Made available in DSpace on 2016-08-18T18:19:30Z (GMT). No. of bitstreams: 1 Dissertacao Genilson.pdf: 3934400 bytes, checksum: f88bea8a3bd3a04623dda92abb3f6064 (MD5) Previous issue date: 2012-08-17 / FUNDAÇÃO DE AMPARO À PESQUISA E AO DESENVOLVIMENTO CIENTIFICO E TECNOLÓGICO DO MARANHÃO / We studied the localization of fermionic fields in a ring-like topological defect constructed with a real scalar field ϕ and immersed in (3, 1)−dimensional spacetime. The process of localization of fermions in the ring is analyzed by studying a Yukawa-like coupling ¯ ΨF(ϕ)Ψ, where F(ϕ) is a function of the real scalar field. Using the usual γ−matrices in (1, 1)−dimensions, we express the Dirac spinor in terms of its chiral left-handed and right-handed components. The amplitudes of fermions support Schr¨odinger-like equations allowing a probabilistic interpretation of them. In our case, to analyze the existence of resonances, we consider the coupling F(ϕ) = (1 − ϕ2)2. The eigenvalue equations are solved using numerical procedures. The eigenvalues that characterize the resonances are obtained for the two chiralities that show exactly the same, confirming the qualitative analysis of the potential are supersymmetric partners. / Estudamos a localização de campos fermiônicos num defeito topológico tipo anel construído com um campo escalar real ϕ e imerso no espaço-tempo de (3, 1)−dimensões. O processo de localização de férmions no anel é analisado estudando um acoplamento tipo Yukawa ¯ΨF(ϕ)Ψ, onde F(ϕ) é uma função do campo escalar real. Utilizando as matrizes−Γ usuais em (1, 1) dimensões, dividimos o espinor de Dirac em termos das duas componentes de quiralidade de mão-esquerda e mão-direita. As amplitudes dos f´ermions suportam equações tipo-Schrodinger possibilitando uma interpretação probabilística das mesmas. Em nosso caso específico, para analisarmos a existência de ressonâncias consideramos o acoplamento F(ϕ) = (1 − ϕ2)2. As equações de autovalores são solucionadas usando procedimentos numéricos. Os autovalores que caracterizam as ressonâncias são obtidas para as duas quiralidades que se mostram exatamente iguais confirmando a análise qualitativa dos potenciais serem parceiros supersimétricos.

In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using eld theoretic techniques like bosonization and renormalization group. This involves the study of currents in Luttinger liquids, and the fate of a persistent current in a 1D system. In the second part of the thesis, we study the different types of Majorana edge modes in a 1D p-wave topological superconductor. Further we extend our analysis to the e ect of an additional s-wave pairing and a Zeeman field on the topological properties, and present a detailed phase diagram and symmetry classification for each of the cases. In the third part, we concentrate on the topological phases in two-dimensional systems. More specifically, we study the experimental realization of SU(3) topological phases in optical lattice experiments, which is characterized by the presence of gapless edge modes at the boundaries of the system. We discuss the specific characteristics required by a such a three component Hamiltonian to have a non-zero Chern number, and discuss a schematic lattice model for a possible experimental realization. The thesis is divided into three chapters, as discussed below: In the first chapter, we study the effect of a boost (Fermi sea displaced by a finite momentum) on one dimensional systems of lattice fermions with short-ranged interactions. In the absence of a boost such systems with attractive interactions possess algebraic superconducting order. Motivated by physics in higher dimensions, one might naively expect a boost to weaken and ultimately destroy superconductivity. However, we show that for one dimensional systems the e ect of the boost can be to strengthen the algebraic superconducting order by making correlation functions fall o more slowly with distance. This phenomenon can manifest in interesting ways, for example, a boost can produce a Luther-Emery phase in a system with both charge and spin gaps by engendering the destruction of the former. In the second chapter, we study the type of Majorana modes and the topological phases that can appear in a one-dimensional spinless p-wave superconductor. We have considered two types of p-wave pairing, 4"" = 4## and 4"" = 4##., and show that in both cases two types of Majorana bound states (MBS) with different spatial dependence emerge at the edges: one purely decaying and one damped oscillatory. Even in the presence of a Zeeman term B, this nature of the MBS persists in each case, where the value of chemical potential and magnetic field B decides which type will appear. We present a corresponding phase diagram, indicating the number and type of MBS in the -B space. Further, we identify the possible symmetry classes for the two cases (based on the ten-fold classification), and also in the presence of perturbations like a s-wave