Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 47-48). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--Florida State University, 2005. / Advisor: Dr. James S. Brooks, Florida State University, College of Arts and Sciences, Dept. of Physics. Title and description from dissertation home page (viewed Sept. 15, 2005). Document formatted into pages; contains xiii, 120 pages. Includes bibliographical references.

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Within condensed matter physics, systems with strong electronic correlations give rise to fascinating phenomena which characteristically require a physical description beyond a one-electron theory, such as high temperature superconductivity, or Mott metal-insulator transitions. In this thesis, a class of strongly correlated electron systems is considered. These systems exhibit fractionally charged excitations with charge +e/2 or -e/2 in two dimensions (2D) and three dimensions (3D), a consequence of both strong correlations and the geometrical frustration of the interactions on the underlying lattices. Such geometrically frustrated systems are typically characterized by a high density of low-lying excitations, leading to various interesting physical effects. This thesis constitutes a study of a model of spinless fermions on the geometrically frustrated kagome lattice. Focus is given in particular to the regime in which nearest-neighbour repulsions V are large in comparison with hopping t between neighbouring sites, the regime in which excitations with fractional charge occur. In the classical limit t = 0, the geometric frustration results in a macroscopically large ground-state degeneracy. This degeneracy is lifted by quantum fluctuations. A low-energy effective Hamiltonian is derived for the spinless fermion model for the case of 1/3 filling in the regime where |t| << V . In this limit, the effective Hamiltonian is given by ring-exchange of order ~ t^3/V^2, lifting the degeneracy. The effective model is shown to be equivalent to a corresponding hard-core bosonic model due to a gauge invariance which removes the fermionic sign problem. The model is furthermore mapped directly to a Quantum Dimer model on the hexagonal lattice. Through the mapping it is determined that the kagome lattice model exhibits plaquette order in the ground state and also that fractional charges within the model are linearly confined. Subsequently a doped version of the effective model is studied, for the case where exactly one spinless fermion is added or subtracted from the system at 1/3 filling. The sign of the newly introduced hopping term is shown to be removable due to a gauge invariance for the case of hole doping. This gauge invariance is a direct result of the bipartite nature of the hole hopping and is confirmed numerically in spectral density calculations. For further understanding of the low-energy physics, a derivation of the model gauge field theory is presented and discussed in relation to the confining quantum electrodynamic in two dimensions. Exact diagonalization calculations illustrate the nature of the fractional charge confinement in terms of the string tension between a bound pair of defects. The calculations employ topological symmetries that exist for the manifold of ground-state configurations. Dynamical calculations of the spectral densities are considered for the full spinless fermion Hamiltonian and compared in the strongly correlated regime with the doped effective Hamiltonian. Calculations for the effective Hamiltonian are then presented for the strongly correlated regime where |t| << V . In the limit g << |t|, the fractional charges are shown to be effectively free in the context of the finite clusters studied. Prominent features of the spectral densities at the Gamma point for the hole and particle contributions are attributed to approximate eigenfunctions of the spinless fermion Hamiltonian in this limit. This is confirmed through an analytical derivation. The case of g ~ t is then considered, as in this case the confinement of the fractional charges is observable in the spectral densities calculated for finite clusters. The bound states for the effectively confined defect pair are qualitatively estimated through the solution of the time-independent Schroedinger equation for a potential which scales linearly with g. The double-peaked feature of spectral density calculations over a range of g values can thus be interpreted as a signature of the confinement of the fractionally charged defect pair. Furthermore, the metal-insulator transition for the effective Hamiltonian is studied for both t > 0 and t < 0. Exact diagonalization calculations are found to be consistent with the predictions of the effective model. Further calculations confirm that the sign of t is rendered inconsequential due to the gauge invariance for g in the regime |t| << V . The charge-order melting metal-insulator transition is studied through density-matrix renormalization group calculations. The opening of the energy gap is found to differ for the two signs of t, reflecting the difference in the band structure at the Fermi level in each case. The qualitative nature of transition in each case is discussed. As a step towards a realization of the model in experiment, density-density correlation functions are introduced and such a calculation is shown for the plaquette phase for the effective model Hamiltonian at 1/3 filling in the absence of defects. Finally, the open problem of statistics of the fractional charges is discussed.

Thesis (Ph.D.) -- McMaster University, 1999. / Disk in pocket. Includes bibliographical references (leaves 232-237). Also available via World Wide Web.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 142-151).

Orientador: Eduardo Miranda / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin. / Made available in DSpace on 2018-08-13T03:42:46Z (GMT). No. of bitstreams: 1 Miranda_DanielCesarBoscode_M.pdf: 4501306 bytes, checksum: ea9cd3602fb6488ef97069a6df6ae49c (MD5) Previous issue date: 2009 / Resumo: O objetivo deste trabalho é estudar os efeitos da desordem nas proximidades da transição metal-isolante de Mott. Para tanto, utilizamos o modelo de Hubbard desordenado em duas dimensões. A teoria que aplicamos para estudar esse modelo é a Teoria Estatística Dinâmica de Campo Médio, que trata de maneira não-trivial os efeitos de desordem e interação elétron-elétron. A aproximação básica da teoria consiste em descrever os efeitos de interação de maneira local. Nela mapeamos o nosso problema original em vários problemas de uma impureza de Anderson, embebidos em banhos que são determinados através de uma condição de autoconsistência. Esses problemas são resolvidos no nosso trabalho aplicando o método do Monte Carlo Quântico, algoritmo Hirsch-Fye, que faz cálculos em temperatura finita. No nosso estudo conseguimos observar a coexistência de soluções metálicas ruins e isolantes ruins num mesmo sistema, para temperaturas um pouco maiores do que a que determina o ponto crítico da transição de Mott. Relacionamos a condutividade local com as energias locais desordenadas, observando que essas energias funcionam como um potencial químico dependente do sítio que altera localmente a dopagem do sistema. Finalmente, verificamos o aumento do valor da interação crítica com a desordem. Esse trabalho é a primeira implementação numérica da Teoria Estatística Dinâmica de Campo Médio com Monte Carlo Quântico, que é o estado da arte de cálculos de sistemas de uma impureza única. Nesse sentido, nosso trabalho representa um importante primeiro passo na implementação do método e fornece um paradigma inicial do seu poder e das suas limitações. / Abstract: The main goal of this work is to study the effects of disorder in the proximity of a Mott metal-insulator transition. For that, we use the disordered Hubbard model in two dimensions. The theory we aply to study this model is the Statistical Dynamical Mean Field Theory, which treats the effects of disorder and electron-electron interactions in a non-trivial fashion. The basic aproximation of that theory is to describe the effects of interactions in a local way. In this theory we map the original system in several Anderson single-impurity problems, embebbed in baths that are determined through a self-consistency condition. These problems are solved in our work through the Quantum Monte Carlo method, with the Hirsch-Fye algorithm, at finite temperature. In our study, we found the coexistence of bubbles of bad metal and bad insulator in the same system, for temperatures a little higher than that which determines the critical point of the Mott transition. We could relate the local conducting properties with the local disordered energies, finding that these energies work like a site-dependent chemical potential which changes locally the doping of the system. Finally, we verified the enhancement of the critical interaction by disorder. This work is the first numerical implementation of the Statistical Dynamical Mean Field Theory with the Quantum Monte Carlo, which is the state of art for calculations of single-impurity systems. In this sense, our work is an important first step in the implementation of the method and sets a preliminary benchmark of its power and limitations. / Mestrado / Física da Matéria Condensada / Mestre em Física

High-quality lattice-matched LaNiO3/LaMnO3 superlattices with monolayer terrace structure have been grown on both (111)- and (001)-oriented SrTiO3 substrates by pulsed laser deposition. In contrast to the previously reported experiments, a magnetic exchange bias is observed that reproducibly occurs in both (111)- and (001)-oriented superlattices with the thin single layers of 5 and 7 unit cells, respectively. The exchange bias is theoretically explained by charge transfer-induced magnetic moments at Ni atoms. Furthermore, magnetization data at low temperature suggest two magnetic phases in the superlattices, with Néel temperature around 10 K. Electrical transport measurements reveal a metal-insulator transition with strong localization of electrons in the superlattices with the thin LaNiO3 layers of 4 unit cells, in which the electrical transport is dominated by two-dimensional variable range hopping.

In this dissertation we report on the application of the Liouville Operator Resolvent technique (LRM) to two hamiltonians used to model highly correlated systems: Falicov-Kimball and Anderson Lattice. We calculate specific heats, magnetic susceptibilities, thermal averages of physical operators, and energy bands. We demonstrate that the LRM is a viable method for investigating many body problems. For the Falicov-Kimball, an exact calculation of the atomic limit shows no sharp metal-insulator transition. A truncation approximation for the full hamiltonian has a smooth evolution from the atomic limit with the opening of a band for the conduction electrons. No phase transition was observed. A bose space calculation using the proper boson norm indicates that the conduction band induces a correlation between localized electrons on nearest-neighbor sites. It is not known if this effect is real or a by-product of the approximation. We applied the LRM to the Anderson Lattice and several of its limiting cases. In the limit of no hybridization, for both the symmetric and asymmetric (mixed-valence) parameter sets, we found that the thermodynamics could be described as competition between closely-lying energy levels. The effects that dominate are those that minimize the thermal average of the hamiltonian. A simple model is presented in which only hybridization between two localized orbitals is allowed. It shows that hybridization can give rise to mixed valence phenomena as the temperature approaches zero. For the full Anderson Lattice hybridization causes relatively small shifts in the occupation numbers of the localized and conduction electrons. However, these shifts can have dramatic effects on the physical properties as demonstrated by the magnetic susceptibilities. Band structures of the eigenenergies of the Liouville operator, for both parameter sets, reveal that low-lying excitations associated with some of the basis vector operators may split out from the fermi level and become significant at low temperatures. In addition, we report on progress toward extending the calculation to bose space using a commutator norm. / Ph. D. / incomplete_metadata

Dans cette thèse nous avons étudié des indicateurs visant à caractériser les propriétés métalliques ou isolantes de systèmes de basse dimensionnalité à partir de calculs théoriques basés sur la fonction d'onde. Ces systèmes sont intéressants car ils permettent une compréhension en profondeur des phénomènes physiques qui peuvent ensuite être extrapolés à des systèmes plus étendus. Afin de réaliser cette étude nous avons utilisé un nouvel outil basé sur la théorie de la conductivité de Kohn : le tenseur de délocalisation total ou total position spread-tensor (TPS). Ce tenseur est défini comme le second cumulant de l'opérateur position : ? = <?|X2|?> - <?|X|?>2. Divisé par le numéro des électrons, il diverge quand la fonction d'onde est fortement délocalisée (forte fluctuation de la position des électrons) et converge vers une valeur finie dans le cas contraire. Ainsi, la conductivité est relié à la délocalisation de la fonction d'onde. Dans ce travail, deux définitions du TPS ont été abordées : une quantité sommée sur le spin (spin-summed TPS, SS-TPS) d'une part, et une décomposition selon le spin (spin-partitioned TPS, SSP-TSP) d'autre part. Cette dernière s'est avérée être un outil très efficace pour l'étude de systèmes fortement corrélés. Au cours de la thèse, nous avons commencé par étudier plusieurs systèmes diatomiques présentant des liaisons de natures différentes à l'aide de calculs d'interaction de configurations totale (FCI). Le TPS présente alors un maximum dans une zone précédant la rupture de liaison avant de converger asymptotiquement vers les valeurs atomiques, comme la consistance de taille du tenseur le laissait présager. Dans le cas de systèmes pour lesquels l'état électronique présente un croisement évité, le TPS diverge, mettant ainsi en évidence la forte délocalisation de la fonction d'onde. Le SS-TPS est donc un indicateur de choix pour suivre la nature de la liaison chimique. Nous avons ensuite considéré des systèmes à valence mixte de type II pour lesquels l'état fondamental présente un double-puits de potentiel avec un croisement évité avec le premier état excité. Il est donc nécessaire ici d'utiliser un traitement multi-configurationnel. Deux systèmes modèles ont ainsi été étudiés : i) deux di- mères H2 en interaction faible au niveau FCI et ii) un composé du type spiro au niveau CAS-SCF (à l'aide d'un code que nous avons implémenté dans Molpro). Dans les deux cas, le TPS présentait un maximum très marqué dans la région du croisement évité, signature d'une forte mobilité électronique. Nous nous sommes également intéressés à trois types de chaines d'atomes d'hydrogène : i atomes équidistants ii) chaines dimérisées à longueur de liaison H2 fixée et iii) chaines dimérisées. Tant le SS-TPS que le SP-TPS montrent des comportements différents selon le type de chaine considérée. Les premières ont un caractère métallique et une délocalisation de spin prononcée dans le régime fortement corrélé. Les secondes sont de nature isolante avec une délocalisation limitée. Les chaines dimérisées, quant à elle, dissocient très rapidement vers un état isolant mais avec une forte délocalisation de spin. Ces chaines demi-remplies ont aussi été traitées à l'aide d'hamiltonien de Hubbard et de Heisenberg. Nous avons ainsi pu rationaliser le comportement des SS-TPS et SP-TPS en variant le rapport de l'intégrale de saut et de la répulsion électron- électron (-t/U) entre sites adjacents. Le caractère ferromagnétique/anti-ferromagnétique a également pu être suivi en modifiant la valeur de la constante de couplage J dans le cas fortement corrélé. Finalement, ces indicateurs ont été mis en oeuvre pour des polyacenes cycliques. Dans ce cas, le TPS a permis de comprendre la nature des fonctions d'onde de l'état fondamental obtenues au niveau CAS-SCF et NEVPT2. / I carried out a theoretical study to characterize metallic and insulating properties of low-dimensional systems using wave function methods. Low-dimensional systems are particularly important because they allow an understanding that can be extrapolated to higher dimensional systems. We have employed a new tool based on the theory of conductivity of Kohn that we have named: total position-spread tensor (TPS). The TPS is defined as the second moment cumulant of the total position operator: ? = <?|X2|?> - <?|X|?>2 . The tensor divided by the number of electrons diverges when the wave function is delocalized (high fluctuation of electrons' positions), and it takes finite values for localized ones. In this way, the electrical conductivity is related to the proper delocalization of the wave function. In addition, the tensor can be divided in spin-summed (SS-TPS) and spin-partitioned tensors (SP-TPS). The latter one becomes a powerful tool to the study of strongly correlated systems. In this dissertation, we started to investigate at full configuration interaction (FCI) level diatomic molecules showing different types of bond. The TPS presented a marked maximum before the bond was broken and in the asymptotic limit one recovers the TPS values of isolated atoms (size consistency). For the case of diatomic systems showing avoided-crossing electronic states, the TPS diverges evidencing the high delocalization of the wave function. Therefore, the SS-TPS is capable of monitoring and characterizing molecular wave functions. We considered mixed-valence systems that are often distinguished by a double-well potential energy surface presenting an avoided-crossing. Thus, such a configuration possesses a strongly multireference nature involving at least two states of the same symmetry. Two different systems were investigated: i) two weakly interacting hydrogen dimers that were investigated at Full CI level, and ii) a spiro like molecule where the TPS tensor was evaluated in a CAS-SCF state-averaged wave function using our implementation of the SS- TPS formalism in MOLPRO. We found that the tensor's component in the direction of the electron transfer (ET) shows a marked maximum in the avoided-crossing region, evidencing the presence of a high electron mobility. The formalisms of the SS- and SP-TPS was applied to one dimensional systems composed by three types of half-filled hydrogen chains: i) equally-spaced chains, ii) fixed-bond dimerized chains, and iii) homothetic dimerized chains. Both the SS- and SP-TPS showed different signatures associated to the three types of systems. Equally-spaced chains have metallic wave functions and a high spin delocalization in the strongly correlated regime. In contrast, fixed-bond dimerized chains have an insulating character and a restricted spin delocalization. Finally, homothetic dimerized chains dissociate very quickly which renders them in the insulating state but with a high spin delocalization. We also studied half-filled chains by using the Hubbard and the Heisenberg Hamiltonians. On the one hand, we were able to depict the response of the SS- and SP-TPS by varying the ratio between the hopping and electron-electron repulsion (-t/U parameter) of topological connected sites. On the other hand, the ferromagnetic and anti-ferromagnetic character of the wave functions were evaluated by varying the coupling constant (J) in the strongly correlated systems. A theoretical study of closed polyacenes (PAH) structures was performed at CAS-SCF and NEVPT2 level. Our methodology for choosing the active space using the Hückel Hamiltonian was able to characterize the ground state of the systems that indeed fulfilled the Ovchinnikov rule. Finally, we applied the SS-TPS to understand the nature of the wave functions of these PAHs.