[pt] A investigação da geometria quântica em semicondutores e isoladores tornou-se significativa devido às suas implicações nas características dos materiais. A noção de geometria quântica surge considerando a métrica quântica do estado de Bloch da banda de valência, que é definido a partir da sobreposição dos estados de Bloch em momentos ligeiramente diferentes. Ao integrar a métrica quântica em toda a zona de Brillouin, introduzimos uma quantidade que chamamos de número de fidelidade, que significa a distância média entre estados de Bloch adjacentes. Além disso, apresentamos um formalismo para expressar o número de fidelidade como um marcador de fidelidade local no espaço real que pode ser definido em qualquer sítio da rede. O marcador pode ser calculado diretamente diagonalizando o hamiltoniano da rede que descreve o comportamento das partículas na rede. Posteriormente, o conceito de número e marcador de fidelidade é estendido para temperatura finita utilizando a teoria de resposta linear, conectando-os a medições experimentais que envolvem analisar o poder de absorção óptica global e local quando o material é exposto à luz linearmente polarizada. Particularmente para materiais bidimensionais, a opacidade do material permite a determinação direta do número de fidelidade espectral, permitindo a detecção experimental do número de fidelidade. Finalmente, um marcador de fidelidade não local é introduzido considerando a divergência da métrica quântica. Este marcador é postulado como um indicador universal de transições de fase quântica, assumindo que o momento cristalino permanece um número quântico válido. Este marcador não local pode ser interpretado como uma função de correlação dos estados de Wannier, que são funções de onda localizadas que descrevem estados eletrônicos em um cristal. A generalidade e aplicabilidade destes conceitos são demonstradas através da investigação de vários isoladores topológicos e transições de fase topológicas em diferentes dimensões. Essas descobertas elaboram o significado dessas quantidades e sua conexão com vários fenômenos fundamentais na física da matéria condensada. / [en] The investigation of quantum geometry in semiconductors and insulators has become significant due to its implications for material characteristics. The notion of quantum geometry arises by considering the quantum metric of the valence-band Bloch state, which is defined from the overlap of the Bloch states at slightly different momenta. By integrating the quantum metric through-out the Brillouin zone, we introduce a quantity that we call fidelity number, which signifies the average distance between adjacent Bloch states. Furthermore, we present a formalism to express the fidelity number as a local fidelity marker in real space that can be defined on every lattice site. The marker can be calculated directly by diagonalizing the lattice Hamiltonian that describes particle behavior on the lattice. Subsequently, the concept of the fidelity number and marker is extended to finite temperature using linear-response theory, connecting them to experimental measurements which involves analyze the global and local optical absorption power when the material is exposed to linearly polarized light. Particularly for two-dimensional materials, the material s opacity enables straightforward determination of the fidelity number spectral, allowing for experimental detection of the fidelity number. Finally, a nonlocal fidelity marker is introduced by considering the divergence of the quantum metric. This marker is postulated as a universal indicator of quantum phase transitions, assuming the crystalline momentum remains a valid quantum number. This nonlocal marker can be interpreted as a correlation function of Wannier states, which are localized wave functions describing electronic states in a crystal. The generality and applicability of these concepts are demonstrated through the investigation of various topological insulators and topological phase transitions across different dimensions. These findings elaborate the significance of these quantities and their connection to various fundamental phenomena in condensed matter physics.

The physics of ultracold atomic gases has been the subject of a long standing theoretical and experimental research over the last half century. The development of evaporative cooling techniques and the realization of the first Bose-Einstein Condensate (BEC) in 1995 gave a great advantage to the field. A great experimental knowledge of the fundamental properties of BECs, such as long-range coherence, superfluidity and topological excitations, has now been acquired. On top of these advances, current research on ultracold atoms is also focusing on quantum simulations, which aim at building analogue models of otherwise difficult to compute physical systems in the lab. In this context, BECs, with their enhanced coherence, many-body dynamics and superfluid character offer a powerful platform for advances in the field. Shortly after the first realization of a BEC, research started also investigating the physics of quantum mixtures of a BECs, either composed of different atomic species or isotopes, or of atoms occupying different hyperfine states. The latter are known as spin mixtures, or spinor condensates. The presence of multiple components interacting through mutual contact interactions enriches the physics of the condensate, introducing ground states with magnetic ordering as well as spin dynamics, which can be order of magnitudes less energetic than the density one. On top of this, hyperfine states can be coherently coupled with an external resonant radiation. Interesting physics arises when the strength of the coupling is comparable with the energy of spin excitations, an example of which is given by the emergence of the internal Josephson effect. This regime has been the subject of intense theoretical studies in the past twenty years, however its experimental realization on ultracold atomic platforms have been proven to be challenging, with experiments strongly limited by coherence times of few tens of milliseconds. In fact, the small energy scale of spin excitations reflects in a high sensitivity coupling to environmental magnetic noise, which affects the resonant condition. The experimental apparatus on which I worked during my Ph.D. solve this problem employing a magnetic shield that surrounds the science chamber, attenuating external magnetic fields by 6 orders of magnitudes. During my Ph.D., I investigated the properties of a coherently coupled mixture of BEC of Sodium 23, performing different experiments in two atomic configurations. The first configuration consist of a mixture of hyperfine states, namely the |F=1, mF = -1> and |F=1, mF = +1>, coupled by a two-photon transition, which is characterized by miscibility in the ground state. Another configuration was instead realized working with a strongly immiscible mixture of |F=1, mF=-1> and |F=2, mF = -2>, realized through with a one photon transition. My first experiment was devoted to the characterization of different methods of manipulation of the coupled miscible mixture in an elongated quasi-1D geometry. In Local Density Approximation (LDA), The dynamics of the system, depends on the atom number difference, the relative phase, and coupling to mean field energy ratio, can be fully described as an internal Josephson junction. We characterized this dynamics on a sample an inhomogeneous spatial profile, developing three different protocols for state manipulations. In a second experiment, I developed a protocol to generate Faraday waves in an unpolarized miscible mixture. Faraday waves are classical non-linear waves characterized by a regular pattern, that originate in classical and quantum fluids via a parametric excitation in the fluid. Interestingly enough, this process resembles the phase of reheating of the early universe, where the oscillation of the inflaton field is thought to have excited particles out of the vacuum. In analogy with this phenomenon, the oscillation of the inflaton field can be simulated with the periodic modulation of the trapping potential. On top of this, in a spin mixture, the parametric modulation can excite either in-phase (density) modes or out-of-phase (spin) modes, as two possible elementary excitations are present in the system. By extracting the spatial periodicity of the generated pattern at different modulation frequencies, I was then able to measure the dispersion relations for both density and spin modes of the system. In the presence of the coherent coupling, when spin excitations becomes gapped, we further demonstrate the scaling of the gap with the strength of the coupling radiation. The third experiment I realized concerned the characterization of the magnetic ground state of a spatially extended immiscible mixture in the presence of the coherent coupling. The Hamiltonian of such a system is formally equivalent to a continuous version of the transverse field Ising model, which describes magnetic materials at zero temperature. In this mapping, a nonlinear interaction term arises from the ratio between the self-interaction energy and the strength of the coupling, which acts as the transverse field. As the ratio between the two quantities is varied above and below one, the ground state of the system spontaneously changes from a paramagnetic phase to an ordered ferromagnetic phase, featuring two equivalent and opposite magnetizations, a signature of the occurrence of a second order quantum phase transition (QPT). Furthermore, in the magnetic model, the degeneracy between the two ferromagnetic ground states can be broken by introducing an additional longitudinal field. In the atomic case, the role of this additional field is taken by the detuning between the coupling radiation and the resonant transition frequency of non-interacting atoms. I characterized the QPT developing protocols to manipulate the spin mixture in its spatially extended ground state, varying the longitudinal field. Leveraging on the inhomogeneity of a BEC trapped in the harmonic potential, a smooth variation of the spin self-interaction energy occurs spontaneously in space, introducing different magnetic regimes at fixed coupling strength. These protocols gave access to a characterization of static properties typical of magnetic materials, such as the presence of an hysteresis cycle. The occurrence of