pairing and various terms involving magnetic field. It is seen that in the presence of a s-wave perturbation, the MBS will now have only one particular nature, the damped oscillating behaviour, unlike that for the unperturbed p-wave case. In the third chapter, we study SU(3) topological phases in two dimension. It is shown by Barnett et.al that N copies of the Hofstadter model with 2N Abelian ux per plaquette is equivalent to an N-component atom coupled to a homogeneous non-Abelian SU(N) gauge field in a square lattice. Such models have non-zero Chern number and for N = 3, can be written in terms of the SU(3) generators. In our work, we uncover two salient ingredients required to express a general three-component lattice Hamiltonian in a SU(3) format with non-trivial topological invariant. We nd that all three components must be coupled via a gauge eld, with opposite Bloch phase (in momentum space, if the NN hopping between two components is teik, then for the other two components, this should be te ik) between any two components, and there must be band inversion between all three components in a given eigenstate. For spinless particles, we show that such states can be obtained in a tripartite lattice with three inequivalent lattice sites, in which the Bloch phase associated with the nearest neighbor hopping acts as k-space gauge eld. The second criterion is the hopping amplitude t should have an opposite sign in the diagonal element for one of the two components, which can be introduced via a constant phase ei along the direction of hopping. The third and a more crucial criterion is that there must also be an odd-parity Zeeman-like term (as k ! k, the term changes sign), i.e. sin(k) z term, where z is the third Pauli matrix defined with any two components of the three component basis. In the presence of a constant vector potential, the kinetic energy of the electron gets modified when the vector potential causes a flux to be enclosed. This can generate the desired odd parity Zeeman term, via a site-selective polarization of the vector potential. This can be achieved in principle by suitable modifications of techniques used in Sisyphus cooling, and with a suitable arrangement of polarizer plates, etc. The topological phase is a firmed by edge state calculation, obeying the bulk-boundary correspondence.

Gegenstand dieser Dissertation ist die experimentelle Untersuchung von Schwere-Fermionen-Systemen mittels Rastertunnelmikroskopie und –spektroskopie (RTM/S). In diesen Materialien führen starke elektronische Korrelationen zur Ausbildung einer besonderen Art von \"schweren\" Ladungsträgern, deren Natur bislang nicht abschließend aufgeklärt werden konnte. Einige grundlegende Aspekte der Physik der Schwere-Fermionen-Systeme werden eingangs der Arbeit dargestellt. Im Anschluss daran werden die experimentellen Methoden der RTM und RTS eingeführt sowie die verwendeten Messaufbauten vorgestellt. Dies geschieht mit Hinblick auf die experimentellen Voraussetzungen für die RTS an Schwere-Fermionen-Systemen, insbesondere auf das spektrale Auflösungsvermögen. Die Präparation geeigneter Probenoberflächen von Schwere-Fermionen-Materialien und deren Auswirkung auf RTM-Experimente nehmen eine zentrale Stellung dieser Arbeit ein und werden daher gesondert behandelt. Vorrangig wurde dabei das Spalten einkristalliner Proben untersucht. In RTS-Untersuchungen des Schwere-Fermionen-Supraleiters CeCoIn5 ist es gelungen, die für einen Supraleiter typische Energielücke im Anregungsspektrum zu messen. Die Daten können über einen weiten Temperaturbereich mit theoretischen Voraussagen für die unkonventionelle Supraleitung in diesem Material verglichen werden. Die Resultate sind im Einklang mit früheren experimentellen Befunden, welche auf einen der Supraleitung vorausgehenden sog. „Precursor“-Zustand hindeuten. Allerdings gibt es, wie auch in anderen untersuchten Schwere-Fermionen-Supraleitern, Hinweise auf Inhomogenitäten der Probenoberfläche. Im Fall des nicht-supraleitenden Kondogitter-Systems YbRh2Si2 konnte durch Spalten von Einkristallen bei tiefen Temperaturen großflächig atomar geordnete Oberflächen erzeugt werden. Es zeigen sich starke Indikationen darauf, dass die Spektroskopie-Daten die Volumeneigenschaften des Materials reflektieren. Ein Vergleich mit theoretischen Rechnungen deutet darauf hin, dass der Kondoeffekt der magnetischen Yb3+-Ionen sich in der Tunnelleitfähigkeit widerspiegelt - bis hin zum Einfluss der sich ausbildenden räumlichen Kohärenz des Kondogitters bei tiefen Temperaturen. Diese Ergebnisse gewähren wichtige Einblicke in die thermische Entwicklung der elektronischen Korrelationen in Kondogitter-Systemen, und demonstrieren somit das große Potential der Rastertunnel-Spektroskopie für die weitere Erforschung der Schwere-Fermionen-Systeme. Die im Abschnitt 6.3 'Tunnelspektroskopie-Resultate an YbRh2Si2' dargestellten Ergebnisse sind in ähnlicher Form auch veröffentlicht in Nature Vol. 474 (2011), Seiten 362-366.

Seltenerd-Eisenpniktide ziehen gegenwärtig großes wissenschaftliches Interesse auf sich, da sie wegen der bei ihnen beobachteten Hochtemperatursupraleitung eine vielversprechende Alternative zu den herkömmlichen Kuprat-Supraleitern darstellen. Neben der Supraleitung weisen diese Systeme ein breites Spektrum magnetischer Eigenschaften auf, die auf dem Wechselspiel von Eisen 3d- und Seltenerd-4f-Elektronen beruhen und teils in Konkurrenz zu, teils aber auch in Koexistenz mit der Supraleitung auftreten. Das theoretische Verständnis dieser Phänomene lässt noch viele Fragen offen, da sich vor allem die 4f-Elektronen infolge ihrer starken räumlichen Lokalisierung und der damit verbundenen hohen Coulomb-Korrelationsenergien einer einfachen Behandlung im Rahmen von Bandstrukturtheorien weitgehend entziehen. Die vorliegende Arbeit beschäftigt sich mit winkelaufgelösten Photoemissionsuntersuchungen an CeFe2P2, CeFePO und CeFeP0.3As0.7O, bei denen Schwer-Fermionen-Verhalten bzw. Ferromagnetismus beobachtet werden kann. Die Wechselwirkung der 4f-Elektronen mit dem überwiegend von Fe 3d-Orbitalen abgeleiteten Valenzband spiegelt sich in den Spektren durch das Auftreten dispergierender Strukturen im Bereich der Kondoresonanz wider. Diese werden in der Arbeit auf der Grundlage von LDA-Bandstrukturrechnungen und dem Periodischen Andersonmodell, welches für einfache Fallbeispiele mittels der DMFT (Dynamical Mean Field Theory) gelöst wird, diskutiert. Anhand der experimentellen Beobachtungen wird ein Mechanismus für die in der Verbindungsklasse beobachteten magnetischen Übergänge, basierend auf charakteristischen Unterschieden in der Bandstruktur, vorgeschlagen sowie ein möglicher Zusammenhang mit der Supraleitung diskutiert.

Understanding the low-temperature properties of strongly correlated materials requires accurate measurement of the physical properties of these systems. Specific heat and nuclear spin-lattice relaxation are two such properties that allow the investigation of the electronic behavior of the system.  In this thesis, nanocalorimetry is used to measure specific heat, but also as basis for new experimental approach, developed to disentangle the different contributions to specific heat at low temperatures. The technique, that we call Thermal Impedance Spectroscopy (TISP) allows independent measurement of the electronic and nuclear specific heat at low temperatures based on the frequency response of the calorimeter-sample assembly. The method also enables simultaneous measurements of the nuclear spin-lattice relaxation time (T1). The nuclear spin lattice relaxation, as 1/T1T, and electronic specific heat, as C/T, provide information about the same quantity, electronic density of states, in the system. By comparing these properties in strongly correlated systems, we can obtain insights of electronic interactions.  Metallic indium is studied using thermal impedance spectroscopy from 0.3 K to 7 K at 35 T. The magnetic field dependence of nuclear spin-lattice relaxation rate is measured. Indium is a simple metallic system and the expected behavior of the nuclear spin-lattice relaxation is similar to that of the electronic specific heat. The results of the measurement are matched with the expectation from a simple metallic system and Nuclear Magnetic Resonance (NMR) measurements. This demonstrates the effectiveness of the new technique.  The heavy-fermion superconductor CeCoIn5 is studied using thermal impedance spectroscopy and ac-calorimetry. This material is located near a quantum critical point (QCP) bordering antiferromagnetism, as evidenced by doping studies. The nature of its quantum criticality and unconventional superconductivity is still elusive. Contrasting specific heat and nuclear spin-lattice relaxation in this correlated system helps to reveal the character of its quantum criticality.  The quantum criticality in CeCoIn5 is also studied using X-ray Absorption Spectroscopy (XAS) across the superconducting transition and X-ray Magnetic Circular Dichroism (XMCD) at 0.1 K and 6 T. The element-specific probe zooming in on cerium in this material indicates two things, a mixed valence of Ce in the superconducting state and a very small magnetic moment, that implies resonance-bond like antiferromagnetic local ordering in the system.

Resumo: O método de segunda quantificação é utilizado para construir o operador espalhamento S no espaço de Fock, no contexto de Thermofield Dynamics (TFD), para o campo de Dirac sujeito a um potencial eletromagnético externo dependente do tempo. Esta descrição é baseada na abordagem construtiva do espaço de Fock, a qual é aplicada ao sistema original e a seu dual. Seguindo a prescrição de TFD, o operador S é utilizado para avaliar o processo de produção de pares elétron-pósitron à temperatura finita, e uma análise do limiar de produção é feita a partir do cálculo da probabilidade total de transição. / Abstract: The second quantization methods is used to build the scattering operator S in Fock space, in the contex of Thermofield Dynamics (TFD), for the Dirac field subject to an external time-dependent electromagnetic potential. This description is based on the constructive approach to the Fock space, wich is applied to the original system and to its dual. Following TFD prescription, the operator S is used to estimate the process of electron-positron pair production at finite temperature, and an analysis of the production threshold is done based on the calculation of the total transition probability. / Orientador: Jeferson de Lima Tomazelli / Coorientador: Bruto Max Pimentel Escobar / Banca: José David Mangueira Vianna / Banca: Ademir Eugênio de Santana / Banca: Fernando Luiz de Campos Carvalho / Banca: Maria Cristina Batoni Abdalla / Doutor

Le sujet de cette thèse est l'analyse du second champ critique supraconducteur (Hc2) ainsi que l'interaction entre la supraconductivité et les points critiques quantiques (PCQ), pour les composés CeCoIn5, URhGe et UCoGe. Dans le composé CeCoIn5, l'étude par résistivité du domaine de liquide de Fermi a permis la localisation précise du PCQ a pression ambiante. Cette analyse permet d'invalider l'hypothèse d'une coïncidence entre Hc2(0) et le PCQ. Dans une deuxième partie, l'évolution sous pression de Hc2 est analysée. Le dôme supraconducteur de ce composé est non-conventionnel avec deux pressions caractéristiques différentes: à ~1.6GPa, la température de transition supraconductrice est maximum alors que c'est à ~0.4GPa que la plupart des grandeurs physiques (maximum de Hc2(0), maximum de la pente dHc2/dT, maximum du saut de chaleur spécifique DC/C, ...) suggèrent la présence d'un PCQ. Nous expliquons cet antagonisme par l'importance des processus de brisure de pairs liés a la proximité du PCQ. Ces deux observations nous permettent de proposer un nouveau diagramme de phase pour CeCoIn5. Dans une troisième partie, les mesures de conduction thermique sur les composés URhGe et UCoGe sont présentées. Elles nous permettent dans un premier temps d'obtenir la transition "bulk" supraconductrice et de confirmer la forme in-habituelle de Hc2 observée en résistivité. La dépendance en températures et en champs de la conduction thermique nous permet d'identifier une contribution non-électronique au transport de chaleur jusqu'aux plus basses températures. D'autre part, nous identifions deux différents domaines supraconducteurs a bas et hauts champs appliqués selon l'axe b. Ces deux domaines sont compatibles avec un modèle de supraconductivité multigaps. Suivant ces observations et des mesures de pouvoir thermoélectrique, nous proposons un modèle de transition de Lifshitz pour ces deux composés.

