Neste trabalho exploramos o emaranhamento em sistemas de muitos férmions. Para o estudo de sistemas inomogêneos, propusemos uma aproximação de densidade local (LDA) para a entropia de emaranhamento de um único sítio com o restante do sistema e uma LDA para o emaranhamento entre blocos de sítios. Analisamos as contribuições universal e não-universal do emaranhamento entre blocos e obtivemos uma expressão para o termo não-universal. Usando o modelo de Hubbard unidimensional, investigamos o emaranhamento em nanoestruturas eletrônicas, quantificando o emaranhamento de um único sítio com relação ao restante da cadeia via entropia de emaranhamento. Para o modelo de Hubbard homogêneo estudamos o comportamento do emaranhamento em função da densidade, da magnetização, da interação eletrônica e de campos magnéticos externos. Encontramos que o emaranhamento é sensível às fases metálica, isolante e supercondutora. Observamos um platô de emaranhamento na região do gap de spin e verificamos que susceptibilidade magnética e emaranhamento estão intrinsecamente relacionados. Obtendo as energias e densidades do modelo de Hubbard inomogêneo através da Teoria do Funcional da Densidade e usando nossa proposta LDA para a entropia de emaranhamento, exploramos o comportamento do emaranhamento na presença de diversas inomogeneidades: superredes, impurezas e confinamento harmônico. Verificamos que o emaranhamento sempre diminui com a inomogeneidade, embora os efeitos de cada inomogeneidade sejam completamente diferentes. Encontramos uma relação entre energias de troca e correlação, de Hartree e cinética, capaz de prever quantitativamente o emaranhamento em função de qualquer das inomogeneidades. / In this work we investigated entanglement in many-fermions systems. To explore inhomogeneous systems we proposed a local density approximation (LDA) for the single-site entanglement entropy. We analysed the universal and nonuniversal contributions to block-block entanglement and obtained an expression for the nonuniversal term. We employ a description in terms of the one-dimensional Hubbard model to investigate the entanglement in electronic nanostructures and to quantify the single-site entanglement with respect to the rest of the chain by means of the entanglement entropy. For the homogeneous Hubbard model we studied the entanglement behavior as a function of density, magnetization, electronic interaction and external magnetic fields. We found that the entanglement is sensitive to the metallic, insulating and superconducting phases. We observed an entanglement plateau in the region of the spin gap and verified that magnetic susceptibility and entanglement are intrinsically related. Energies and densities of the inhomogeneous Hubbard model, obtained from Density Functional Theory, combined with our proposal of an LDA for the entanglement entropy, were used to explore the behavior of the entanglement entropy in the presence of several inhomogeneities: superlattices, impurities and harmonic confinement. We verified that entanglement always decreases with the inhomogeneity, although the effect of each inhomogeneity is completely different. For the same model we found a relation of exchange-correlation, Hartree and kinetic energies, able to predict quantitatively the entanglement as a function of any inhomogeneity.

No description available.

Thesis advisor: Ziqiang Wang / Gutzwiller wave function is an important theoretical technique for treating local electron-electron correlations nonperturbatively in condensed matter and materials physics. It is concerned with calculating variationally the ground state wave function by projecting out multi-occupation configurations that are energetically costly. The projection can be carried out analytically in the Gutzwiller approximation that offers an approximate way of calculating expectation values in the Gutzwiller projected wave function. This approach has proven to be very successful in strongly correlated systems such as the high temperature cuprate superconductors, the sodium cobaltates, and the heavy fermion compounds. In recent years, it has become increasingly evident that strongly correlated systems have a strong propensity towards forming inhomogeneous electronic states with spatially periodic superstrutural modulations. A good example is the commonly observed stripes and checkerboard states in high-$T_\mathrm c$ superconductors under a variety of conditions where superconductivity is weakened. There exists currently a real challenge and demand for new theoretical ideas and approaches that treats strongly correlated inhomogeneous electronic states, which is the subject matter of this thesis. This thesis contains four parts. In the first part of the thesis, the Gutzwiller approach is formulated in the grand canonical ensemble where, for the first time, a spatially (and spin) unrestricted Gutzwiller approximation (SUGA) is developed for studying inhomogeneous (both ordered and disordered) quantum electronic states in strongly correlated electron systems. The second part of the thesis applies the SUGA to the $t$-$J$ model for doped Mott insulators which led to the discovery of checkerboard-like inhomogeneous electronic states competing with $d$-wave superconductivity, consistent with experimental observations made on several families of high-$T_{\mathrm c}$ superconductors. In the third part of the thesis, new concepts and techniques are developed to study the Mott transition in inhomogeneous electronic superstructures. The latter is termed ``SuperMottness'' which is shown to be a general framework that unifies the two paradigms in the physics of strong electronic correlation: Mott transition and Wigner crystallization. A cluster Gutzwiller approximation (CGA) approach is developed that treats the local ($U$) and extended Coulomb interactions ($V$) on equal footing. It is shown with explicit calculations that the Mott-Wigner metal-insulator transition can take place far away from half-filling. The mechanism by which a superlattice potential enhances the correlation effects and the tendency towards local moment formation is investigated and the results reveal a deeper connection among the strongly correlated inhomogeneous electronic states, the Wigner-Mott physics, and the multiorbital Mott physics that can all be united under the notion of SuperMottness. It is proposed that doping into a superMott insulator can lead to coexistence of local moment and itinerant carriers. The last part of the thesis studies the possible Kondo effect that couples the local moment and the itinerant carriers. In connection to the sodium rich phases of the cobaltates, a new Kondo lattice model is proposed where the itinerant carriers form a Stoner ferromagnet. The competition between the Kondo screening and the Stoner ferromagnetism is investigated when the conduction band is both at and away from half-filling. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

A Teoria do funcional da Densidade (DFT) é muito empregada no estudo da densidade eletrônica e energia do estado fundamental de sistemas interagente de muitos elétrons. Uma de suas desvantagens é que, apesar de formalmente exata, a DFT depende de aproximações no funcional de troca e correlação Exc[n]. Uma de suas vantagens é a possibilidade de trabalhar com a conexão adiabática, que permite conectar explicitamente o sistema interagente de interesse com uma versão não-interagente de mesma densidade. Baseado em seu escopo esta dissertação tem como objetivo tratar da DFT no modelo de Hubbard unidimensional. Uma das vantagens em trabalhar com o Hubbard é a existência de uma solução formalmente exata para a energia do modelo homogêneo e unidimensional via ansatz de Bethe, tal solução serve de base para os nossos cálculos e resultados. Outra vantagem do modelo de Hubbard é a existência de um gap que aproximações usuais na DFT falham em reproduzir. Um de nossos resultados é calcular o gap de duas formas. Uma através da derivada da solução via ansatz de Bethe e outro é tratar o Hamiltoniano pela conexão adiabática, calcular o gap pelo potencial químico, este último calculado pelo ansatz de Bethe. Ao final comparamos a precisão dos métodos, apenas para descobrir que o método via potencial químico é mais preciso. Por último usamos a conexão adiabática e a aproximação de Hartree-Fock para teorizar um funcional híbrido no modelo de Hubbard unidimensional. / The Density Functional Theory (DFT) is a widely used in the study of electronic density and energy of the ground-state of interacting systems consisting of many electrons. One of its disadvantages is that, although it is formally exact, the DFT depends on approximations of the exchange-correlation functional Exc[n]. One of its advantages consists of the possibility of working with the adiabatic connection, which allows a explicit connection between the interacting system of our interest and a non-interacting system that yields the same density. Based on its scope this dissertation aims to address the DFT in the one-dimensional Hubbard model. One of the Hubbards model advantage consists of the existence of a formally exact solution to the energy of the homogeneous one-dimensional model via Bethe ansatz, such a solution serves as the basis for our calculations and results. Anothe Hubbards model advantage is the existence of a gap that usual approximations in DFT fail to calculate. One of our results is to calculate the gap in two different ways. One through the derivative of the Bethe ansatz solution and the other is to address the Hamiltonian through the adiabatic connection, calculate the gap through the chemical potential, the latter calculated via Bethe ansatz. In the end we compare their precisions, only to find that the one via chemical potential is more precise. At last we use the adiabatic connection and the Hartree-Fock approximation to theorize a hybrid functional in the one-dimensional Hubbard model.

Neste trabalho estudamos o magnetismo no modelo de Hubbard em uma dimensão (1DMH) via Teoria do Funcional da Densidade (DFT). Dentro desse contexto, abordamos três tópicos: (i) Baseados numa recente proposta de generalização da DFT para magnetismo não colinear, estudamos numericamente por meio de diagonalização exata o comportamento magnético do 1DMH adaptado para o caso não colinear. (ii) Desenvolvemos e aplicamos o formalismo da DFT para magnetismo não colinear no espaço discreto e comparamos os resultados do cálculo do sistema Kohn-Sham (KS) com os obtidos no passo (i) através da diagonalização exata. Aqui testamos uma proposta de aproximação para o funcional de troca e correlação no estado de onda de densidade de spin (SDW). (iii) Construímos e testamos uma aproximação da densidade local (LDA) para o funcional de troca e correlação baseados na solução exata do modelo de Hubbard homogêneo, dada pelo Ansatz de Bethe (BA). Comparamos os resultados do cálculo numérico oriundos da BA-LDA com os provenientes da diagonalização exata, obtendo resultados satisfatórios tanto para o estado SDW como para vários sistemas não homogêneos (impurezas, super-redes, potencial binário e potencial degrau). O bom acordo entre a diagonalização exata e a DFT mostra que esta última pode ser aplicada com sucesso nos casos em que a diagonalização exata é inviável. Paralelamente, adaptamos o formalismo da DFT-SDW, usado no passo (i) para aplicação em cálculos ab initio de estrutura de bandas na aproximação Muffin- Tin. Objetivando, nesse úl¬timo contexto, desenvolver as equações matemáticas necessárias para a implementação numérica desse método, fornecendo assim o formalismo necessário para futuros cálculos ab initio / In this work we study the magnetism of the Hubbard Model in one dimension (1DMH) via the Density Functional Theory (DFT). In this context, we considered three different phys¬ical context topics: (i) based on a recent generalization proposed to DFT for non-collinear magnetism, we performed an exact numerical diagonalization in order to study the magnetic behavior of the 1DMH; (ii) we developed and applied the DFT formalism, using the Kohn-Sham (KS) scheme, for non-collinear magnetism in the discreet space and we compared the results with those obtained in the step (i) through exact diagonalization. In that approach we tested an approximation for exchange and correlation functional in the framework of the spin density wave state (SDW); (iii) finally, we built and tested a local density approximation (LDA) for the functional of exchange and correlation based on the exact solution of the homogeneous Hubbard model, given by the Bethe Ansatz (BA). We compared the results of BA-LDA obtained from the numerical calculation using the exact diagonalization, yielding satisfactory results for the SDW state, as well as several inhomogeneous systems (impurity, super-lattice, binary and step potential). The good agreement between exact diagonalization and DFT shows that this last can be applied with success in the cases the diagonalization exact is not viable. We also adapted the DFT-SDW formalism, used in the step (i), for applications in ab initio calculations of band structure in the Muffin-Tin approximation. Our goal, in this last context, is to develop the necessary mathematical equations for the numerical implementation of this method, thus provinding the necessary formalism for future ab initio calculations.

Os supercondutores de alta temperatura crítica apresentam propriedades diferentes dos supercondutores convencionais, uma destas propriedades importantes é a simetria não isotrópica do parâmetro de ordem. Neste trabalho se apresenta um modelo que mostra a presença de simetria d-wave em uma classe de supercondutores de alta Tc, assim como a condição para a existência de ondas de densidade nos estados de equilíbrio. Se analisa primeiro um sistema de três corpos, um bipolaron e dois elétrons, com o objetivo de estudar o efeito da repulsão coulombiana local e não local sobre a simetria do parâmetro de ordem para o caso exato e também o limite de acoplamento forte. Se mostra também a construção de um Hamiltoniano efetivo que desacopla a interação el etron-bipolaron com o fim de abordar o problema coletivo de infinitos corpos e vemos como o modelo proposto prediz a formação de ondas de densidade para uma região especifica dos parâmetros físicos do Hamiltoniano estudado. / High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows the presence of symmetry d-wave in a class of superconductors of high Tc , as well as the condition for the existence of density waves in the states of equilibrium. We first analyze a three-body system, a bipolaron and two electrons, in order to study the effect of local and non-local Coulomb repulsion on the symmetry of the order parameter for the exact case and also the strong coupling limit. It is also shown the construction of an effective Hamiltonian that decouples the electron-bipolaron interaction in order to approach the collective problem of infinite bodies and we see how the proposed model predicts the formation of density waves for a specific region of the physical parameters of the studied Hamiltonian.

Tam Ka Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 142-145). / Text in English; abstracts in English and Chinese. / Tam Ka Ming. / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Models for Many Body Systems --- p.1 / Chapter 1.2 --- High Temperature Superconductor --- p.5 / Chapter 1.3 --- Reasons of Study Double Layers --- p.9 / Chapter 1.4 --- "Incommensurate Magnetic Excitation, Order Parameters" --- p.10 / Chapter 1.5 --- Thesis Organization --- p.10 / Chapter 2 --- Monte Carlo Methods --- p.12 / Chapter 2.1 --- General Aspects of Monte Carlo Simulation --- p.12 / Chapter 2.2 --- "Markov Chain, Metropolis Algorithm, Heat-Bath Algorithm" --- p.18 / Chapter 2.3 --- Quantum Monte Carlo --- p.21 / Chapter 2.4 --- Variational Quantum Monte Carlo --- p.22 / Chapter 2.5 --- Green Function Monte Carlo --- p.27 / Chapter 2.6 --- Auxiliary Field Monte Carlo --- p.35 / Chapter 2.7 --- Summary of Quantum Monte Carlo --- p.38 / Chapter 3 --- Constrained Path Monte Carlo --- p.40 / Chapter 3.1 --- Various Formulas Used in Constrained Path Monte Carlo --- p.40 / Chapter 3.2 --- Constrained Path Monte Carlo --- p.47 / Chapter 3.3 --- Constrained Path Approximation --- p.51 / Chapter 3.4 --- Measurements --- p.52 / Chapter 3.5 --- Method of Avoiding Numerical Instability --- p.55 / Chapter 4 --- Parallelisation of CPMC Program --- p.57 / Chapter 4.1 --- Architecture of Parallel Machine --- p.57 / Chapter 4.2 --- Communication Methods in Parallel Program --- p.65 / Chapter 4.3 --- Comparison of Parallel and Serial Program --- p.74 / Chapter 4.4 --- Measure of Parallel Program --- p.85 / Chapter 4.5 --- Analysis of Serial CPMC Program --- p.89 / Chapter 4.6 --- Analysis of the Parallel CPMC Program --- p.93 / Chapter 5 --- Results from CPMC --- p.101 / Chapter 5.1 --- Hubbard Model with Next Nearest Neighbour Hopping --- p.101 / Chapter 5.2 --- Spin and Charge Correlations --- p.104 / Chapter 5.3 --- Vertex Contributions --- p.111 / Chapter 6 --- Mean Field Calculations of bilayer --- p.119 / Chapter 6.1 --- Objective --- p.119 / Chapter 6.2 --- Theoretical Model --- p.121 / Chapter 6.3 --- Method of Solving the Model --- p.122 / Chapter 6.4 --- Finding Susceptibility by RPA --- p.131 / Chapter 6.5 --- Results --- p.136 / Chapter 6.6 --- Summary --- p.140 / Chapter 7 --- Summary --- p.141 / Bibliography --- p.142

[pt] Neste trabalho aplicamos o método RPA renormalizada ao modelo de Hubbard estendido para a cadeia unidimensional com preenchimento meio. Inicialmente verificamos a inúncia do termo de interação entre primeiros vizinhos, V , nas susceptibilidades de carga e longitudinal de spin e comparamos com os resultados de Hubbard puro. Para pequenas interações entre os primeiros vizinhos, a influência de V é muito pequena. À medida que V cresce, seu efeito é de diminuir a frequência dos plasmons e dificultar o aparecimento de magnons. Em seguida determinamos as susceptibilidades de spin e de carga, numericamente, para U = 3,4 e 5 com V entre 0 e próximo de U. Partindo da fase de onda de densidade de spin (SDW) e quando V cresce, o pico de plasmon na susceptibilidade de cargas em 2kF se aproxima de ômega = 0, indicando uma instabilidade para formação de uma onda de densidade de carga (CDW). Isto permite determinar a fronteira de separação entre as duas fases. De acordo com a RPA convencional, esta transformação ocorre em U = 2V mas o processo de renormalização desloca esta fronteira ligeiramente para o interior da região da fase CDW, em conformidade com outros métodos que não fazem a aproximação de campo médio. / [en] In this work we apply the Random Phase Approximation (RPA) to the Extended Hubbard Model in one dimension. Initially we investigate the effect of the first neighbor interaction term, V , on the spin and charge susceptibilities. When V is small, its influence is also very small but as it grows, it tends to lower the plasmon frequency and to inhibit the condition for the existence of magnons. We also have calculated numerically both the spin and the charge susceptibilities for U = 3,4 and 5 with V in the region (0; U). Starting from the SDW region and increasing V we found that the plasmon peak in the charge susceptibility for 2kF tends to omega = 0, indicating an instability against the formation of a CDW ground state. This allows us to determine the phase separation line between the two phases. According to the conventional RPA, this transition occurs for U = 2V but due to the renormalization process, we nd that this frontier shifts slightly to the interior of the CDW region, in agreement with methods not using the mean eld approximation.

In the chapter 3, we study ferromagnetic fluctuations on two types of bilayer triangular lattices by the single-band Hubbard model. We start from the tight-binding model to obtain energy spectrum, the density of sates, and the spin susceptibility. With finite Coulomb interaction turned on, we apply the random phase approximation and use the determinant quantum Monte Carlo method to study spin susceptibility for the two bilayer triangular lattices and make comparisons of their magnetic properties. The effects of the interlayer coupling is also examined in detail. / In the chapter 4, we addresses the issue of the ferromagnetism in graphene-based samples. To study magnetic correlations in graphene, we systematically carry out quantum Monte Carlo simulations of the Hubbard model on a honeycomb lattice. In the filling region below the Van Hove singularity, the system shows a short-range ferromagnetic correlation, which is slightly strengthened by the on-site Coulomb interaction and markedly by the next-nearest-neighbor hopping integral. The ferromagnetic properties depend on the electron filling strongly, which may be manipulated by the electric gate. Due to its resultant high controllability of ferromagnetism, graphene-based samples may facilitate the new development of many applications. / In the chapter 5, we examined theoretically the magnetism of impurity adatoms in graphene by quantum Monte Carlo simulation technique based on Hirsch-Fye algorithm. When tuning the Fermi energy of graphene by gate voltage with available experiments, the values of occupancy and local moment for impurity can be changed. Furthermore, with medium and large hybridizations between impurity and graphene atoms, the local moment can be switched on and off by Kondo effects. We also use maximum entropy method to study the spectral density from Green's function for impurity, and we find very unconventional behaviors which are absolutely different from the cases in the normal metal. These signatures of spectral density enlarge the possibility for controlling the impurity magnetism by gate voltage. / In this research thesis, we mainly study three strongly correlated systems: Hubbard model in bilayer triangular lattice which corresponds to the real material of NaxCoO2 · yH 2O, strong-interaction electrons in graphene system and Anderson impurity in graphene. Our numerical method is determinant quantum Monte Carlo method which will be introduced in the chapter 2. / Hu, Feiming = 阻錯系統的量子門特卡洛研究 / 胡飛鳴. / Adviser: Lin Hai-Qing. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 107-126). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Hu, Feiming = Zu cuo xi tong de liang zi Mente Kaluo yan jiu / Hu Feiming.

For the study of cobalt oxide materials, we investigate the spin susceptibility behavior when the temperature and interaction strength vary in the whole filling region, on a triangular lattice. We find the high density of state (DOS) around the van Hove singularity point is important to the existence of a certain itinerant ferromagnetic short-range correlation. Also we study different spin singlet and triplet pairing channels in this region, and find the triplet channels especially the f-wave pairing susceptibility presents the quickest growth via the lowing of temperature. However, it is subtle to stabilize the f-wave pairing since the effective pairing interaction was found to be very small. / In the last part we discuss a special case in quantum phase transition, in which the Green's function of the system can be analytically obtained. We study the entanglement of the system to identify the quantum phase transition in the system. / We investigate several novel strong correlated phenomena in the geometrically frustrated system in this thesis. On a parallel computational grid, we do the state-of-the-art quantum Monte Carlo (QMC) numerical simulation to the extended single-band Hubbard model. We observe a wide range of measurements to clarify and demonstrate the system properties in different electron density, temperature, interaction strength. The results of the single-band Hubbard model on the triangular lattice can help us understand the magnetic property and superconductivity of the cobalt oxide materials. The results of the attractive Hubbard model on the honeycomb lattice can be used to discuss some properties of the "Bardeen-Cooper-Schrieffer (BCS) state to Bose-Einstein condensation (BEC) crossover" picture, such as Dirac Fermions' behaviors and the coexistence of fermionic and bosonic degrees of freedom in the system. / We study the BCS-BEC picture of high Tc superconductor systems. On a honeycomb lattice, we measure a wide range of observables, such as double occupancy, uniform spin susceptibility, on site pair correlation vertex, on-site pair correlation length, potential energy, kinetic energy, to monitor the BEC-type and BCS-type behaviors coexisting in the system. In different regions of the interaction strength-temperature parametric plane, we find that the BEC-type and BCS-type behaviors dominate at different regions of the interaction strength-temperature parametric plane, and they have crossover in the intermediate interaction strength region. / Su, Shiquan. / Adviser: Hai-Qing Lin. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3570. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 101-107). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / Su, Shiquan.