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Quantum computers will be the next revolution in computer science. Molecular simulations, medicine research, route optimalisation and material science are just a few examples that will greatly benefit from this new form of computation. Currently, the biggest challenge arises in the instability of the qubits, the smallest building block of the quantum computer. External interference or interactions can knock these qubits off balance, causing a loss of information. This thesis contributes to the theoretical physics understanding of a new qubit candidate: the topological qubit. Contrary to an ordinary computer, a quantum computer does many computations simultaneously. The fact that qubits can be in 2 phases at once, makes this possible. Qubits are not a [0] OR [1], like a usual bit, but rather a combination: [0] + [1]. This combination is fragile, disturbances can break this sum, resulting in a [0] OR [1]. Topological qubits are protected against these kind of decay processes, because the [0] and [1] are spatially widely separated. This eliminates the sensitivity to interference. This thesis is dedicated to the study of parafermions, one particular type of topological qubit or topological system. These exotic parafermions are particles that can only appear in 1- or 2-dimensional materials. The various chapters discuss the conditions required for the combination state to survive in the context of parafermions. Also the effect of specific distortions is shown to have little effect on qubit state.

Quantum computers will be the next revolution in computer science. Molecular simulations, medicine research, route optimalisation and material science are just a few examples that will greatly benefit from this new form of computation. Currently, the biggest challenge arises in the instability of the qubits, the smallest building block of the quantum computer. External interference or interactions can knock these qubits off balance, causing a loss of information. This thesis contributes to the theoretical physics understanding of a new qubit candidate: the topological qubit. Contrary to an ordinary computer, a quantum computer does many computations simultaneously. The fact that qubits can be in 2 phases at once, makes this possible. Qubits are not a [0] OR [1], like a usual bit, but rather a combination: [0] + [1]. This combination is fragile, disturbances can break this sum, resulting in a [0] OR [1]. Topological qubits are protected against these kind of decay processes, because the [0] and [1] are spatially widely separated. This eliminates the sensitivity to interference. This thesis is dedicated to the study of parafermions, one particular type of topological qubit or topological system. These exotic parafermions are particles that can only appear in 1- or 2-dimensional materials. The various chapters discuss the conditions required for the combination state to survive in the context of parafermions. Also the effect of specific distortions is shown to have little effect on qubit state.

Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states, such as projected entangled pair states aimed at simulating the physics of two-dimensional models. In this work, we advocate the paradigm that for two-dimensional fermionic models, matrix-product states are still applicable to significantly higher accuracy levels than direct embeddings into one-dimensional systems allow for. To do so, we exploit schemes of fermionic mode transformations and overcome the prejudice that one-dimensional embeddings need to be local. This approach takes the insight seriously that the suitable exploitation of both the manifold of matrix-product states and the unitary manifold of mode transformations can more accurately capture the natural correlation structure. By demonstrating the residual low levels of entanglement in emerging modes, we show that matrix-product states can describe ground states strikingly well. The power of the approach is exemplified by investigating a phase transition of spinless fermions for lattice sizes up to $10\ifmmode\times\else\texttimes\fi{}10$.

We start with a variational approach and derive a set of coupled integral equations for the bound states of $N$ identical spin-$\uparrow$ fermions and a single spin-$\downarrow$ fermion in a generic multiband Hubbard Hamiltonian with an attractive onsite interaction. As an illustration we apply our integral equations to the one-dimensional sawtooth lattice up to $N \le 3$, i.e., to the $(3+1)$-body problem, and reveal not only the presence of tetramer states in this two-band model but also their quasi-flat dispersion when formed in a flat band. Furthermore, for $N = \{4, 5, \cdots, 10 \}$, our DMRG simulations and exact diagonalization suggest the presence of larger and larger multimers with lower and lower binding energies, conceivably without an upper bound on $N$. These peculiar $(N+1)$-body clusters are in sharp contrast with the exact results on the single-band linear-chain model where none of the $N \ge 2$ multimers appear. Hence their presence must be taken into account for a proper description of the many-body phenomena in flat-band systems, e.g., they may suppress superconductivity especially when there exists a large spin imbalance., 15 pages with 7 figures; to appear in PRA

