For nearly a decade, quasi-one-dimensional conductors have been the subject of intensive study. Theoretically, much attention has been devoted to the development of one-dimensional Fermi gas models, some which may be solved exactly, and to the calculation of their response functions. After a review of this theory, a different approach is adopted in the investigation of two models. The dielectric response theory of the three-dimensional Coulomb gas has been applied to an anisotropic system in which the particles interact with an effective one-dimensional long-range potential. Within the framework of the approximation of Singwi, Tosi, Land, and Sjolander, the dielectric properties of the model are examined in order to determine the conditions under which it is unstable with respect to formation of a charge density wave state. It is found that the positive neutralizing background must be polarizable in order for such an instability to occur. The same approximation method, when applied to a one-dimensional fermion gas with a ʃ-function interaction may be compared with the exact solution of Yang. This solution, which exists in the form of coupled integral equations, has been calculated numerically, and, as predicted by the Lieb-Mattis theorem, the ground state is found to be non-magnetic. The approximation of Singwi et al. proves to give better correlation energies than other inexact methods, particularly at higher densities. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Orientador: Pascoal José Giglio Pagliuso / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-24T07:35:54Z (GMT). No. of bitstreams: 1 HolandaJunior_LinoMartinsde_D.pdf: 3936724 bytes, checksum: 5a1e9e5453184dac769d35041c7414d0 (MD5) Previous issue date: 2014 / Resumo: Nesta Tese de Doutorado desenvolvemos estudos de Ressonância de Spin Eletrônico (ESR) em compostos intermetálicos, incluindo os férmions pesados ?-YbAlB4, ?-YbAlB4 and ? -YbAlxFe1-xB4, os metais ?-LuAlB4, AlB2 e o isolante Kondo, FeSi. Nossas medidas foram feitas em um espectrômetro modelo ELEXSYS-CW Bruker usando uma cavidade ressonante do tipo TE102 para a faixa de frequência em banda X (?~ 9.4GHz). A técnica de Ressonância de Spin Eletrônico aplicada aos compostos Férmions pesados foi sempre um desafio devido a presença de fortes correlações eletrônicas que tendem a alargar as linhas de ESR. Porem, nos últimos anos essa técnica ganhou renovado interesse após a descoberta do sinal de ESR na rede Kondo YbRh2Si2. Após esse trabalho, ESR voltou a ser considerada uma técnica importante para explorar os elétrons 4f e suas interações microscópicas em compostos de terras raras, uma vez que ela sonda diretamente o íon no sitio da rede. A motivação desse trabalho e, portanto, usar a técnica de ESR para entender a dinâmica dos elétrons 4f pesados em uma rede de Kondo, para os novos compostos férmions pesados ?-YbAlB4, -YbAlB4 and ?-YbAlxFe1-xB4. Neste trabalho buscou-se utilizar a técnica de ESR nesses compostos para alcançar o entendimento microscópio dos critérios que permitem a observação de um sinal de ESR em férmios pesados. Alem do mais, quando o sinal e observado, a sonda de ESR e propícia para acompanhar a evolução dos elétrons 4f em altas temperaturas para quase-partículas pesadas em baixas temperaturas. Nossas observações nos permitiram propor um cenário qualitativo baseado na existência de um modo ressonante acoplado entre ons Kondo e os elétrons de condução. Nos discutimos as características físicas gerais para que compostos férmios pesados sejam candidatos a apresentarem tal sinal de ESR. Ainda neste trabalho, estudamos os compostos intermetálicos ?-LuAlB4, AlB2 e FeSi com propriedades estruturais ou eletrônicas similares as dos compostos ?-YbAlB4, ?-YbAlB4 and ?-YbAlxFe1-xB4 em busca de uma generalizac~ao mais abrangente do cenário proposto neste trabalho / Abstract: In this work, we have performed an Electron Spin Resonance (ESR) study in intermetallic compounds including the heavy fermions ?-YbAlB4, ?-YbAlB4 and ? -YbAlxFe1-xB4, the Fermi liquid metals ?-LuAlB4, AlB2 and the Kondo insulator, FeSi. Our measurements were made on a spectrometer Bruker CW-model ELEXSYS using a resonant cavity TE102 in X Band ( ?~ 9.4GHz). The Electron Spin Resonance technique applied to heavy fermions compounds was little explored due to difficulty in finding ESR signal of Kondo ions due to the large coupling between the resonating spins and conduction electrons. However, in recent years this technique has become focus of great attention especially after the discovery of the ESR signal in a Kondo lattice YbRh2Si2. In this context, ESR was brought to the scene as one of the main techniques to bring insights to this problem since it could probe directly the f electrons of Kondo ions and their interaction with the conduction electrons. The motivation of this work is to use the ESR technique to investigate new heavy fermions compounds and to understand when these systems can present an ESR signal. In these cases ESR can help to understand more deeply how localized f electrons at high-T evolve to itinerant heavy quasi-particles in a low-T metallic state. Our observations for ?-YbAlB4, -YbAlB4 and ?-YbAlxFe1-xB4, allowed us to make some qualitative speculations about this phenomenon and within this scenario, we propose some general characteristics for heavy fermions compounds to become candidates to present ESR signal. In this work we have also measured ?-LuAlB4, AlB2 and the Kondo insulator, FeSi, in an attempt to generalize the ESR results found for ?-YbAlB4, ?-YbAlB4 and ?-YbAlxFe1-xB4 to a more broad family of compounds / Doutorado / Física / Doutor em Ciências

Orientador: Silvio Antonio Sachetto Vitiello / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-28T00:18:16Z (GMT). No. of bitstreams: 1 Madeira_Lucas_M.pdf: 4273856 bytes, checksum: 8543c0dd916e2ec3fc638a5d31b32787 (MD5) Previous issue date: 2015 / Resumo: Nessa dissertação nós investigamos dois sistemas de muitos corpos. Na primeira parte nós escolhemos uma abordagem clássica para estudar a adsorção de gases nobres pesados, Ne, Ar, Kr, Xe e Rn, em substratos de grafeno. Nós apresentamos evidências de camadas adsorvidas comensuradas, as quais dependem fortemente da simetria do substrato, para duas estruturas: camadas de Ne na rede sqrt{7} X sqrt{7} e Kr na rede sqrt{3} X sqrt{3}. Para estudar o derretimento nós introduzimos um parâmetro de ordem e sua susceptibilidade. O calor específico e a susceptibilidade em função da temperatura foram calculados para os gases nobres pesados em diversas densidades. A posição e largura característica dos picos do calor específico e da susceptibilidade foram determinadas. Finalmente, nós investigamos a distância dos primeiros vizinhos e a distância entre a camada e o substrato, identificando contribuições relacionadas aos picos do calor específico e da susceptibilidade. A segunda parte da dissertação trata de uma linha de vórtice no gás unitário de Fermi. Gases fermiônicos ultrafrios são notáveis devido à possibilidade experimental de variar as interações interpartículas através de ressonâncias de Feshbach, o que possibilita a observação do crossover BCS-BEC. No meio do crossover encontra-se um estado fortemente interagente, o gás unitário de Fermi. Uma linha de vórtice corresponde a uma excitação desse sistema com unidades de circulação quantizadas. Nós construímos funções de onda, inspiradas na função BCS, para descrever o estado fundamental e também o sistema com uma linha de vórtice. Nossos resultados para o estado fundamental elucidam aspectos da geometria cilíndrica do problema. O perfil de densidade é constante no centro do cilindro e vai a zero suavemente na borda. Nós separamos a contribuição devido à parede da energia do estado fundamental e determinamos a energia por partícula do bulk, epsilon_0=(0.42 +- 0.01) E_{FG}. Nós também calculamos o gap superfluído para essa geometria, Delta=(0.76 +- 0.01) E_{FG}. Para o sistema com a linha de vórtice nós obtivemos o perfil de densidade, o qual corresponde a uma densidade não nula no centro do vórtice, e a energia de excitação por partícula, epsilon_{ex}=(0.0058 +- 0.0003) E_{FG}. Os métodos empregados nessa dissertação, Dinâmica Molecular, Monte Carlo Variacional e Monte Carlo de Difusão, nos dão uma base sólida para a investigação de sistemas relacionados, e outros sistemas, de muitos corpos no futuro / Abstract: In this dissertation we investigated two many-body systems. For the first part we chose a classical approach to study the adsorption of heavy rare-gases, Ne, Ar, Kr, Xe and Rn, on graphene substrates. We presented evidences of commensurate adlayers, which depend strongly on the symmetry of the substrate, for two structures: Ne adlayers in the sqrt{7} X sqrt{7} superlattice and Kr in the sqrt{3} X sqrt{3} lattice. In order to study the melting of the system we introduced an order parameter, and its susceptibility. The specific heat and susceptibility as a function of the temperature were calculated for the heavy noble gases at various densities. The position and characteristic width of the specific heat and susceptibility peaks of these systems were determined. Finally, we investigated the first neighbor distance and the distance between the adlayer and the substrate, identifying contributions related to specific heat and melting peaks. The second part of the dissertation deals with a vortex line in the unitary Fermi gas. Ultracold Fermi gases are remarkable due to the experimental possibility to tune interparticle interactions through Feshbach resonances, which allows the observation of the BCS-BEC crossover. Right in the middle of the crossover lies a strongly interacting state, the unitary Fermi gas. A vortex line corresponds to an excitation of this system with quantized units of circulation. We developed wavefunctions, inspired by the BCS wavefunction, to describe the ground state and also for a system with a vortex line. Our results for the ground state elucidate aspects of the cylindrical geometry of the problem. The density profile is flat in the center of the cylinder and vanishes smoothly at the wall. We were able to separate from the ground state of the system the wall contribution and we have determined the bulk energy as epsilon_0=(0.42 +- 0.01) E_{FG} per particle. We also calculated the superfluid pairing gap for this geometry, Delta=(0.76 +- 0.01) E_{FG}. For the system with a vortex line we obtained the density profile, which corresponds to a non-zero density at the core, and the excitation energy, epsilon_{ex}=(0.0058 +- 0.0003) E_{FG} per particle. The methods employed in this dissertation, Molecular Dynamics, Variational Monte Carlo and Diffusion Monte Carlo, give us a solid basis for the investigation of related and other many-body systems in the future / Mestrado / Física / Mestre em Física / 2012/24195-2 / FAPESP

This dissertation reports on infrared optical spectroscopic studies of a novel class of materials named Dirac materials, which cover a broad range of materials including Topological Insulators (TI) and Dirac/Nodal-line semimetals. These materials share a similar low-energy Hamiltonian that can be described by massless/massive Dirac fermions. Adding out-of-plane magnetic field generates additional features in the optical spectra that allow us to distinguish Dirac fermions with usual fermions with parabolic bands. I will first demonstrate identifications of surface states (SS) of TI using Faraday rotation spectroscopy, where both the top and bottom SS can be identified and found to host carriers of opposite sign. Secondly, I will generalize the power-law behavior for two-dimensional (2D) and three-dimensional (3D) Dirac semimetals to dispersive nodal-line semimetals. This leads to the discoveries of Dirac nodal-lines in topological semimetal NbAs2. Finally, the optical signatures of electronic correlations are discussed and the unexplored overlapping area between strongly correlated systems and Dirac semimetals are studied. The prominent correlation effects in nodal-line semimetal ZrSiSe uncovered by a combination of optical and magneto-optical spectroscopies will be discussed.

Lattice gauge theory is an important approach to understanding quantum chromodynamics (QCD) due to the large coupling constant in the theory at low energy. In this thesis, we report our study of the topological properties of the gauge fields and we calculate 𝘮_η and 𝘮_η' which are related to the topology of the gauge fields. We also develop two algorithms to speed up the inversion of the Dirac equation which is computationally demanding in lattice QCD calculations. The topology of lattice gauge fields is important but difficult to study because of the large local fluctuations of the gauge fields. In chapter 2, we probe the topological properties of the gauge fields through the measurement of closed quark loops, field strength and low-lying eigenvectors of the Shamir domain wall operator. The closed quark loops suggest the slow evolution of topological modes during the generation of QCD configurations. The chirality of the low-lying eigenvectors is studied and the lattice eigenvectors are compared to the eigenvectors in the continuous theory. The topological charges are calculated from the eigenvectors and the results agree with the topological charges calculated from the smoothed gauge fields. The fermion correlators are also obtained from the eigenvectors. The non-trivial topological properties of QCD gauge fields are important to the mass of the η and η', 𝘮_η and 𝘮_η'. Lattice QCD is an area where 𝘮_{\eta}$ and 𝘮_{\eta'}$ can be calculated by using gauge fields that are sampled over different topological sectors. We calculate 𝘮_η and 𝘮_η' in chapter 3 by including the fermion correlators and the topological charge density correlators. The errors of 𝘮_η and 𝘮_η' are reduced to the percent level and the mixing angle between the octet, singlet states in the SU(3) limit and the physical eigenstates is calculated. An algorithm that reduces communication and increases the usage of the local computational power is developed in chapter 4. The algorithm uses the multisplitting algorithm as a preconditioner in the preconditioned conjugate gradient method. It speeds up the inversion of the Dirac equation during the evolution phase. In chapter 5, we utilize two lattices, called the coarse lattice and the fine lattice, that lie on the renormalization group trajectory and have different lattice spacings. We find that the low-mode space of the coarse lattice corresponds to the low-mode space of the fine lattice. Because of the correspondence, the coarse lattice can be used to solve the low modes of the fine lattice. The coarse lattice is used in the restart algorithm and the preconditioned conjugate gradient algorithm where the latter is called the renormalization group based preconditioned conjugate gradient algorithm (RGPCG). By using the near-null vectors as the filter, RGPCG could reduce the operations of the matrix multiplications on the fine lattice by 33% to 44% for the inversion of Dirac equation. The algorithm works better than the conjugate gradient algorithm when multiple equations are solved.

No description available.

This thesis describes the application of coupled-cluster theory to model systems of metallic solids and cold-atom gases. First, I give an overview of both ground- and excited-state coupled cluster theory as background for the main topics in this thesis. Next, I evaluate the accuracy of several cost-saving approaches in estimating the coupled cluster correlation energy for a model metallic system, the uniform electron gas, in the complete basis set and thermodynamic limits. After that, I present calculations of the spectral function of the uniform electron gas in these same limits, the results of which are rationalized by applying a bosonized coupled-cluster theory to an approximate, simplified Hamiltonian that couples plasmons to a structureless core hole state. Finally, I show how coupled-cluster theory captures the many-body nature of two-component Fermi gases with tunable, attractive interactions.

The Liouville resolvent method is an unconventional technique used for finding a Green function for a Hamiltonian. Implementation of the method entails the calculation of commutators of a second-quantized Hamiltonian operator with particular generalized stepping operators that are elements of a Hilbert space and that represent transitions between many-particle states. These commutators produce linear combinations of stepping operators, so the results can be arrayed as matrix elements of the Liouville operator L̂ in the Hilbert space of stepping operators. The resulting L̂ matrix is usually of infinite order, and in principle its eigenvalues and eigenvectors can be used to construct the Green function from the L̂ resolvent matrix. Approximations are usually necessary, at least in the form of truncation of the L̂ matrix, and if one produces a sequence of such matrices of increasing order and calculates the eigenvalues and eigenvectors of these matrices, a sequence of approximations for the L̂ resolvent matrix can be produced. This sequence is mathematically guaranteed to converge to the exact result for the L̂ resolvent matrix (except at its singularities). The accuracy of an approximation depends on the order of the matrix at which the sequence is truncated. Application of the method to a Hamiltonian representing interactions between fermions and bosons involves complications arising from the large number of terms generated by the commutation properties of boson operators. This dissertation describes the method and its use in the study of fermion-boson couplings. Approximations to second order in stepping operators are calculated for simplified Froehlich and Lee models. Limited thermodynamic results are obtained from the Lee model. Exact energy eigenvalues are obtained by operator algebra for simplified Froehlich, Lee and Dirac models. These exact solutions comprise the main contribution of this research and will prove to be valuable starting points for further research. Suggestions are made for further research. / Ph. D. / incomplete_metadata

L'effet Hawking prédit, dans un espace-temps décrivant l'effondrement d'une étoile à symétrie sphérique vers un trou noir de Schwarzschild, qu'un observateur statique, situé à l'infini, observera un flux thermal de particules quantiques à la température de Hawking. La première démonstration mathématique de l'effet Hawking pour des champs quantiques libres est due à Bachelot, dont le travail sur les champs de Klein-Gordon a été ensuite étendu aux champs de Dirac, d'abord par Bachelot lui-même, puis par Melnyk. Ces travaux, placés dans le cadre d'une symétrie sphérique, ont été complétés par Häfner, qui donna une démonstration rigoureuse de l'effet Hawking pour des champs de Dirac, autour d'une étoile s'effondrant vers un trou noir de Kerr. Le but de cette thèse est d'étudier l'effet Hawking non plus dans un modèle de champs quantiques libres, où les problèmes posés se ramènent à l'étude d'équations aux dérivées partielles linéaires, mais dans un modèle de champs de Dirac en interaction. L'interaction est supposée à support compact, statique, et localisée à l'extérieur de l'étoile. Nous choisissons de traiter le cas d'un modèle jouet, dans un espace-temps de dimension 1+1, situation à laquelle on peut se ramener, au moins dans le cas libre, en utilisant la symétrie sphérique du problème. Nous étudions le comportement de champs de fermions de Dirac dans différentes situations : d'abord, pour une observable suivant l'effondrement de l'étoile ; puis pour une observable stationnaire ; enfin, pour une interaction dépendante du temps, localisée près de la surface de l'étoile. Dans chacun de ces cas, nous montrons l'existence de l'effet Hawking et donnons l'état limite correspondant. / The Hawking effect predicts that, in a space- time describing the collapse of a spherically symmetric star to a Schwarzschild black hole, a static observer at infinity sees the Unruh state as a thermal state at Hawking temperature. The first mathematical proof of the Hawking effect, in the original setting of Hawking, is due to Bachelot. His work on Klein-Gordon fields has been extended to Dirac fields, in the first place by Bachelot himself, and by Melnyk after that. Those works, placed in the setup of a spherically symmetric star, have been completed by Häfner, who gave a rigorous proof of the Hawking effect for Dirac fields, outside a star collapsing to a Kerr black hole. The aim of this thesis is to study the Hawking effect not for a model of free quantum fields, in which case the problems can be reduced to studies on linear partial differential equations, but for a model of interacting Dirac fields. The interaction will be considered as a static, compactly-supported interaction, living outside the star. We choose to study a toy model in a 1+1 dimensional space-time. Using the fact that the problem is spherically symetric, one can, at least in the free case, reduce the real problem to this toy model. We study the behavior of Dirac fermions fields in various situations : first, for an observable following the star's collapse ; then, for a static observable ; finally, for a time-dependent interaction, fixed close to the star's boundary. In each of those cases, we show the existence of the Hawking Effect and give the corresponding limit state.

Dans cette thèse, j'ai étudié l'évolution de la surface de Fermi sous l'influence d'un champ magnétique dans des systèmes massifs facilement polarisables à basse température. La première partie est dévouée aux cas du supraconducteur ferromagnétique UCoGe et du supraconducteur paramagnétique CeIrIn5, où la surface de Fermi peut être modifiée sans transition magnétique. Dans UCoGe, plusieurs anomalies successives ont été détectées dans l'effet Seebeck, la résistivité et l'effet Hall, sans transition nette dans l'aimantation. L'observation d'oscillations quantiques montre que ces anomalies sont reliées à des changements de topologie de la surface de Fermi, aussi appelés transitions de Lifshitz. Dans CeIrIn5, une anomalie est détectée dans l'effet Seebeck à HM = 28 T et les oscillations quantiques observées en magnétométrie torque montrent qu'une transition de Lifshitz à lieu à ce champ.Dans la deuxième partie, j'ai étudié comment varie la surface de Fermi à travers une transition magnétique du premier ordre induite par le champ magnétique dans le supraconducteur ferromagnétique URhGe avec le champ selon l'axe de difficile aimantation b et le supraconducteur antiferromagnétique UPd2Al3 avec le champ dans le plan basal. Dans URhGe, l'effet Seebeck permet d'observer un changement de la surface de Fermi à la transition de réorientation des spins à HR = 11.75 T et avec la résistivité confirme le caractère premier ordre de la transition en plus de fournir la localisation dans le diagramme de phase du point tricritique. Dans UPd2Al3, une nouvelle branche de la surface de Fermi est observée dans les oscillations quantiques de de Haas-van Alphen dans l'état antiferromagnétique et l'effet Seebeck montre que la surface de Fermi change à la transition métamagnétique à HM = 18 T. En outre, quatre nouvelles branches sont observées dans la phase polarisée au delà de HM et qui ne peuvent être associées à celles calculées dans les états paramagnétique et antiferromagnétique. / In this thesis, we have studied the evolution of the Fermi surface under the influence of a magnetic field in bulk materials that can be easily polarized at low temperature. The first part was devoted to the cases of the ferromagnetic superconductor UCoGe with a magnetic field applied along the easy magnetization c-axis and the paramagnetic superconductor CeIrIn5 with the field along the c-axis. In UCoGe, several successive anomalies were detected in resistivity, Hall effect and thermoelectric power, without any thermodynamic transition being detected in magnetization. The direct observation of quantum oscillations showed that these anomalies are related to topological changes of the Fermi surface, also known as Lifshitz transitions. In CeIrIn5, the thermoelectric power detected an anomaly at HM = 28 T and the quantum oscillations observed in torque magnetometry showed that a Lifshitz transition occurs at this field.In the second part of this thesis, we studied the evolution of the Fermi surface through first order magnetic transitions induced by magnetic field. In the ferromagnetic superconductor URhGe with the field applied along the hard magnetization b-axis and the antiferromagnetic superconductor UPd2Al3 with the field in the basal plane. In URhGe, the thermoelectric power allowed to observe a change in the Fermi surface at the spin reorientation transition at HR = 11.75 T defining the ferromagnetic state and along with resistivity confirmed the first order character of the transition as well as give a location of the tricritical point. In UPd2Al3, a new branch was observed in de Haas-van Alphen experiment in the antiferromagnetic phase and the thermoelectric power showed that the Fermi surface is reconstructed at the metamagnetic transition at HM = 18 T where the antiferromagnetic state is suppressed and could suggest that the Fermi surface changes before this transition. Additionally, four new branches were observed in the polarized paramagnetic phase, above HM, that cannot be associated with calculated branches in the paramagnetic of antiferromagnetic states.