Orientador: Julio Marny Hoff da Silva / Banca: Saulo Henrique Pereira / Banca: Marco André Ferreira Dias / Banca: José Abdalla Helayel-Neto / Banca: Alexis Roa Aguirre / Resumo: Na presente tese apresentaremos de forma detalhada o estudo sistemático de uma teoria quântica com férmions de dimensão de massa um que obedecem as estatísticas de Fermi-Dirac, abordando essencialmente sua construção, quantização do campo, análise dos observáveis físicos e aplicações quânticas. Forneceremos todos os detalhes de uma descoberta teórica inesperada da partícula de spin $1/2$ que compõe um conjunto completo de autoespinores com helicidade dual do operador conjugação de carga. Esses espinores recebem o nome de Elko, um acrônimo proveniente do Alemão \textit{Eigenspinoren des Ladungskonjugationsoperators}. Veremos que o elo entre os espaços de representação $(1/2, 0)$ e $(0, 1/2)$ não é dado pela simetria de paridade mas sim pela 'Mágica das matrizes de Pauli', e, portanto, como consequência a dinâmica de tais campos será regida única e exclusivamente pela dinâmica de Klein-Gordon. Tal fato faz com que o propagador associado ao Elko guarde muita similaridade com o propagador do campo escalar. Intrinsicamente, em sua formulação embrionária, as somas de spin para o Elko mostram um termo que quebra explicitamente a covariância relativística, levando então à apreciação da \textit{Very Special Relativity}, que nada mais é do que um subgrupo do grupo de Lorentz, cuja álgebra deixa as somas de spin invariantes ou covariantes. Entretanto, mostraremos que existe uma liberdade na definição da estrutura dual, a qual permite que seja construída uma teoria local e invariante p... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The present thesis covers in details a systematic study of a quantum theory based on mass dimension one fermions which satisfy the Fermi-Dirac statistics, essentially addressing its construction, field quantization, analysis of physical observables and quantum applications. We provide all the details of an unexpected theoretical discovery of a spin 1/2 particle which composes a complete set of dual helicity spinors of the charge conjugation operator. Such spinors are called Elko, an acronym for the German word Eigenspinoren des Ladungskonjugationsoperators. We show that the relation between the representation spaces (1/2,0) and (0,1/2) is given by the "Magic of Pauli matrices" rather than parity symmetry, therefore, as a consequence the dynamic of such fields is governed solely and exclusively by the Klein-Gordon dynamic. Such fact makes the Elko propagator to be very similar to the scalar field propagator Intrinsically, in its embryonic formulation, Elko spin sums shows up a term that explicitly breaks relativistic covariance, leading to the appreciation of Very Special Relativity, a theory which is based on a subgroup of the Lorentz group, whose algebra leaves the spin sums invariant or covariant. However, we show a freedom in the dual structure definition, which allows the construction of a local and Lorentz invariant theory, thus, leading to a very interesting and promising new physics / Doutor

Le sujet de cette thèse est l'analyse du second champ critique supraconducteur (Hc2) ainsi que l'interaction entre la supraconductivité et les points critiques quantiques (PCQ), pour les composés CeCoIn5, URhGe et UCoGe. Dans le composé CeCoIn5, l'étude par résistivité du domaine de liquide de Fermi a permis la localisation précise du PCQ a pression ambiante. Cette analyse permet d'invalider l'hypothèse d'une coïncidence entre Hc2(0) et le PCQ. Dans une deuxième partie, l'évolution sous pression de Hc2 est analysée. Le dôme supraconducteur de ce composé est non-conventionnel avec deux pressions caractéristiques différentes: à ~1.6GPa, la température de transition supraconductrice est maximum alors que c'est à ~0.4GPa que la plupart des grandeurs physiques (maximum de Hc2(0), maximum de la pente dHc2/dT, maximum du saut de chaleur spécifique DC/C, ...) suggèrent la présence d'un PCQ. Nous expliquons cet antagonisme par l'importance des processus de brisure de pairs liés a la proximité du PCQ. Ces deux observations nous permettent de proposer un nouveau diagramme de phase pour CeCoIn5. Dans une troisième partie, les mesures de conduction thermique sur les composés URhGe et UCoGe sont présentées. Elles nous permettent dans un premier temps d'obtenir la transition "bulk" supraconductrice et de confirmer la forme