We consider a disordered Hubbard model, and show that, at sufficiently weak disorder, a single spin-down mobile impurity can thermalize an extensive initially localized system of spin-up particles. Thermalization is enabled by resonant processes which involve correlated hops of the impurity and localized particles. This effect indicates that certain localized insulators behave as "supercooled" systems, with mobile impurities acting as ergodic seeds. We provide analytical estimates, supported by numerical exact diagonalization (ED), showing how the critical disorder strength for such mechanism depends on the particle density of the localized system. In the $U\rightarrow\infty$ limit, doublons are stable excitations, and they can thermalize mesoscopic systems by a similar mechanism. The emergence of an additional conservation law leads to an eventual localization of doublons. Our predictions apply to fermionic and bosonic systems and are readily accessible in ongoing experiments simulating synthetic quantum lattices with tunable disorder., Comment: 5 pages + supplementary material (8 pages)

Cold-atom quantum simulators offer unique possibilities to prepare, manipulate, and probe quantum many-body systems. However, despite the high level of control in modern experiments, not all observables of interest are easily accessible. This thesis aims at establishing protocols to measure currently elusive static and dynamic properties of quantum systems. The experimental feasibility of these schemes is illustrated by means of numerical simulations for relevant applications in many-body physics and quantum simulation. In particular, we introduce a general method for measuring dynamical correlations based on non-Hermitian linear response. This enables unbiased tests of the famous fluctuation-dissipation relation as a probe of thermalization in isolated quantum systems. Furthermore, we develop ancilla-based techniques for the measurement of currents and current correlations, permitting the characterization of strongly correlated quantum matter. Another application is geared towards revealing signatures of supersolidity in spin-orbit-coupled Bose gases by exciting the relevant Goldstone modes. Finally, we explore a scenario for quantum-simulating post-inflationary reheating dynamics by parametrically driving a Bose gas into the regime of universal far-from-equilibrium dynamics. The presented protocols also apply to other analog quantum simulation platforms and thus open up promising applications in the field of quantum science and technology.

In recent decades enormous progress has been made in studying the geometrical structure of the quantum state space. Far from an abstraction, this geometric struc- ture is defined operationally in terms of the distinguishability of states connected by parameterizations that can be controlled in a laboratory. This geometry is manifest in the kinds of response functions that are measured by well established experimen- tal techniques, such as inelastic neutron scattering. In this thesis we explore the properties of the state space geometry in the vicinity of the ground state of two paradigmatic models of low dimensional magnetism. The first model is the spin-1 anti-ferromagnetic Heisenberg chain, which is a central example of symmetry pro- tected topological physics in one dimension, exhibiting a non-local string order, and symmetry protected short range entanglement. The second is the Kitaev honeycomb model, a rare example of an analytically solvable quantum spin liquid, characterized by long range topological order. In Chapter 2 we employ the single mode approximation to estimate the genuine multipartite entanglement in the spin-1 chain as a function of the unaxial anisotropy up to finite temperature. We find that the genuine multipartite entanglement ex- hibits a finite temperature plateau, and recove the universality class of the phase transition induced by negative anisotropy be examining the finite size scaling of the quantum Fisher information. In Chapter 4 we map out the zero temperature phase diagram in terms of the QFI for a patch of the phase space parameterized by the anisotropy and applied magnetic field, establishing that any non-zero anisotropy en- hances that entanglement of the SPT phase, and the robustness of the phase to finite temperatures. We also establish a connection between genuine multipartite entanglement and state space curvature. In Chapter 3 we turn to the Kitaev honeycomb model and demonstrate that, while the QFI associated to local operators remains trivial, the second derivative of such quantities with respect to the driving parameter exhibit divergences. We characterize the critical exponents associated with these divergences. Thesis Doctor of Philosophy (PhD) Systems composed of many bodies tend to order as their energy is reduced. Steam, a state characterized by the complete disorder of the constituent water molecules, condenses to liquid water as the temperature (energy) decreases, wherein the water molecules are organized enough for insects to walk atop them. Water freezes to ice, which is so ordered that it can hold sleds and skaters. Quantum mechanics allows for patterns of organization that go beyond the solid-liquid-gas states. These patterns are manifest in the smallest degrees of freedom in a solid, the electrons, and are responsible for fridge magnets and transistors. While quantum systems still tend to order at lower energies, they are characterized by omni-present fluctuations that can conceal hidden forms of organization. One can imagine that the states of matter live in a vast space, where each point represents a different pattern. In this thesis we show that by probing the geometry of this space, we can detect hidden kinds of order that would be otherwise invisible to us.

