Le modèle de Hubbard bi-dimensionnel (2D) est souvent considéré comme le modèle minimal pour les supraconducteurs à haute température critique à base d'oxyde de cuivre (SCHT). Sur un réseau carré, ce modèle possède les phases qui sont communes à tous les SCHT, la phase antiferromagnétique, la phase supraconductrice et la phase dite du pseudogap. Il n'a pas de solution exacte, toutefois, plusieurs méthodes approximatives permettent d'étudier ses propriétés de façon numérique. Les propriétés optiques et de transport sont bien connues dans les SCHT et sont donc de bonne candidates pour valider un modèle théorique et aider à comprendre mieux la physique de ces matériaux. La présente thèse porte sur le calcul de ces propriétés pour le modèle de Hubbard 2D à couplage faible ou intermédiaire. La méthode de calcul utilisée est l'approche auto-cohérente à deux particules (ACDP), qui est non-perturbative et inclue [i.e. inclut] l'effet des fluctuations de spin et de charge à toutes les longueurs d'onde. La dérivation complète de l'expression de la conductivité dans l'approche ACDP est présentée. Cette expression contient ce qu'on appelle les corrections de vertex, qui tiennent compte des corrélations entre quasi-particules. Pour rendre possible le calcul numérique de ces corrections, des algorithmes utilisant, entre autres, des transformées de Fourier rapides et des splines cubiques sont développés. Les calculs sont faits pour le réseau carré avec sauts aux plus proches voisins autour du point critique antiferromagnétique. Aux dopages plus faibles que le point critique, la conductivité optique présente une bosse dans l'infrarouge moyen à basse température, tel qu'observé dans plusieurs SCHT. Dans la résistivité en fonction de la température, on trouve un comportement isolant dans le pseudogap lorsque les corrections de vertex sont négligées et métallique lorsqu'elles sont prises en compte. Près du point critique, la résistivité est linéaire en T à basse température et devient progressivement proportionnelle à T[indice supérieur 2] à fort dopage. Quelques résultats avec sauts aux voisins plus éloignés sont aussi présentés.

Il y a beaucoup de mystères entourant les cuprates supraconducteurs. Certaines expériences montrent que de l'ordre de charge serait présent dans les mêmes conditions que la supraconductivité. Les phénomènes seraient peut-être en compétition. On tentera de modéliser l'ordre de charge à l'aide du modèle de Hubbard. Des méthodes d'amas seront utilisées pour résoudre approximativement le modèle. Ensuite, on tente de mettre l'ordre de charge en compétition avec la supraconductivité pour en voir les effets.

Huang Zhongbing. / "4 November, 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 123-131). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

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Systems with competing orders are of great interest in condensed matter physics. When two phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states. In the first part of the thesis, we study the attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis. The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments. We drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors. In the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems. We then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange. For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’ states. For S=1/2, this lattice nematic takes the form of a valence bond solid. With J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO. We discuss implications for the honeycomb lattice Hubbard model.

Systems with competing orders are of great interest in condensed matter physics. When two phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states. In the first part of the thesis, we study the attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis. The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments. We drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors. In the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems. We then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange. For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’ states. For S=1/2, this lattice nematic takes the form of a valence bond solid. With J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO. We discuss implications for the honeycomb lattice Hubbard model.

We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length lampta_2 on disorder and interaction strength is investigated. Our results demonstrate that the recently proposed enhancement of lampta_2 as compared to the results for single particles is entirely due to the finite size of the systems considered. This is shown for a Hubbard-like onsite interaction and also a long-range interaction.

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.

Stuttgart, University, Diss., 2007.

Thèses (Ph.D.)--Université de Sherbrooke (Canada), 2000. / Titre de l'écran-titre (visionné le 20 juin 2006). Publié aussi en version papier.