Made available in DSpace on 2014-06-11T19:23:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-04-11Bitstream added on 2014-06-13T19:29:34Z : No. of bitstreams: 1 simon_ra_me_bauru.pdf: 585170 bytes, checksum: 22e864a53f831e4bf21be6c6b81ed2f3 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Na área de pesquisa em sistemas de elétrons fortemente correlacionados, o modelo das super-redes Hubbard tem sido utilizada para explicar e prever comportamentos de heteroestruturas, como multicamadas magnéticas, que apresentam propriedades diferentes e incomuns, comparadas com as dos sistemas homogêneos análogos, E.G., ordenamentos magnéticos e de carga. Neste contexto, foram estudados nesta dissertação os efeitos da introdução de um novo valor , 'T IND. C', para o parâmetro de hopping de elétron nas interfaces de camadas diferentes da super-rede, ou seja, introduziu-se uma modulação na condução entre as camadas. Variou-se 'T IND. C'entre 0.1T e T, onde T é o parâmetro de hopping entre sítios da mesma camada. Para a lacuna de carga encontramos um comportamento dependente da densidade eletrônica na rede. Em geral, momentos magnéticos locais e a ocupação eletrônica nos sítios, apresentam uma distribuição mais uniforme para 'T IND. C'=0.1T. No entanto, nas densidades onde ocorre um aumento abrupto na lacuna de carga com a diminuição de 'T IND. C', essa uniformidade é mais pronunciada, possivelmente devido a uma comensurabilidade entre a distribuição dos elétrons na cadeia e a estrutura da super-rede. Para as funções de correlação de carga, que foram estudadas através do fator de estrutura, encontramos em alguns casos uma dependência em 'T IND. C' do período do ordenamento correspondente. / In the research field of strongly correlated electron systems, the Hubbard superlattice model has been used for explain and predict the behavior of heterostructures, such as magnetic multilayers, whose unusual properties differ from the properties of the analogous homogeneous counterpart. In this context, we have studied here the effects of introducing a new value for the hopping parameter, 'T IND. C', for electrons between different layers, E.G., we introduced a modulation in the electronic conduction between layers. We consider 'T IND. C' in the range 0.1T to T, where T is the hopping parameter for sites inside the layers. For the charge gap, we found a behavior that depends on the electronic density in the lattice. Local magnetic and electronic occupation on sites, generally, show a greater uniformity with decreasing 'T IND. C'. However, for electronic densities where is an abrupt increase in the charge gap for decreasing 'T IND. C', this uniformity is enhanced, probably due to a commensurability between the electronic distribution in the chain and the underlying superlattice structure. For the charge correlation functions, that were studied through their structure factor, we found in some cases a dependency in 'T IND. C' of the correlations oscillation period.

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.

No description available.

Magnetic frustration is a phenomenon arising in spin systems when spin interactions cannot all be satisfied at the same time. A typical example of geometric frustration is a triangle with Ising-spins at its vertices and antiferromagnetic interaction. While we can easily anti-align two neighbouring spins, it is not possible for the third one to simultaneously anti-align with both of them. Another flavour of magnetic frustration is the so called exchange frustration, where different spin components interact in an Ising fashion on different bonds. Moreover, frustrated spin systems give rise to exotic states of matter, such as spin liquids, spin ices and nematic phases. As frustrated systems are rarely analytically solvable, numerical techniques are of the utmost importance in this framework. This dissertation is concerned with a specific class of models, namely one- and quasi-one-dimensional spin systems and studies their properties by making use of the density matrix renormalisation group technique. This method has been shown to be extremely powerful and reliable to study chain and ladder models. We consider examples of both geometric and exchange frustration. For the former, we take into consideration one of the prototypical examples of geometric frustration in one dimension: the J1-J2 model with ferromagnetic nearest-neighbour interaction J1<0 and antiferromagnetic next-nearest-neighbour interaction J2>0. Our results show the existence of a Haldane gap supported by a special AKLT-like valence bond solid state in a specific region of the coupling ratio. Furthermore, we consider the effect of dimerisation of the first-neighbour coupling. This dimerisation affects the critical point and the ground state underlying the spin gap. These models are of interest in the context of cuprate chain materials such as LiVCuO4, LiSbCuO4 and PbCuSO4(OH)2. Concerning exchange frustration, we consider the celebrated Kitaev-Heisenberg model: it is an extension of the exactly solvable Kitaev model with an additional Heisenberg interaction. The Kitaev-Heisenberg model is currently the minimal model for candidate Kitaev materials. The extended model is not analytically solvable and numerics are needed to study the properties of the system. While both the original Kitaev and the Kitaev-Heisenberg models live on a honeycomb lattice, we here perform systematic studies of the Kitaev-Heisenberg chain and of the two-legged ladder. While the chain cannot support a Kitaev spin liquid state, it shows nevertheless a rich phase diagram despite being a one-dimensional system. The long-range ordered states of the honeycomb can be understood in terms of coupled chains within the Kitaev-Heisenberg model. Following this reasoning, we turn our attention to the Kitaev-Heisenberg model on a two-legged ladder. Remarkably, the phase diagram of the ladder is extremely similar to that of the honeycomb model and the differences can be explained in terms of the different dimensionalities. In particular, the ladder exhibits a topologically non-trivial phase with no long-range order, i.e., a spin liquid. Finally, we investigate the low-lying excitations of the Kitaev-Heisenberg model for both the chain and the ladder geometry.

Multireference coupled cluster (MRCC) methods are a highly accurate approach for sys- tems with quasi-degeneracies, where the static correlation plays an important role. How- ever, while canonical MRCC is successful for many systems, it can be used only for small sized systems. Nonetheless, it was shown that large systems can be described by the domain-based local pair natural orbital approach (DLPNO). In our group, we developed DLPNO-MkCCSD, DLPNO-TCCSD and DLPNO-MkCCSD(T) methods, which were able to recover more than 99.7% of the canonical correlation energy, while the computation of systems with more than 2000 basis functions took only a few hours on a single CPU core. Moreover, we also implemented a tailored variant of MRCC which successfully described excited states of cyclobutadiene, while the traditional MRCC under-performed.

Quantification of stochastic or quantum systems by a joint probability density or wave function is a notoriously difficult computational problem, since the solution depends on all possible states (or realizations) of the system. Due to this combinatorial flavor, even a system containing as few as ten particles may yield as many as $10^{10}$ discretized states. None of even modern supercomputers are capable to cope with this curse of dimensionality straightforwardly, when the amount of quantum particles, for example, grows up to more or less interesting order of hundreds. A traditional approach for a long time was to avoid models formulated in terms of probabilistic functions, and simulate particular system realizations in a randomized process. Since different times in different communities, data-sparse methods came into play. Generally, they aim to define all data points indirectly, by a map from a low amount of representers, and recast all operations (e.g. linear system solution) from the initial data to the effective parameters. The most advanced techniques can be applied (at least, tried) to any given array, and do not rely explicitly on its origin. The current work contributes further progress to this area in the particular direction: tensor product methods for separation of variables. The separation of variables has a long history, and is based on the following elementary concept: a function of many variables may be expanded as a product of univariate functions. On the discrete level, a function is encoded by an array of its values, or a tensor. Therefore, instead of a huge initial array, the separation of variables allows to work with univariate factors with much less efforts. The dissertation contains a short overview of existing tensor representations: canonical PARAFAC, Hierarchical Tucker, Tensor Train (TT) formats, as well as the artificial tensorisation, resulting in the Quantized Tensor Train (QTT) approximation method. The contribution of the dissertation consists in both theoretical constructions and practical numerical algorithms for high-dimensional models, illustrated on the examples of the Fokker-Planck and the chemical master equations. Both arise from stochastic dynamical processes in multiconfigurational systems, and govern the evolution of the probability function in time. A special focus is put on time propagation schemes and their properties related to tensor product methods. We show that these applications yield large-scale systems of linear equations, and prove analytical separable representations of the involved functions and operators. We propose a new combined tensor format (QTT-Tucker), which descends from the TT format (hence TT algorithms may be generalized smoothly), but provides complexity reduction by an order of magnitude. We develop a robust iterative solution algorithm, constituting most advantageous properties of the classical iterative methods from numerical analysis and alternating density matrix renormalization group (DMRG) techniques from quantum physics. Numerical experiments confirm that the new method is preferable to DMRG algorithms. It is as fast as the simplest alternating schemes, but as reliable and accurate as the Krylov methods in linear algebra.

