This work presents a study of the electronic structure of four transition metal oxides (TMOs) using spectroscopic data and a variety of theoretical models. TMOs are a class of materials made from d-block metals in the periodic table, and one or more oxygen atoms. The nature of d-electrons is examined and theoretical models used to treat d-electron systems are tested against experimental data. Background theory of condensed matter physics is outlined. An overview of density functional theory (DFT) as a theoretical model for calculating the electronic structure of materials is presented. A variety of exchange-correlation (XC) functionals used within the DFT framework are outlined and tested for their applicability to the TMO systems in question. X-ray spectroscopy is briefly outlined and used to test the validity of the different XC functionals. All four compounds, AgO, Ag2O, CuO, and Cu2O require a Hubbard U term in the XC functional to most accurately reproduce experimental results. The effects of varying the value of U is examined in depth. The oxygen K-edge X-ray emission spectra (XES) exhibits a“two peak” structure for all compounds; the effect of varying the U value is to change the intensity ratio of the two peaks. The ratio of the two peaks as a function of U shows a linear trend in all compounds. A simple line is fit to the peak ratio vs. U curve. A common line between all compounds would provide an important metric with which to predict the appropriate U value needed in similar materials based on simple experimental data. However, the parameters of the fitted line were not common between the four compounds and any metric derived from this method would be system-dependent and not widely applicable to other systems. There are, however, interesting trends in the data when the U value is varied that provide subjects for future research. A number of fundamental quantities are determined both from experiment and theoretical calculations. Calculated bandgap values are shown to be lower than the experimental values for most functionals tested. This is not unexpected as DFT methods are known to predict much smaller bandgaps than expected. The Heyd-Scuseria-Ernzerhof (HSE) functional used for Ag2O and Cu2O does predict the bandgaps very accurately. The core-hole effect is estimated and proven to be negligible in these systems. Charge transfer and on-site Coulomb repulsion energies, important quantities in the electronic behaviour of TMOs, are determined and compared to previously reported values.

Les applications reliées à la génération d'énergie motivent la recherche de matériaux ayant un fort pouvoir thermoélectrique (S). De plus, S nous renseigne sur certaines propriétés fondamentales des matériaux, comme, par exemple, la transition entre l'état cohérent et incohérent des quasi-particules lorsque la température augmente. Empiriquement, la présence de fortes interactions électron-électron peut mener à un pouvoir thermoélectrique géant. Nous avons donc étudié le modèle le plus simple qui tient compte de ces fortes interactions, le modèle de Hubbard. La théorie du champ moyen dynamique (DMFT) est tout indiquée dans ce cas. Nous nous sommes concentrés sur un système tridimensionnel (3d) cubique à face centrée (fcc), et ce, pour plusieurs raisons. A) Ce type de cristal est très commun dans la nature. B) La DMFT donne de très bons résultats en 3d et donc ce choix sert aussi de preuve de principe de la méthode. C) Finalement, à cause de la frustration électronique intrinsèque au fcc, celui-ci ne présente pas de symétrie particule-trou, ce qui est très favorable à l'apparition d'une grande valeur de S. Ce travail démontre que lorsque le matériau est un isolant à demi-remplissage à cause des fortes interactions (isolant de Mott), il est possible d'obtenir de grands pouvoirs thermoélectriques en le dopant légèrement. C'est un résultat pratique important. Du point de vue méthodologique, nous avons montré comment la limite de fréquence infinie de S et l'approche dite de Kelvin, qui considère la limite de fréquence nulle avant la limite thermodynamique pour S, donnent des estimations fiables de la vraie limite continue (DC) dans les domaines de température appropriée. Ces deux approches facilitent grandement les calculs en court-circuitant la nécessité de recourir à de problématiques prolongements analytiques. Nous avons trouvé que la méthode de calcul à fréquence infinie fonctionne bien lorsque les échelles d'énergie sont relativement faibles. En d'autres termes, cette approche donne une bonne représentation de S lorsque le système devient cohérent. Les calculs montrent aussi que la formule Kelvin est précise lorsque la fonction spectrale des électrons devient incohérente, soit à plus haute température. Dans la limite Kelvin, S est essentiellement l'entropie par particule, tel que proposé il y a longtemps. Nos résultats démontrent ainsi que la vision purement entropique de S est la bonne dans le régime incohérent, alors que dans le régime cohérent, l'approche à fréquence infinie est meilleure. Nous avons utilisé une méthode à la fine pointe, soit le Monte-Carlo quantique en temps continu pour résoudre la DMFT. Pour permettre une exploration rapide du diagramme de phase, nous avons dû développer une nouvelle version de la méthode des perturbations itérées pour qu'elle soit applicable aussi à forte interaction au-delà de la valeur critique de la transition de Mott. Un autre sujet a aussi été abordé. L'effet orbital du champ magnétique dans les systèmes électroniques fortement corrélés est une question très importante et peu développée. Cela est d'autant plus essentiel depuis la découverte des oscillations quantiques dans les supraconducteurs à haute temperature (haut-T[indice inférieur c]). Par désir de développer une méthode la moins biaisée possible, nous avons dérivé la DMFT lorsqu'un champ se couplant à l'opérateur énergie cinétique par la substitution de Peierls est présent. Ce type d'approche est nécessaire pour comprendre entre autres l'effet de la physique de Mott sur des phénomènes tels que les oscillations quantiques. Nous avons obtenu un résultat très important en démontrant rigoureusement que la relation d'auto-cohérence de la DMFT et le système intermédiaire d'impureté quantique restent les mêmes. L'effet du champ peut être contenu dans la fonction de Green locale, ce qui constitue la grande différence avec le cas habituel. Ceci permet de continuer à utiliser les solutionneurs d'impuretés standards, qui sont de plus en plus puissants. Nous avons aussi développé la méthode pour le cas d'un empilement de plans bidimensionnels selon z, ce qui permet d'étudier l'effet orbital du champ dans des nanostructures et même dans les matériaux massifs, si le nombre de plans est suffisant pour obtenir la limite tridimensionnelle.

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

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

We study the phase transition super uid-Mott insulator in optical lattices through model Jaynes-Cummings-Hubbard using the fermion approximation. Initially we did a review of the Jaynes-Cummings model that is a model that describes the interaction between an atom with two levels and a quantized electromagnetic eld. Then we stu- died the properties of the phase transition super uid-Mott insulator (SF-MI) through the model Bose-Hubbard and we discuss the characteristics of the two quantum phases and the conditions for phase transition. Apply the model Jaynes-Cummings-Hubbard in order to study the in uence of topology of network Bravais linear, square, single cubic (SC), body-centered cubic (BCC) and face-centered cubic (FCC) in the phase transi- tion SF-MI to different numbers of excitation and different detuning values between the atom and the eld and we found that the Mott lobes and the critical hopping terms are not renormalizable only for the FCC network. But the regime from many excitations, the critical hopping is renormalizable to all networks and is independent of detuning. Then we study the Jaynes-Cummings-Hubbard model for a chain with the addition of the Kerr effect (nonlinear optical effect) through the approximation of fermions (FA). We observed that the Kerr effect does not cause large changes in the energy spectrum. However, the properties of the phase transition SF-MI undergoes signicant changes due to the Kerr effect. Another important feature which has been observed is that the Kerr effect favors the phase MI. / Estudamos a transi¸c ao de fase superfluido-isolante de Mott (SF-MI) em redes ´opticas via modelo Jaynes-Cummings-Hubbard utilizando a aproxima¸c ao de f´ermions. Inicialmente fazemos uma revis ao do modelo Jaynes-Cummings que descreve a intera¸c ao de um ´atomo de dois n´ıveis com um campo eletromagn´etico quantizado. Em seguida estudamos as propriedades da transi¸c ao de fase SF-MI no modelo Bose-Hubbard e discutimos as caracter´ısticas das duas fase qu anticas e as condi¸c oes para a transi¸c ao de fase. Aplicamos o modelo Jaynes-Cummings-Hubbard com a finalidade de estudarmos a influ encia da topologia das redes de Bravais linear, quadrada, c´ubica simples (SC), c´ubica de corpo centrado (BCC) e c´ubica de faces centradas (FCC) na transi¸c ao de fase SF-MI para diferentes n´umeros de excita¸c ao e diferentes valores de dessintonia entre o ´atomo e o campo e encontramos que os l´obulos de Mott n ao s ao renormaliz ´aveis apenas para a rede FCC. Mas no regime de muitas excita¸c oes, as redes BCC e FCC passam a ter o mesmo comportamento enquanto que as demais continuam com sua depend encia no n´umero de vizinhos. Em seguida, estudamos o modelo de Jaynes-Cummings-Hubbard para uma cadeia com a adi¸c ao do efeito tipo Kerr (efeito ´optico n ao-linear) atrav´es da aproxima¸c ao de f´ermions (FA). Observamos que o efeito tipo Kerr n ao provoca grandes altera¸c oes no espectro de energia. No entanto, as propriedades de transi¸c ao de fase SF-MI passam por mudan¸cas significativas devido ao efeito tipo Kerr. Outra caracter´ıstica importante que foi observada ´e que o efeito tipo Kerr favorece a fase MI.

Recent research involving magnetic polymers have given very promising results. It is observed in these polymers, the ability to remain magnetized even in the absence of magnetic field which is of great importance to developing new technologies. In order to deepen the knowledge these polymers, in special, its magnetic properties, many researchers have developed theories and methods. In this paper, we use the model developed by Hubbard in 1963. It is a relatively simple model, with important approaches that do not compromise on fundamental analysis, such polymers. With the Hubbard model as a basis, we take a model for the polymer chain in the case of a chain of sub-lattices which one contains the term and the other metal would be the term ligand of the chain. The chain is described as AXBX+1, where A and B are sub-lattices and X gives the size of the chain. We developed this model observing their magnetic properties according to the interaction applied and the number of particles per site building the magnetic phase diagram for different networks AXBX+1. / Recentemente as pesquisas envolvendo polímeros magnéticos têm dado resultados muito promissores. Observa-se nestes polímeros, a capacidade de manteremse magnetizados mesmo na ausência de campo magnético o que é de grande importância para desenvolvimento de novas tecnologias. A fim de aprofundar o conhecimento sobre estes polímeros, em especial, suas propriedades magnéticas, muitos pesquisadores desenvolveram teorias e métodos. Neste trabalho, utilizaremos o modelo desenvolvido por Hubbard em 1963. Trata-se de um modelo relativamente simples, com aproximações importantes que não comprometem análises fundamentais sobre estes polímeros. Com o modelo de Hubbard como base, tomamos um modelo para a cadeia polimérica tratando-se de uma cadeia com sub-redes as quais uma delas contém o termo metálico e a outra teria o termo ligante da cadeia. A cadeia é descrita como AXBX+1, onde A e B são as sub-redes e X dá a dimensão da cadeia. Desenvolvemos este modelo observando suas propriedades magnéticas de acordo com a interação aplicada e o número de partículas por sítio da rede construindo o diagrama de fases magnéticas para diversas redes AXBX+1.

No description available.

京都大学 / 0048 / 新制・課程博士 / 博士(人間・環境学) / 甲第22792号 / 人博第963号 / 新制||人||228(附属図書館) / 2020||人博||963(吉田南総合図書館) / 京都大学大学院人間・環境学研究科相関環境学専攻 / (主査)教授 森成 隆夫, 教授 吉田 鉄平, 准教授 藤原 直樹 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM

No description available.

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.