in-habituelle de Hc2 observée en résistivité. La dépendance en températures et en champs de la conduction thermique nous permet d'identifier une contribution non-électronique au transport de chaleur jusqu'aux plus basses températures. D'autre part, nous identifions deux différents domaines supraconducteurs a bas et hauts champs appliqués selon l'axe b. Ces deux domaines sont compatibles avec un modèle de supraconductivité multigaps. Suivant ces observations et des mesures de pouvoir thermoélectrique, nous proposons un modèle de transition de Lifshitz pour ces deux composés. / The subject of this thesis is the analyze of the superconducting upper critical field (Hc2) and the interaction between superconductivity and quantum critical points (QCP), for the compounds CeCoIn5, URhGe and UCoGe. In CeCoIn5, study by mean of resistivity of the Fermi liquid domain allows us to localize precisely the QCP at ambient pressure. This analyze rule out the previously suggested pinning of Hc2(0) at the QCP. In a second part, the evolution of Hc2 under pressure is analyzed. The superconducting dome is unconventional in this compound with two characteristic pressures: at 1.6GPa, the superconducting transition temperature is maximum but it is at 0.4GPa that physical properties (maximum of Hc2(0), maximum of the initial slope dHc2/dT, maximum of the specific heat jump DC/C,... ) suggest a QCP. We explain this antagonism with pair-breaking effects in the proximity of the QCP. With these two experiments, we suggest a new phase diagram for CeCoIn5. In a third part, measurements of thermal conductivity on URhGe and UCoGe are presented. We obtained the bulk superconducting phase transition and confirmed the unusual curvature of the slope dHc2/dT observed by resistivity. The temperatures and fields dependence of thermal conductivity allow us to identify a non-electronic contribution for heat transport down to the lowest temperature (50mK) and probably associated with magnon or longitudinal fluctuations. We also identified two different domains in the superconducting region, These domains are compatible with a two bands model for superconductivity. Thermopower measurements on UCoGe reveal a strong anisotropy to current direction and several anomaly under field applied in the b direction. We suggest a Lifshitz transition to explain our observations in these two compounds.

Nesta tese obtemos, de um ponto de vista matemáticamente rigoroso, a parte inferior do espectro de energia-momento de dois modelos de teorias quânticas de campo com tempo imaginário em redes de dimensão $d+1$ (resultados explícitos para o caso $d = 3$ e matrizes de Dirac) que contém férmions: um modelo puramente fermiônico com interação quártica nos campos fermiônicos de $N$ componentes (modelo de Quatro-Férmions) e um modelo de cromodinâmica quântica. Para o modelo de Quatro-Férmions, $\\kappa$ é o parâmetro de hopping, $M_0$ é a massa bare dos férmions e $\\lambda$ é o parâmetro de interação. Uma expansão de polímeros garante a existência das funções de correlação no limite termodinâmico, na região onde $|\\frac{\\kappa}|$ é pequeno. A análise do espectro é baseada em representações espectrais para funções de correlação de dois e quatro férmions. A análise das funções de correlação adequadas é simplificada pelo uso de simetrias, em particular, de uma {\\em nova} simetria de Reflexão Temporal que aparece no nível das funções de correlação. A determinação do espectro é executada através de um estudo detalhado das taxas de decaimento das funções de correlação. Até próximo ao limiar de três partículas, o espectro de energia e momento exibe curvas de dispersão isoladas que são identificadas com partículas e estados ligados de duas partículas. No subespaço de uma partícula, o espectro consiste em uma curva de dispersão isolada. A massa da partícula é de ordem $-\\ln \\kappa$. O espectro de duas partículas aparece como soluções de uma equação de Bethe-Salpeter, resolvida primeiro em uma aproximação em escada. O espectro de duas partículas contém uma banda de duas partículas livres de largura finita. A existência de estados ligados acima ou abaixo da banda de duas partículas depende do fato do modelo apresentar ou não dominação gaussiana. Um parâmetro $\\aleph$ é dado para medir a dominação gaussiana. Para $\\aleph=0$, nenhum estado ligado ocorre. Para $\\aleph>0$, o estado ligado ocorre abaixo da banda de duas partículas. Para $\\aleph<0$, o estado ligado aparecem acima desta