatz, and we renormalize the CPE using a standard expansion of the ground state energy. We showcase the OET for the one band Hubbard model in d=1, 2, and ∞, using a partitioning between kinetic and potential energy, yielding two realizations denoted as K and X. OET shows favorable agreement with exact or state-of-the-art results over all parameter space, and has a negligible computational cost. Physically, K describes the Fermi liquid, while X gives an analogous description of both the Luttinger liquid and the Mott insulator. Our approach should find broad applicability in lattice model Hamiltonians, in addition to real materials systems. The VDAT can immediately be applied to generic quantum models, and in some cases will rival the best existing theories, allowing the discovery of new physics in strongly correlated electron scenarios. Alternatively, the OET provides a practical formalism for encapsulating the complex physics of some model and allowing extrapolation over all phase space. Both of the formalisms should find broad applications in both model Hamiltonians and real materials.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18058号 / 理博第3936号 / 新制||理||1567(附属図書館) / 30916 / 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 池田 隆介, 教授 川上 則雄, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM