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Thesis (Ph.D.)--Mississippi State University. Department of Physics and Astronomy. / Title from title screen. Includes bibliographical references.

Made available in DSpace on 2016-12-12T20:15:52Z (GMT). No. of bitstreams: 1 Jardel C Rosa.pdf: 4774739 bytes, checksum: 9ea21d5b6cb09221260d2f1f58e1333f (MD5) Previous issue date: 2016-09-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we propose a model to study the effect of electron correlation in the phase diagrams of itinerant magnetocaloric materials, where the conduction electrons are described by the Hubbard model, and that also includes the exchange interaction Jf d between localized and itinerant moments, an external magnetic field, and the exchange interaction Jf f between localized moments. We discuss the applicability of the model to intermetallic materials containing rare earth elements and transition metals, where the simultaneous presence of interacting localized moments and itinerant magnetism produces a peculiar behavior that is reflected in their magnetocaloric properties. As a first step, we treat the model within the mean-field approximation. From the computaion of the magnetization curves on a simple cubic lattice, we obtain the phase diagrams and investigate the magnetic phase transition and the magnetocaloric effect. In a second step, we use the alloy analogy approximation to treat Hubbard model, which provides a more detailed and realistic description for these materials. / Neste trabalho, propomos um modelo para estudar o efeito da correlação eletrônica nos diagramas de fases de materiais magnetocalóricos itinerantes, no qual os elétrons de condução d são descritos pelo modelo de Hubbard, e que inclui ainda uma interação de troca Jf d entre os momentos localizados e itinerantes, um campo magnético externo, e uma interação de troca Jf f entre os momentos localizados. Discutimos a aplicabilidade do modelo em materiais intermetálicos contendo elementos de terras raras e metais de transição, onde a presença simultânea de momentos localizados interagentes e do magnetismo itinerante produz um comportamento peculiar, que é refletido nas suas propriedades magnetocalóricas. Num primeiro estágio, tratamos o modelo dentro da aproximação de campo médio. A partir do cálculo das curvas de magnetização em uma rede cúbica simples, obtemos os diagramas de fases e investigamos as transições de fase magnéticas e o efeito magnetocalórico. Num segundo estágio, utilizamos a aproximação da analogia de liga para tratar o modelo de Hubbard, que fornece uma descrição mais detalhada e realista para esses materiais.

Title: Modelling of Ultracold Gases in Multidimensional Optical Lattices Author: Miroslav Urbanek Department: Department of Chemical Physics and Optics Supervisor: doc. Ing. Pavel Soldán, Dr. Abstract: Optical lattices are experimental devices that use laser light to confine ultracold neutral atoms to periodic spatial structures. A system of bosonic atoms in an optical lattice can be described by the Bose-Hubbard model. Although there exist powerful analytic and numerical methods to study this model in one dimension, their extensions to multiple dimensions have not been as successful yet. I present an original numerical method based on tree tensor networks to simulate time evolution in multidimensional lattice systems with a focus on the two-dimensional Bose-Hubbard model. The method is used to investigate phenomena accessible in current experiments. In particular, I have studied phase collapse and revivals, boson expansion, and many-body localization in two-dimensional optical lattices. The outcome of this work is TEBDOL - a program for modelling one-dimensional and two-dimensional lattice systems. Keywords: Bose-Hubbard model, multidimensional system, optical lattice, tensor network

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The study about magnetic properties of strongly correlated electrons has been an problem of interest in physics by the great technological importance of various materials with this characteristic. A well-known theoretical approach, known as the Hubbard model, has been used in an attempt to describe such phenomena. This model considers the interactions and electron mobility in a simplified way for describing phenomena like itinerant magnetism and the metal-insulator transition. In this study were analyzed the thermodynamic clusters properties of structures with fcc lattice symmetry containing 4, 5, 6, 7 and 8 sites. An exact numerical diagonalization method was used, where the subspaces of the problem were separatly analyzed and put together on, which is a procedure that reduces the processing data time. In order to improve the diagram of quantum states also carried out a ground state analysis of the clusters, known in the literature and obtained from systems with 4, 5 and 6 sites. On this subject a new diagram was developed showing the quantum states transition using the Lanczos method, applied to clusters with 4 to 8 sites in this case. Finally, a comparison was made between the thermodynamic properties and the results found in the new quantum state diagram. The agreement between them is good. / O estudo de propriedades magnéticas de elétrons fortemente correlacionados tem sido um problema de interesse da física pela grande importância tecnológica de vários materiais com essa característica. Uma famosa abordagem teórica, conhecida como modelo de Hubbard, vem sendo utilizada na tentativa de descrever esse tipo fenômeno. Esse modelo considera interações e a mobilidade eletrônica descrevendo de forma simplificada fenômenos como magnetismo itinerante e transição metal-isolante. Neste trabalho foram analisadas propriedades termodinâmicas de clusters de estruturas com simetria da rede fcc contendo 4, 5, 6, 7 e 8 sítios. Foi utilizado um método de diagonalização numérica exata, onde os subespaços do problema foram analisados separadamente e reunidos posteriormente, procedimento que reduz o tempo de processamento dos dados. Foi também realizada uma análise do estado fundamental dos clusters com o intuito de aprimorar o diagrama de estados quânticos, conhecido na literatura, obtido a partir de sistemas com 4, 5 e 6 sítios. Sobre esse assunto, foi desenvolvido um novo diagrama que indica a transição de estados quânticos a partir da utilização do método de Lanczos, neste caso, aplicado a clusters de 4 a 8 sítios. Por fim, foi feita uma análise comparativa entre as propriedades termodinâmicas e os resultados encontrados no novo diagrama de estados quânticos que mostraram boa coerência entre si.

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.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18780号 / 理博第4038号 / 新制||理||1581(附属図書館) / 31731 / 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 戸塚 圭介, 教授 川上 則雄, 教授 佐々 真一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

We study the unusual phases seen in charge transfer salts (CTS) at 1/2 and 1/4 filling. We use the Holstein-Hubbard model (HHM) and the Peierls extended Hubbard model (PEH) to study competing phases in CTS. In the 1/2illed HHM the Holstein coupling promotes a Peierls charge-density wave phase while the on-site Coulomb repulsion U gives rise to antiferromagnetic correlations and a Mott insulating state. Takada et al. have shown possibility of a third metallic phase between the Mott and the Peierls phase. We investigate the presence of an intermediate phase between the Mott and Peierls phase using Stochastic Series Expansion (SSE) method. We used charge and spin susceptibilities to determine the phase boundaries. As the coupling is increased a spin gap opens followed by the Peierls transition. The intermediate phase is metallic and has a spin gap but no charge gap. Transitions from the Mott to intermediate and intermediate to Peierls state are Kosterlitz-Thouless type (KT). As the coulomb repulsion is increaed beyond certain value the two KT transitions fuse to give a single first order transition. Similar behavior is seen at 1/4illed HHM. We also studied the temperature dependence of charge ordering (CO) in 1/4illed CTS. Most previous theoretical studies of the on CTS have concentrated on ground state or T=0 properties. Here we show the evolution of charge ordered (CO) state with temperature and directly related the experimental phase diagram with our theoretical results. Our calculations show that as temperature is lowered the Wigner crystal state gives way to spin-Peierls state with a different pattern of CO. Also we show that the critical value of nearest neighbor Coulomb repulsion is depends on the total spin and is different for different spin subspace.

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