Electronic structure of materials from first principles is essential for one-to-one comparisons between theories and experiments. However, the many-body effects resulting from electron correlation and their interplay with other degrees of freedom pose a great challenge to design an ab initio approximate method with good accuracy and efficiency at the same time. In this thesis, we present our recent developments of ab initio many-body theory for solids based on the finite-temperature Green’s function formalism. We begin by reviewing the basic concepts and definitions of realistic electronic Hamiltonians (Ch. 2) as well as Green’s functions at finite temperature (Ch. 3). Overviews of self-consistent many-body perturbation theories and quantum embedding theories are then presented in Chs. 4 and 5 as complementary materials for the following chapters. In Ch. 6, we present algorithms and implementation details for the finite-temperature self-consistent GW (scGW) method in Gaussian-type orbitals for solids. Our implementation is based on the finite-temperature Green’s function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of self-energies are explicitly evaluated. We show agreement with other, differently formulated finite-temperature scGW implementations. By migrating computationally intensive calculations to GPUs, we obtain scalable results on large supercomputers with nearly optimal performance. Inclusion of relativistic effects in scGW is discussed in Ch. 7. Our formulation of relativistic scGW is based on the exact two-component formalism with one-electron approximation (X2C1e) and non-relativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and their interplay with electron correlation without adjustable parameters. We examine the effect of the X2C1e by comparison to the established four-component formalism and reach excellent agreement. The simplicity of X2C1e enables construction of higher order theories, such as embedding theories, on top of perturbative calculations. In Ch. 8, we use self-energy embedding theory (SEET) to study the spectra of the prototypical undistorted cubic perovskites SrVO3 and SrMnO3. In the strongly correlated metallic SrVO3, we find that the usual attribution of the satellite peaks at -1.8 eV to Hund or Hubbard physics in the t2g orbitals is inconsistent with our calculations. In the strongly correlated insulator SrMnO3 we recover insulating behavior due to a feedback effect between the strongly correlated orbitals and the weakly correlated environment. Our calculation shows a systematic convergence of spectral features as the space of strongly correlated orbitals is enlarged, paving the way to a systematic parameter-free study of correlated perovskites. Lastly, in Ch. 9, we apply the Green’s function coupled cluster singles and doubles (GFCCSD) impurity solver to realistic impurity problems in strongly correlated solids within the framework of SEET. We describe the implementation details of our Green’s function coupled cluster (GFCC) solver, investigate its performance, and highlight potential advantages and problems on examples of impurities created for antiferromagnetic MnO and paramagnetic SrMnO3. GFCCSD provides satisfactory descriptions for weakly and moderately correlated impurities with sizes that are intractable by existing accurate impurity solvers such as exact diagonalization. However, when correlations become strong, the singles and doubles approximation used in GFCC could lead to instabilities in searching for the particle number present in impurity problems.

This thesis focuses on the intrinsic scattering of phonons by a general quantum degree of freedom, i.e. a fluctuating field Q with a priori completely general correlations, constrained only by unitarity and translational invariance. The scattering rates induced by this interaction are computed using quantum scattering theory. The phonon non-equilibrium dynamics is studied via kinetic theory and Boltzmann’s equation.The computed scattering rates involve two- and four-point correlation functions of the Q field. We obtain general and explicit forms for these correlations which isolate the contributions to the Hall conductivity. We then evaluate these correlation functions, and hence the thermal transport, in the case of a general interaction between one phonon and two free fields. We treat both the bosonic and the fermionic cases.We then consider the illustrative example of an ordered two-dimensional antiferromagnet. In this case the Q field is the most general composite of two magnon operators arising from spin-strain coupling allowed by the symmetries. Thermal conductivity in this model is studied both analytically and numerically, and evidence is shown of a non-vanishing phonon Hall effect.So as to clarify the role of correlations in a magnetically disordered phase, we finally consider the case of a spinon Fermi surface U(1) spin liquid. In this case the Q field is a composite of two spinon operators. We propose a model of spin-phonon coupling which leads to non-vanishing thermal Hall conductivity., Dans cette thèse, l’on étudie la diffusion intrinsèque des phonons par un degré de liberté quantique générique, c’est-à-dire un champ Q dont les corrélations, a priori complètement générales, sont restreintes uniquement par l’unitarité et l’invariance par translation. Les taux de diffusion résultant de cette interaction sont calculés via la théorie quantique de la diffusion. La dynamique hors d’équilibre des phonons, elle, est étudiée via la théorie cinétique et l’équation de Boltzmann. Les taux de diffusion obtenus font intervenir des fonctions de corrélation à deux et quatre points du champ Q. Nous obtenons des formes générales et explicites pour ces corrélations, qui isolent les contributions spécifiques à la conductivité de Hall. Nous calculons ensuite explicitement ces fonctions de corrélation, et les conductivités thermiques qui en résultent, pour une interaction générique entre un phonon et deux opérateurs libres, bosoniques d’une part, fermioniques d’autre part.Afin d’illustrer ce formalisme par l’exemple, nous considérons le cas d’un matériau antiferromagnétique 2D. Q est alors un opérateur à deux magnons, issu d’un couplage entre les spins et le réseau aussi général que possible compte tenu des symétries. Nous étudions analytiquement et numériquement la conductivité thermique dans ce modèle, et mettons en évidence un effet Hall phononique. Pour élucider le rôle des corrélations dans une phase magnétiquement désordonnée, nous considérons enfin le cas d’une surface de Fermi dans un liquide de spin U(1). Q est alors un opérateur à deux spinons. Nous proposons un modèle de couplage spin-phonon rendant compte d’un effet Hall thermique.

