We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

We study correlated two-level quantum impurity models coupled to a metallic conduction band in the hope of gaining insight into the physics of nanoscale quantum dot systems. We focus on the possibility of formation of a spin-1 impurity local moment which, on coupling to the band, generates an underscreened (USC) singular Fermi liquid state. By employing physical arguments and the numerical renormalization group (NRG) technique, we analyse such systems in detail examining in particular both the thermodynamic and dynamic properties, including the differential conductance. The quantum phase transitions occurring between the USC phase and a more ordinary Fermi liquid (FL) phase are analysed in detail. They are generically found to be of Kosterlitz-Thouless type; exceptions occur along lines of high symmetry where first-order transitions are found. A `Friedel-Luttinger sum rule' is derived and, together with a generalization of Luttinger's theorem to the USC phase, is used to obtain general results for the $T=0$ zero-bias conductance --- it is expressed solely in terms of the number of electrons present on the impurity and applicable in both the USC and FL phases. Relatedly, dynamical signatures of the quantum phase transition show two broad classes of behaviour corresponding to the collapse of either a resonance or antiresonance in the single-particle density of states. Evidence of both of these behaviours is seen in experimental devices. We study also the effect of a local magnetic field on both single- and two-level quantum impurities. In the former case we attempt to resolve some points of contention that remain in the literature. Specifically we show that the position of the maximum in the spin resolved density of states (and related peaks in the differential conductance) is not linear in the applied field, showing a more complicated form than a simple `Zeeman splitting'. The analytic result for the low-field asymptote is recovered. For two-level impurities we illustrate the manner in which the USC state is destroyed: due to two cancelling effects an abrupt change in the zero-bias conductance does not occur as one might expect. Comparison with experiment is made in both cases and used to interpret experimental findings in a manner contrary to previous suggestions. We find that experiments are very rarely in the limit of strong impurity-host coupling. Further, features in the differential conductance as a function of bias voltage should not be simply interpreted in terms of isolated quantum dot states. The many-body nature of such systems is crucially important to their observed properties.

We investigate systems comprising chains and rings of quantum dots, coupled to two metallic leads. Such systems allow to study the competition between orbital and spin degrees of freedom in a nanodevice, and the effect this subtle interplay has on two-channel Kondo (2CK) physics. We demonstrate that a rich range of strongly correlated electron behaviour results, with non-Fermi liquid 2CK phases and non-trivial phase transitions accessible. We employ physical arguments and the numerical renormalization group (NRG) technique to analyse these systems in detail, examining in particular both thermodynamic and dynamical properties. When leads are coupled to either end of a chain of dots, we show that the resulting behaviour on low temperature/energy scales can be understood in terms of simpler paradigmatic quantum `impurity' models. An effective low-energy single-spin 2CK model is derived for all odd-length chains, while the behaviour of even-length chains is related fundamentally to that of the classic `two-impurity Kondo' model. In particular, for small interdot coupling, we show that an effective coupling mediated though incipient single-channel Kondo states drives all odd chains to the 2CK fixed point (FP) on the lowest temperature/energy scales. A theory is also developed to describe a phase transition in even chains. We derive an effective channel-anisotropic 2CK model, which indicates that the critical FP of such models must be the 2CK FP. This physical picture is confirmed using NRG for various chain systems. We also examine the effect of local frustration on 2CK physics in mirror-symmetric ring systems. The importance of geometry and symmetry is demonstrated clearly in the markedly different physical behaviour that arises in systems where two leads are either connected to the same dot, or to neighbouring dots. In the latter case, we show for all odd-membered rings that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot couplings. A frustration-induced phase transition thus occurs, the 2CK phases being separated by a novel critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasidegenerate local trimer states acts to destabilise the 2CK FPs, and the critical FP is shown to consist of a free pseudospin together with effective single-channel spin quenching. While connecting both leads to the same dot again results in two parity-distinct phases, a simple level-crossing transition now results due to the symmetry of the setup. The proposed geometry also allows access to a novel ferromagnetically-coupled two-channel local moment phase. Driven by varying the interdot couplings and occurring at the point of inherent magnetic frustration, such transitions in ring structures provide a striking example of the subtle interplay between internal spin and orbital degrees of freedom in coupled quantum dot systems, and the resulting effect on Kondo physics.

Na aproximação de potencial local (L\\downarrow1) a transformação de grupo de renormalização para o modelo O(N) de Heisenberg hierárquico é descrita por uma equação a derivadas parciais (EDP). Neste trabalho investigamos, na criticalidade (sistema à temperatura inversa crítica), a somabilidade da série de potências em 1/N que formalmente satisfaz essa EDP. / In the local potential approximation (L\\downarrow1) the renormalization group transformation for the hierarchical O(N) Heisenberg model is described by a partial differential equation (PDE). In this work we investigate, at criticality (system at inverse critical temperature), the summability of the formal power series in 1/N which formally satisfies that PDE.