FAPEMIG - Fundação de Amparo a Pesquisa do Estado de Minas Gerais / Neste trabalho, investigamos propriedades estáticas e dinâmicas de sistemas fortemente correlacionados quase-unidimensionais. A principal técnica utilizada no estudo de tais sistemas foi o grupo de renormalização da matriz de densidade. Neste contexto, um dos sistemas que consideramos foram as escadas de Heisenberg de N pernas com spin-s. Para estas escadas, investigamos propriedades estáticas, tais como energia por sítio no limite termodinâmico e gap de spin. Em particular, verificamos a validade da conjectura de Haldane-Sénéchal-Sierra para o comportamento do gap de spin das escadas de Heisenberg. Ainda para sistemas com geometria de escadas, outro problema que analisamos foi a entropia de emaranhamento de escadas quânticas críticas. Neste caso, propusemos uma conjectura para o comportamento de escala desta entropia. A fim de verificar nossa conjectura, consideramos as escadas férmions livres, de Heisenberg e escadas de Ising quânticas. Por fim, investigamos o comportamento das correlações dinâmicas de sistemas fortemente correlacionados unidimensionais. Para este caso, apresentamos um estudo detalhado do comportamento assintótico das autocorrelações de spin dinâmicas no bulk e na borda de tais sistemas. / In this work, we investigated static and dynamical properties of quasi-one-dimensional strongly correlated systems. The main technique used in the study of such systems was the density matrix renormalization group. In this context, one of the systems that we considered were the spin-s N-leg Heisenberg ladders. For these ladders, we investigated static properties, such as the energy per site in the thermodynamic limit and the spin gap. In particular, we checked the validity of the Haldane-Sénéchal-Sierra's conjecture for the spin gap behavior of the Heisenberg ladders. Also for systems with ladders geometry, another problem that we analyzed was the entanglement entropy of quantum critical ladders. In this case, we proposed a conjecture for the scaling behavior of this entropy. In order to check our conjecture, we consider free fermions, Heisenberg ladders and quantum Ising ladders. Finally, we investigated the behavior of the dynamical correlations in one-dimensional strongly correlated systems. For this case, we presented a detailed study of the asymptotic behavior of the dynamical spin autocorrelations at the bulk and the boundary of such systems. / Tese (Doutorado)

No description available.

Porphyrins are an important class of biomolecules, which are heavily studied, both ex- perimentally and computationally. But, despite the intensive efforts, for many questions we still aren't able to consistently find an agreement between theory and experiment. One of the still unresolved issues is the character of the ground state of the Fe(II)-porphyrin molecule. We used a model of the Fe(II)-porphyrin molecule to study the effects of geometrical changes on the spin states. By carrying out extensive DMRG-CASSCF cal- culations topped with TCCSD correlation treatment we are able to link the effects of these geometrical changes to the experimental results, and predict a quintet ground state for the isolated Fe(II)-porphyrin molecule. Also, using a ligated porphyrin belonging to the iron porphyrin carbene class of molecules, we demonstrate by combining the CASSCF and AC0 methods that geometrical changes outside the porphyrin core cannot be over- looked. 1

<p>In this thesis we discuss in detail the density-matrix renormalization group (DMRG) for simulating low-energy properties of quantum spin models. We implement an original DMRG routine on the S=1/2 antiferromagnetic Heisenberg chain and benchmark its efficiency against exact results (energies, correlation functions, etc.) as well as conformal field-theoretical calculations due to finite-size scaling (ground-state energy and spin gap logarithmic corrections). Moreover, we apply the DMRG to a two-leg square ladder system, where in addition to bilinear exchange terms, we also consider an additional cyclic four-spin ring-exchange. The transposition of four spins gives rise to biquadratic exchange terms which are non-trivial to implement in the DMRG. Intermediate results of the ring-exchange are presented along with the difficulties presently encountered.</p> / Master of Science (MSc)