Magnetic double perovskite oxides have steadily emerged as an important class of functional materials. A clear understanding of the complex interactions that govern the magnetic behavior, and thereby, the functionality in these mixed valence compounds, however, remains elusive. In this study, we show that the complex nanostructure that forms in these compounds is at the root of their magnetic behavior. Using complementary experimental and micromagnetic simulation results, we have uncovered the complex nanostructure of polycrystalline Sm2CoMnO6, a typical double perovskite oxide, and established how the nanostructure drives its magnetic behavior. Our results show that Sm2CoMnO6 exhibits a Griffiths phase with the formation of ferromagnetic clusters above the ordering temperature. The isothermal magnetization curves show no sign of saturation, even at the highest measured field (9 T), and irreversibility in the entire magnetic field range. Despite a very clear indication of the presence of antiferromagnetic antisite defects, surprisingly, no antisite defect-induced exchange bias occurs. This is explained from the micro magnetic simulations that confirm the presence of ferromagnetic nanoclusters and nanosized, random, and uncorrelated antisite defects, resulting in no exchange bias. This work provides a clear understanding of the role of antisite defects, in particular, on how their structure can lead to the presence/absence of exchange bias. The fundamental insight offered in this work fills an important knowledge gap in the field and will be of immense value in realizing the true potential of double perovskite oxides for future technological applications. (C)& nbsp;2022 The Author(s). Published by Elsevier B.V.

Soft matter often features charged units. These charges interact through Coulomb forces, the treatment of which is difficult due to their long-range nature. This thesis gives results for three many-body systems where every long-range interaction is included, without approximations.In Chapter 1, we report exact results for a one-dimensional electroneutral salt-free suspension made of two fixed colloids and ℕ neutralizing mobile counterions, with dielectric jumps at the colloids' position. This includes the partition function, density profile and pressure. Moreover, the known relation between the contact density and pressure when counterions are confined between the colloids is generalized to the permeable situation. We find that for any ℕ counterions system there may be like-charge attraction, unlike when the dielectric is homogeneous in which case ℕ must be even. In the limit ℕ → ∞ at fixed colloid's charge, the mean-field (i.e. Poisson-Boltzmann equation) prediction is recovered. In Chapter 2, we consider the previous system out of equilibrium within a homogeneous dielectric space, as a model for the dynamics of two electrical double-layers. Using a combination of exact calculations where possible and Brownian dynamics simulations, we compute the relaxation time towards equilibrium (τ). The parity of ℕ is determinant for the relaxation dynamics: when odd, the two double-layers never decouple, irrespective of their separation ⌊; this is the regime of like-charge attraction, where τ exhibits a diffusive scaling in ⌊² for large ⌊. Contrarily, for even ℕ, the relevant length scale is the Bjerrum length instead of ⌊. This leads to distinctly different dynamics: for ℕ even, thermal effects are detrimental to relaxation, increasing τ, while they accelerate relaxation for ℕ odd. We also show the dynamical mean-field theory (i.e. Poisson-Nernst-Planck equation) is recovered for large ℕ, remaining operational down to a few counterions (ℕ>3).In Chapter 3, we determine exactly the short-distance effective potential between two ``guest'' charges immersed in a two-dimensional two-component charge-asymmetric plasma composed of positively (q₁ = +1) and negatively (q₂ = -1/2) charged point particles. The result is valid in the collapse-free regime, where the Coulombic coupling (dimensionless inverse temperature) β 2, this model features like-charge attraction. Finally, we show opposite-charges cannot repel at short-distances., La materia blanda a menudo presenta unidades cargadas. Estas cargas interactúan a través de las fuerzas de Coulomb, cuyo tratamiento es difícil debido a su naturaleza de largo alcance. Esta tesis da resultados para tres sistemas de muchos cuerposdonde se incluye cada interacción de largo alcance, sin aproximaciones. En el Capítulo 1, presentamos los resultados exactospara una suspensión unidimensional electroneutra sin sal hecha de dos coloides fijos y N contraiones móviles neutralizantes, con saltos dieléctricos en la posición de los coloides. Esto incluye la función de partición, el perfil de densidad y la presión. Además, la relación conocida entre la densidad de contacto y la presión cuando los contraiones están confinados entre los coloides se generaliza al eliminar esta restricción. Encontramos que para cualquier sistema de N contraiones puede haber atracción entre cargas similares, a diferencia de cuando el dieléctrico es homogéneo donde N debe ser par. En el límite N →∞ y fijando la carga del coloide, se recupera la predicción del campo medio (es decir, la ecuación de Poisson-Boltzmann). En el Capítulo 2, consideramos el sistema anterior fuera de equilibrio dentro de un espacio dieléctrico homogéneo, como modelo para la dinámica de dos doble capas eléctricas. Utilizando cálculos exactos donde es posible y simulaciones de dinámica browniana, calculamos el tiempo de relajación hacia el equilibrio (τ). La paridad de N es determinante para la dinámica de relajación: cuando son impares, las dos doble capas nunca se desacoplan, independientemente de su separación L; este es el régimen de atracción de cargas similares, donde τ exhibe una escala difusiva en L2 para grandes L. Por el contrario, para N par, la escala de longitud relevante es la longitud de Bjerrum en lugar de L. Esto conduce a dinámicas claramente diferentes: para N par, los efectos térmicos son perjudiciales para la relajación, aumentando τ, mientras que aceleran la relajación para N impar. También mostramos que la teoría dinámica del campo medio (es decir, la ecuación de Poisson-Nernst-Planck) se recupera para N grande, permaneciendo operativa incluso para cuando son pocos contraiones (N > 3). En el Capítulo 3, determinamos exactamente el potencial efectivo a corta distancia entre dos cargas "huésped" sumergidas en un plasma bidimensional de carga asimétrica de dos componentes compuesto de partículas puntales cargas positivas (q1 = +1) y negativas (q2 = −1/2). Elresultado es válido en el régimen libre de colapso, donde el acoplamiento Coulombico (temperatura inversa adimensional) β < 4. Para β > 2, este modelo presenta atracción entre cargas similares. Finalmente, mostramos que las cargas opuestas no pueden repelerse a distancias cortas., La matière molle met souvent en jeu des unités chargées. Ces charges interagissent par l'intermédiaire des forces de Coulomb. Dans de tels cas, il est souvent nécessaire de traiter toutes les interactions en raison de leur longue portée. Cette thèse présente des résultats pour trois systèmes à plusieurs corps; toutes les interactions à longue portée sont incluses, sans approximations.Dans le chapitre 1, nous rapportons des résultats exacts pour une suspension colloïdale, unidimensionnelle électriquement neutre et sans sel, constituée de deux colloïdes fixes ainsi que de ℕ contre-ions mobiles neutralisants, avec des sauts diélectriques à la position des colloïdes. Cela inclut la fonction de partition, le profil de densité et la pression. De plus, la relation connue entre la densité de contact et la pression lorsque les contre-ions sont confinés entre les colloïdes est généralisée en levant cette restriction. Nous constatons que pour tout système de ℕ contre-ions, il peut y avoir une attraction de même charge, contrairement au diélectrique homogène où ℕ doit être pair pour ce faire. Dans la limite ℕ → ∞ à charge de colloïde fixe, la prédiction du champ moyen (c'est-à-dire l'équation de Poisson-Boltzmann) est retrouvée.Dans le chapitre 2, nous considérons le système précédent hors d'équilibre au sein d'un espace diélectrique homogène, comme modèle de la dynamique de deux double-couches électriques. En utilisant des calculs exacts, lorsque cela est possible, et des simulations de dynamique brownienne, nous calculons le temps de relaxation vers l'équilibre (τ). La parité de ℕ est déterminante pour la dynamique de relaxation : lorsque ℕ est impair, les deux double-couches ne se découplent jamais, quelle que soit leur séparation ⌊ ; c'est le régime d'attraction de même charge, où τ se comporte de façon diffusive, variant comme ⌊² pour les grands ⌊. Au contraire, pour ℕ pair, l'échelle de longueur pertinente est la longueur de Bjerrum au lieu de ⌊. Cela conduit à des dynamiques nettement différentes : pour ℕ pair, les effets thermiques sont préjudiciables à la relaxation, augmentant τ, tandis qu'ils accélèrent la relaxation pour ℕ impair. Nous montrons également que la théorie du champ moyen dynamique (c'est-à-dire l'équation de Poisson-Nernst-Planck) est valide pour ℕ grand, restant opérationnelle jusqu'à quelques contre-ions (ℕ > 3). Au chapitre 3, nous déterminons exactement le potentiel effectif à courte distance entre deux charges test différentes immergées dans un plasma à deux dimensions, composé de particules ponctuelles positivement (q₁ = +1) et négativement (q₂ = -1/2) chargées. Le résultat est valable dans le régime sans effondrement, où le couplage coulombien (température inverse sans dimension) β < 4. À un couplage coulombien élevé β > 2, ce modèle présente une attraction de même charge. Enfin, nous montrons que les charges opposées ne peuvent pas se repousser à courte distance.

