We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder 1 c ss U= 2. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

La cosmologie moderne amène à étudier la théorie quantique des champs en espace-temps courbe. Les champs scalaires légers, notamment, génèrent un mécanisme simple pour l'inflation et les fluctuations primordiales. Cependant, les calculs de boucles de ces modèles contiennent des divergences infrarouges et séculaires qui requièrent des techniques de resommation. Dans ce but, on implémente le groupe de renormalisation non perturbatif pour des champs scalaires en espace-temps de De Sitter. Dans un premier temps, on applique l'Approximation de Potentiel Local (APL). On démontre que les effets infrarouges sont responsables d'une restauration de la symétrie, et qu'une masse est générée en accord avec l'approche stochastique. On étudie ensuite la limite d'espace-temps plat de notre formalisme en prenant la courbure $H\to 0$, ce qui reproduit un certain nombre de résultats connus. Enfin, on s'intéresse à l'expansion dérivative, qui va au-delà de l'APL. Son implémentation semble trop complexe dans le cas général d'un espace-temps courbe, mais les symétries de De Sitter permettent de trouver une représentation simple. On définit une prescription pour tous les ordres de l'expansion, puis on implémente le flot du terme de premier ordre dans le cas simple où la dépendance en champ est négligée / The nonperturbative renormalization group for quantum field theory in de Sitter space.The study of cosmology draws us to the topic of quantum fields in curved space-time. In particular, light scalar fields offer a simple mechanism for inflation and primordial fluctuations. When computing loop corrections to these models however, infrared and secular divergences appear which call for resummation techniques. To this end, we implement the nonperturbative renormalization group for quantum scalar fields on a fixed de Sitter background. First, the Local Potential Approximation (LPA) is applied. We show that there is always symmetry restoration due to infrared effects, and that mass is generated in agreement with the stochastic approach. Next, we study the flat space limit of our formalism by taking the curvature $H\to0$, and we check that it reproduces a number of known results. Finally, we discuss the derivative expansion, which goes beyond the LPA. Its implementation seems too complex in general curved space-times, but de Sitter symmetries allow for a simpler representation. We define a prescription for all orders of the expansion, and discuss the flow of the first order term in the simple case where we neglect the field dependency (LPA')

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18062号 / 理博第3940号 / 新制||理||1568(附属図書館) / 30920 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 石田 憲二, 准教授 藤本 聡 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19522号 / 理博第4182号 / 新制||理||1600(附属図書館) / 32558 / 京都大学大学院理学研究科化学専攻 / (主査)教授 吉村 一良, 教授 有賀 哲也, 教授 北川 宏 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20895号 / 理博第4347号 / 新制||理||1624(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々 真一, 教授 川上 則雄, 教授 早川 尚男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This thesis presents renormalization group (RG) analyses of two strongly correlated condensed matter systems. In the first part, the phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnetic model on a spatially anisotropic triangular lattice is discussed. This model, together with a Dzyaloshinskii-Moriya (DM) interaction, describes the magnetic properties of the layered Mott insulator Cs$_{2}$CuCl$_{4}$. Employing a real-space RG approach, it is found, in agreement with a previous similar study, that a fragile collinear antiferromagnetic (CAF) state can be stabilized at sufficiently strong anisotropies. The presented RG analysis only indicates the presence of the CAF and spiral states in the phase diagram, with no extended quantum-disordered state at strong anisotropies. Specifically, it reveals a fine-tuning of couplings that entails the persistence of ferromagnetic correlations between second-nearest chains over large length scales even in the CAF phase. This has important implications on how numerical studies on finite-size systems should be interpreted, and reconciles the presence of the CAF state with the observation of only ferromagnetic correlations in numerical studies. The effect of a weak DM interaction within this RG approach is examined. It is concluded that Cs$_{2}$CuCl$_{4}$ is well within the stability region of the spiral ordering. In the second part, the fate of a neck-narrowing Lifshitz transition in two-dimensions and in the presence of weak interactions is studied. Such a transition is a topological quantum phase transition, with no change in symmetry. At the critical point of this transition, the density of states at the Fermi energy is logarithmically divergent and a van Hove singularity appears. It is found that, at the critical point, the Wilsonian effective action is intrinsically non-local. This non-locality is attributed to integrating out an emergent soft degree of freedom. Away from the critical point, a local perturbative RG description is presented, and it is shown that weak attractive interactions grow as $\log^2L$ ($L$ is the physical length). However, this local description is restricted to a finite momentum range that shrinks as the critical point is approached. / Thesis / Candidate in Philosophy

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24410号 / 理博第4909号 / 新制||理||1701(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 福間 將文, 教授 橋本 幸士, 准教授 吉岡 興一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

No description available.

In this thesis, we study the unconventional superconductivity in Sr2RuO4 (SRO) and related systems. The superconducting state in SRO remains a puzzle after more than 28 years of study. Early experiments had pointed toward a topological non-trivial time-reversal symmetry breaking (TRSB) chiral p-wave order. This pairing candidate has attracted a large amount of attention, partly in relation to the possibility of topological quantum computation, and has stimulated studies on higher chirality superconducting systems. In the first part of this thesis, we study the spontaneous edge current in chiral d- and f-wave superconductors. We show that these currents, which vanish in the continuum limit at zero temperature, are generally non-vanishing but tiny, compared to the simplest chiral p-wave case. In the presence of strong surface roughness, the direction of the edge current in the chiral d-wave case can be reversed, compared with that of a specular ideal surface with specular scattering. However, it is shown that this current reversal is non-universal beyond the continuum limit. The chiral p-wave scenario in SRO is overturned by recent Knight shift measurements, highlighting the importance of exploring different pairing symmetries for SRO. Recently, $d_{x^2-y^2} \pm ig_{(x^2-y^2)xy}$, $s' \pm id_{xy}$ and mixed helical p-wave pairings have been proposed as order parameter candidates. However, the stability of these states, especially of the $d_{x^2-y^2} \pm ig$ pairing, remains unclear. In the second part of the thesis, we study the leading superconducting instabilities in SRO in the presence of sizable atomic spin-orbit coupling (SOC), non-local SOC, and non-local interactions. We find that it is difficult to stabilize chiral p-wave pairing in SRO models; this is because, among the triplet p-wave states, the atomic SOC favors helical states over the chiral state. The presence of both d- and g-wave pairings, including a $d_{x^2-y^2} \pm ig$ state, is found when the second nearest neighbor (in-plane) repulsions, together with orbital-anisotropy of the non-local interactions and/or the B2g channel non-local SOC are included. We further analyze the properties, such as nodal structures, in-plane field spin-susceptibility, and spontaneous edge current, of the realized $d_{x^2-y^2} \pm ig$ pairing and find that this state is more compatible with existing experimental measurements than the $s' \pm id_{xy}$ and the mixed helical p-wave proposals. / Dissertation / Doctor of Philosophy (PhD)

No description available.