banda. Os resultados obtidos nesta aproximação em escada podem ser estendidos para o modelo completo através de um controle rigoroso das contribuições que diferenciam essas duas situações. Em uma segunda parte, idéias análogas são aplicadas para analisar o espectro do modelo de cromodinâmica quântica. Em particular, nós mostramos a existência dos pentaquarks no regime de acoplamento forte (acoplamento entre as plaquetas $0 <\\beta= \\frac{g^2_0} \\ll \\kappa $). O modelo possui simetria de calibre $SU(3)_c$ e de sabor $SU(2)_f$. Os pentaquark revelados são superposições de estados ligados de mésons e bárions. Apenas estados com um número ímpar de férmions e abaixo do limiar de energia meson-bárion são considerados. O pentaquark é determinado usando uma aproximação em escada para uma equação Bethe-Salpeter. Na ordem dominante em $\\beta$, a massa deste estado é aproximadamente $-5 \\ln\\kappa$ e sua energia de ligação é de ordem $\\textrm(\\kappa^2)$. O estado mais fortemente ligado tem isospin $I=\\frac$. Para $I=\\frac$ não há estados ligados. Estes resultados mostram uma dependência nos spins dos méson e bárion. Esta análise mostra que um potencial de troca de quark-anti-quark de $\\textrm(\\kappa^2)$ é a interação dominante, mas não há uma interpretação de troca de mésons. / In this thesis, we obtain, from a mathematically rigorous point of view, the low-lying energy-momentum spectrum of two $3+1$ dimensional imaginary time lattice quantum filed theory with fermion fields (we give explicit results for the case $d = 3$ and Dirac matrices): a pure fermionic model with quartic interaction in the $N$-component fermion field and a quantum chromodynamics model. For the Four-Fermion model, $\\kappa$ denotes the hopping parameter, $M_0$ the fermion bare mass and $\\lambda$ the interaction parameter. A polymer expansion show the existence of the model correlation functions in the thermodynamic limit, in the region where $|\\frac{\\kappa}|$ is small enough. The analysis of the spectrum is based on spectral representations of two- and four- point correlation functions. The analysis of such adequate correlation functions is simplified by the help of symmetries, in particular, by a {\\em new} Time Reflection symmetry, which appear in the level of correlation functions. The exact determination of the spectrum is done using a detailed study of the decay rates of the correlations. Up to near the 3 particle threshold, the energy-momentum spectrum exhibits isolated dispersion curves that are identified as particles and bound states. In the one-particle subspace, the spectrum consist in just a isolated dispersion curve. The mass of the associated particle is of order $-\\ln \\kappa$. The two-particle spectrum shows up as solutions of a Bethe-Salpeter equation, which is solved first in a ladder approximation. The two-particle spectrum contains a two free particles band of finite width. The existence of bound states above or below the band depends on wherever the model Gaussian domination holds. A parameter $\\aleph$ is given to measure the Gaussian domination. For $\\aleph=0$, no bound state occurs. For $\\aleph>0$, a bound state appears bellow the two-particles band. For $\\aleph<0$, the bound state appears above this band. The result obtained in this ladder approximation can be extended to the full model by a rigorous control of the contributions that differ these two cases. In a second part, analog ideas are applied to analyze the spectrum of a quantum chromodynamics model. In particular, we show the existence of pentaquarks in the strong coupling regime (plaquette coupling $0 <\\beta= \\frac{g^2_0} \\ll \\kappa $). The model has a $SU(3)_c$ gauge symmetry and a $SU(2)_f$ flavor symmetry. The reveled pentaquarks are superpositions of meson-baryon bound states. Only states with an odd number of fermions and bellow the meson-baryon threshold are considered. The pentaquark are determined using a ladder approximation to the Bethe-Salpeter equation. In the dominant order in $\\beta$, the bound state mass is $\\approx -5 \\ln\\kappa$ and the binding energy is of order $\\textrm(\\kappa^2)$. The most strongly bounded bound state has isospin $I=\\frac$. For $I=\\frac$, there is no bound state. These results shows a dependence in the spins of the meson and baryon. This analysis show that a $\\textrm(\\kappa^2)$ quark-anti-quark exchange potential is the dominant interaction, although there is not a meson exchange interpretation.