Cuprates are materials that have attracted a lot of attention when it was discovered that they become superconducting at temperatures above the boiling point of nitrogen. Since then, a large amount of experimental and theoretical works have been devoted to the understanding of the phase diagram of these materials. One of the main controversial point is the nature of the state from which superconductivity emerges, the pseudogap. Indeed, it defies the Fermi liquid theory for metals and presents a series of competing electronic instabilities that are difficult to disentangle. In this thesis, I present a new idea to describe the pseudogap phase and the superconducting transition within the framework of fractionalization. The recent observation of Pair Density Wave, i.e. modulated particle-particle pairs, on top of the usual Cooper pairing from conventional superconductivity shows that translation symmetry and pairing are both important to the physics of cuprates. Our idea is based on the fact that this Pair Density Wave is difficult to stabilize, due to multiple reasons such as disorder, and that the system will thus break it down into uniform particle-particle pairs that will condense in the superconducting state and modulated particlehole pairs that will break the translation symmetry. This fractionalization has strong consequences on the electronic and phononic degrees of freedom that we show matches the puzzling experimental observations in the pseudogap phase. The idea that modulated particle-particle pairs can contribute to the electrical transport outside the pseudogap phase is also explored to explain the anomalous “strange metal” phase above the optimal doping., Les cuprates supraconducteurs désignent une classe de matériaux qui ont attiré beaucoup d’attention lorsqu’il a été découvert qu’ils devenaient supraconducteurs à une température supérieure à celle de l’azote liquide. Depuis lors, une quantité importante de travaux, théoriques et expérimentaux, ayant pour but de comprendre le diagramme de phase de ces matériaux ont été conduits. Cependant, il n’y a aujourd’hui toujours pas de consensus sur la nature de la phase de laquelle la supraconductivité émerge, appelée pseudogap. Cette phase n’est pas décrite par la théorie des liquides de Fermi et présente de multiples autres instabilités électroniques en compétition qui sont difficiles à réconcilier dans un seul cadre théorique. Dans cette thèse, je présente une nouvelle idée pour décrire le pseudogap et la phase supraconductrice associée en utilisant le principe de la fractionnalisation. L’observation récente d’Onde de Densité de Paires, c’est-à-dire de paires électronélectron modulées dans l’espace, nous apprend que la symétrie par translation est, elle aussi, brisée dans le pseudogap. Notre idée est donc que ces Ondes de Densité de Paires sont fractionnalisées en paires électron-électron uniformes, qui sont à l’origine de l’état supraconducteur, et en paires électron-trou modulées qui sont responsables de la brisure de la symétrie par translation. Cette fractionnalisation a de nombreuses conséquences sur les propriétés électroniques qui correspondent aux observations expérimentales faites dans le pseudogap. La présence de ces paires électron-électron présentant une modulation spatiale peut aussi expliquer certains résultats inhabituels sur le transport électrique dans le régime sur-dopé.

We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations and we analyze coupled self-consistent mean-field equations of the Green functions after expressing the spin and fermion operators in terms of Grassmann variables. The specific heat and effective mass are analyzed with the solutions satisfying the symmetry imposed by the coupling layout. At low temperature, we find that these solutions induce stripes along the lines of couplings with the same sign, and that a low fermion density yields a small effective mass., 16 pages, 9 figures

A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schrödinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce the topological phase diagram of a multiband Hubbard model as a function of crystal field and Hubbard parameters. The roles of band filling and interband fluctuations are elucidated.