In dieser Doktorarbeit werden wir das Renormierungsproblem von Gravitationstheorien im Kontext der Renormierungsgruppe (RG) unter Anwendung von perturbativen und nicht-perturbativen Methoden untersuchen. Insbesondere werden wir uns auf verschiedene Gravitationsmodelle und Näherungen konzentrieren, in welchen die zentrale Rolle von einem skalaren Freiheitsgrad eingenommen wird. Wir konzentrieren uns besonders auf zwei Ansätze für Quantengravitation, die in letzter Zeit viel Aufmerksamkeit erhalten haben, nämlich den asymptotisch sicheren Fall der Gravitation und die Hořava-Lifshitz Quantengravitation. Das Prinzip der Asymptotischen Sicherheit beruht auf der Annahme, dass das hochenergetische Gravitationsregime von einem nicht-Gaußschen Fixpunkt bestimmt wird, der nicht-perturbative Renormierung und Endlichkeit der Korrelationsfunktionen sicherstellt. Wir werden die Existenz eines solchen nicht-trivialen Fixpunktes mit Hilfe der funktionalen Renormierungsgruppe untersuchen. Insbesondere werden wir den einzigen konformen Freiheitsgrad quantisieren. Die Frage nach der Existenz eines nicht-Gaußschen Fixpunktes in einem unendlich- dimensionalen Parameterraum, das heißt für eine generische f(R)-Theorie, kann jedoch nicht mit einem solchen konform reduzierten Model analysiert werden. Deshalb werden wir es untersuchen, indem wir eine skalare dynamische Äquivalentstheorie, das heißt eine generische Brans-Dicke Theorie in der lokal-Potential Näherung mit ω = 0, quantisieren. Schließlich werden wir mittels einer perturbativen RG Methode die asymptotische Freiheit der Hořava-Lifshitz Gravitationstheorie analysieren. Diese Gravitationstheorie beruht auf der Entstehung einer Anisotropie zwischen Raum und Zeit, die Newtons Konstante zu einer marginalen Koppelung werden lässt und explizit die Unitarität bewahrt. Insbesondere werden wir die Einschleifenkorrektur in 2+1 Dimensionen berechnen, indem wir nur den konformen Freiheitsgrad quantisieren. / In this Ph.D. thesis we will study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we will focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Hořava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We will then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson’s renormalization group. In particular we will quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we will study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω = 0 in the local potential approximation. Finally, we will investigate, using a perturbative RG scheme, the asymptotic freedom of the Hořava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton’s constant to a marginal coupling and explicitly preserves unitarity. In particular we will evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.

This thesis is an investigation of the subject of extra dimensions in particle physics. In recent years, there has been a large interest in this subject. In particular, a number of models have been suggested that provide solutions to some of the problem with the current Standard Model of particle physics. These models typically give rise to experimental signatures around the TeV energy scale, which means that they could be tested in the next generation of high-energy experiments, such as the LHC. Among the most important of these models are the universal extra dimensions model, the large extra dimensions model by Arkani-Hamed, Dimopolous, and Dvali, and models where right-handed neutrinos propagate in the extra dimensions. In the thesis, we study phenomenological aspects of these models, or simple modifications of them. In particular, we focus on Kaluza–Klein dark matter in universal extra dimensions models, different aspects of neutrino physics in higher dimensions, and collider phenomenology of extra dimensions. In addition, we consider consequences of the enhanced renormalization group running of physical parameters in higher-dimensional models. / QC 20120427

No description available.

No description available.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 166-181).

[pt] O Modelo Padrão é uma das teorias mais bem sucedidas da física de partículas. Com a descoberta do bóson de Higgs, além de ter sido uma demonstração robusta do poder preditivo do Modelo Padrão, foi aberto um novo caminho para a investigação de nova física interagindo por meio do portal de Higgs, incluindo cenários motivados por matéria escura e bariogênese. Investigamos a estabilidade do potencial e os pólos de Landau do Modelo Padrão sob efeito da interação entre o bóson de Higgs e uma partícula escalar. Focamos no regime onde os escalares são gerados primariamente via um off-shell Higgs. Prevemos o espaço de parâmetros disponível para acessar a teoria em diferentes valores de massa do campo escalar. / [en] The Standard Model is one of the most successful theories in particle physics. With the discovery of the Higgs boson, a new pathway has been opened to investigate possible new physics interacting through the Higgs portal, including scenarios motivated by dark matter and baryogenesis. Supposing there is a neutral scalar state in the Standard Model coupled to it only through the Higgs portal, we investigate the potential stability and the Landau poles of the extended Standard Model potential. We focus on the regime in which the scalars are primarily generated via an off-shell Higgs. We predict the available parameter space to probe the theory for different mass values.