Orientador: Eduardo Miranda Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin Resumo: O propósito desse trabalho é estudar o papel da desordem em sistemas de spins fortemente interagentes de baixa dimensionalidade. Do ponto de vista teórico, cadeias de spin são extremamente atrativas por apresentarem uma nova física de baixas energias que vem da competição entre o ordenamento magnético e as .utuações quânticas. A introdução de desordem, onipresente no contexto experimental, é um elemento que pode desestabilizar as fases puras dando origem a uma nova física. Essa é a motivação principal do estudo de seu papel. Neste trabalho nós estudamos 4 sistemas de spins antiferromagnéticos desordenados:(i ) as escadas de spins-1/2 dos tipos 2 pernas e zig-zag, (ii ) as cadeias isotrópicas de spins SU(N), (iii ) a cadeia anisotrópica de spins SU(4), e (iv ) revisitamos a cadeia de spins-1/2. O estudo destes sistemas foi realizado aplicando generalizações da técnica do grupo de renormalização no espaço real para desordem forte. No caso do primeiro sistema, nós mostramos que as escadas de spins sempre renormalizam em cadeias de spins muito bem conhecidas. A escada de 2 pernas renormaliza para uma cadeia de spins-1/2 dimerizada antiferromagnética desordenada e, portanto, possui duas fases. Para dimerização forte ou equivalentemente desordem fraca, o sistema se encontra na fase de Haldane onde há um "gap" e a desordem é irrelevante. Para dimerização fraca ou equivalentemente desordem forte, o "gap" de Haldane se fecha e o sistema se encontra numa fase de Griffiths onde as quantidades termodinâmicas são controladas por um expoente não universal denominado expoente dinâmico z . Em contraste, a escada zig-zag renormaliza ou para uma cadeia de spins-1/2 antiferromagnética desordenada ou para uma cadeia de spins com acoplamentos ferro e antiferromagnéticos desordenada. Se a desordem e a frustração são suficientemente fracas, a escada renormaliza para a primeira cadeia, caso contrário esta pertence à mesma classe de universalidade da segunda. Além disso, relacionamos o expoente dinâmico da cadeia de spins com acoplamentos ferro e antiferromagnéticos com a distribuição de ponto fixo desses acoplamentos. Finalmente, através de argumentos simples, consideramos dizimações de acoplamentos correlacionados. Nesse caso, torna-se bem claro que a frustração é responsável pelo surgimento de acoplamentos ferromagnéticos que põem a escada na bacia de atração do ponto fixo das cadeias com acoplamentos ferro e antiferromagnéticos. Com relação à cadeia SU(N), desenvolvemos uma generalização do método do grupo de renormalização para desordem forte para uma cadeia isotrópica antiferromagnética de spins que pertencem à representações irredutíveis totalmente anti-simétricas do grupo SU(N), com N maior ou igual a 2. Conseguimos resolver as equações de fluxo analiticamente e descobrimos que essas cadeias pertencem a uma nova classe de universalidade cujos pontos fixos são de desordem infinita e, por tal motivo, nossos resultados se tornam assintoticamente exatos. Próximo a esses pontos fixos, os expoentes característicos são universais, i. e., independentes da desordem inicial da cadeia, e dependem somente do posto N do grupo de simetria. Devido às similaridades entre as regras de aglomeração de spins quando da dizimação de uma cadeia de spins com acoplamentos ferro e antiferromagnéticos e da dizimação da cadeia isotrópica de spins SU(N) no limite N ® µ , fomos capazes de calcular analiticamente, através de expansões de 1/N , a função correlação da primeira cadeia.Com relação à cadeia de spins SU(4), modificamos a generalização do método de grupo de renormalização para levar em conta a anisotropia dos acoplamentos. Conseguimos determinar o diagrama de fases através de cálculos analíticos e numéricos. Todos os pontos fixos encontrados são universais e de desordem infinita, entretanto, os expoentes característicos dependem de uma maneira não trivial da anisotropia do sistema. Por fim, revisitamos a cadeia de spins-1/2 antiferromagnética. Calculamos a amplitude da função de correlação média e a relacionamos com a amplitude da entropia de emaranhamento da mesma. Além disso, argumentamos em favor da universalidade dessas amplitudes Abstract: The purpose of this thesis is the study of the role of quenched disorder in low-dimensional strongly interacting quantum spin systems. From the theoretical point of view, spin chains are extremely attractive due to their unconventional behavior that originates in the competition between magnetic ordering and quantum fluctuations. The introduction of disorder, ubiquitous in experimental realizations, is an element that can destabilize the clean phases giving rise to new physical behavior. That is the main motivation of this study. In this thesis, we study 4 random antiferromagnetic spin systems: (i ) the spin-1/2 two-leg and zigzag ladders, (ii ) the isotropic SU(N) spin chains, (iii ) the anisotropic SU(4) spin chain, and (iv ) we also revisit the spin-1/2 chain. For such a task, we use generalizations of the strong disorder real-space renormalization group method. Concerning the first systems, we show that the ladders are always renormalized to well-known spin chains. The two-leg ladder is renormalized to a random dimerized antiferromagnetic spin-1/2 chain, hence exhibiting two phases. For strong dimerization or equivalently weak disorder the system is in the gapful Haldane phase where disorder is irrelevant. Otherwise, the Haldane gap closes and the system is driven into a nonuniversal Griffiths phase, where the thermodynamical quantities are controled by the dynamical exponent z. In contrast, the zigzag ladder is renormalized either to a random antiferromagnetic spin-1/2 chain or to a random spin chain with both ferro- and antiferromagnetic couplings. If the randomness and frustration are sufficiently weak, the ladder is renormalized to the former chain, but otherwise it belongs to the same universality class of the latter one. In addition, we related the dynamical exponent of the ferro- and aniferromagnetic spin chain with its fixed point coupling constant distributions. Moreover, through simple qualitative arguments, we determined the phase diagram of the zigzag ladder with correlated disorder. That calculation clearly showed that frustration is responsible for the appearance of ferromagnetic couplings, which place the system in the basin of attraction of the fixed point of the ferro- and antiferromagnetic spin chains. With respect to theSU(N) spin chain, we developed a generalization of the strong-disorder renormalization group method to the case of an antiferromagnetic isotropic spin chain whose spins belong to the totally antisymmetric irreducible representations of the SU(N) group, with N greater than or equal to 2. We solved the flow equations analytically and found that such chains belong to a new universality class whose fixed point distributions are characterized by infinite disorder, rendering our results asymptotically exact. The characteristic exponents of these fixed points are universal, i. e., independent of the bare disorder, and depend only on the symmetry group rank. Due to the similarities of the spin clustering rules between the ferro- and antiferromagnetic spin chain and the isotropic SU(N) spin chain in the limit of N ® µ, we were able to analytically calcu- late, through a 1/N expansion, the mean correlation function of the former chain. In the case of the SU(4) spin chain, we modified the generalization of the renormalization group method to take into account the coupling anisotropy. We determined the phase diagram through analytical and numerical calculations. All fixed points found are universal and of infinite-randomness type. However, the characteristic exponents depend in a nontrivial fashion on the anisotropy. Finally, we revisited the antiferromagnetic spin-1/2 chain. We calculated the amplitude of the mean correlation function and related it with the amplitude of the entanglement entropy of the chain. In addition, we gave arguments in favor of the universality of these amplitudes Doutorado Física da Matéria Condensada Doutor em Ciências

Neuromorphic computing which aims to mimic the collective and emergent behavior of the brain's neurons, synapses, axons, dendrites offers an intriguing, potentially disruptive solution to society's ever-growing computational needs. Although much progress has been made in designing circuit elements that mimic the behavior of neurons and synapses, challenges remain in designing networks of elements that feature a collective response behavior. We present simulations of networks of circuits and devices based on superconducting and Mott-insulating oxides that display a multiplicity of emergent states that depend on the spatial configuration of the network. Our proposed network designs are based on experimentally known ways of tuning the properties of these oxides using light ions. We show how neuronal and synaptic behavior can be achieved with arrays of superconducting Josephson junction loops, all within the same device. We also show how a multiplicity of synaptic states could be achieved by designing arrays of devices based on hydrogenated rare-earth nickelates. Together, our results demonstrate a new research platform that utilizes the collective macroscopic properties of quantum materials to mimic the emergent behavior found in biological systems., Comment: 11 pages, 8 figures

The dimer Mott insulator l-(BEDT-STF)2GaCl4 undergoes no magnetic order down to the lowest temperatures, suggesting the formation of a novel quantum disordered state. Our frequency and temperature-dependent investigations of the dielectric response reveal a relaxor-like behavior below T ≈ 100 K for all three axes, similar to other spin liquid candidates. Optical measurement of the charge-sensitive vibrational mode n27(b1u) identifies a charge disproportionation Dr ≈ 0.04e on the dimer that exists up to room temperature and originates from inequivalent molecules in the weakly coupled dimers. The linewidth of the charge sensitive mode is broader than that of typical organic conductors, supporting the existence of a disordered electronic state., Deutsche Forschungsgemeinschaft