the phase transition was instead validated by a measurement of the magnetic susceptibility and corresponding fluctuations, which both show a divergence when crossing the QPT critical point. At last, I developed a protocol to smoothly manipulate the position of magnetic domain walls, the least energetic excitations in a ferromagnet. While the previous study focused on static properties, the last experimental investigation presented in this thesis was devoted to the study of the dynamics of the metastable ferromagnetic region of the BEC. As a result of the presence of an hysteresis cycle, it is possible to engineer states of the ferromagnetic energy landscape that are homogeneously prepared either in the global minimum, with trivial dynamics, or in the metastable, higher energy, local minima. In the latter case, a classical system should eventually decay towards the global minimum, driven by temperature fluctuations which overtop the energy barrier separating the two minima. For a quantum system described by a field theory, such as a ferromagnetic BEC, the decay towards the global minimum occurs by tunneling through the barrier, triggered by quantum fluctuations. The event of tunneling is known as False Vacuum Decay (FVD), and is of outstanding relevance also for high energy physics and cosmology, were the first theoretical models were developed. In the FVD model, the decay towards the global minimum, the true vacuum, is a stochastic process that occurs only if a resonant bubble of true vacuum is formed. Once formed, the bubble will eventually expand throughout the whole system, as the true vacuum is energetically favorable. The probability for such a bubble to form can be approximately calculated analytically in 1D, and should depend exponentially on the height of the barrier the field has to tunnel through. Due to the exponentially long time scale of the process, experimental observations of FVD were still lacking. Thanks to the enhanced coherence time of the superfluid ferromagnetic mixture, and to the precise control of the barrier height through the detuning from atomic resonance, we were able to observe the event of bubble nucleation in a ferromagnetic BEC. To corroborate the observation, I measured the characteristic timescale of the decay for different values of the control parameters. Results were successfully compared first with numerical simulation, and then validated by instanton theory.

No description available.

This thesis covers most of my work in the field of ultracold atoms loaded in optical lattices. This thesis can be divided into five different parts. In Chapter 1, after a brief introduction to the field of optical lattices I review the fundamental aspects pertaining to the physics of systems in periodic potentials and a short overview of the experiments on ultracold atoms in an optical lattice. In Chapter 2 we develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this poten¬tial, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator(MI), density-wave(DW), and supersolid (SS) phases in the plane of the chemical potential and on-site repulsion ; we present phase diagrams for representative values of , the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI ,DW ,and SSphases. We explore the implications of our study for experiments on cold-atom dipolar con¬densates in optical lattices in a confining potential. In Chapter3 we present an extensive study of Mottinsulator( MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with har¬monic traps. For this we develop an inhomogeneous mean-field theory. Our results for the BH model with one type of spinless bosons agrees quantitatively with quan¬tum Monte Carlo(QMC) simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional(3D) systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also generalize our inhomogeneous mean-field theory to study BH models with har¬monic traps and(a) two species of bosons or(b) spin-1bosons. With two species of bosons we obtain rich phase diagrams with a variety of SF and MI phases and as¬sociated shells, when we include a quadratic confining potential. For the spin-1BH model we show, in a representative case, that the system can display alternating shells of polar SF and MI phases; and we make interesting predictions for experi¬ments in such systems. . In Chapter 4 we carry out an extensive study of the phase diagrams of the ex-tended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it contains Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane ¬insulator(HI) phases. We show that the critical exponents and central charge for the HI-DW,MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) uni¬versality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition. We show explicitly that different bound¬ary conditions lead to different phase diagrams.. In Chapter 5 we obtain the excitation spectra of the following three generalized of Bose-Hubbard(BH) models:(1) a two-species generalization of the spinless BH model, (2) a single-species, spin-1 BH model, and (3) the extended Bose-Hubbard model (EBH) for spinless interacting bosons of one species. In all the phases of these models we show how to obtain excitation spectra by using the random phase approximation (RPA). We compare the results of our work with earlier studies of related models and discuss implications for experiments.

This thesis considers quantum impurity models that exhibit a quantum phase transition (QPT) between a Fermi liquid strong coupling (SC) phase, and a doubly-degenerate non-Fermi liquid local moment (LM) phase. We focus on what can be said from exact analytic arguments about the LM phase of these models, where the system is characterized by an SU(2) spin degree of freedom in the entire system. Conventional perturbation theory about the non-interacting limit does not hold in the non-Fermi liquid LM phase. We circumvent this problem by reformulating the perturbation theory using a so-called `two self-energy' (TSE) description, where the two self-energies may be expressed as functional derivatives of the Luttinger-Ward functional. One particular paradigmatic model that possesses a QPT between SC and LM phases is the pseudogap Anderson impurity model (PAIM). We use infinite-order perturbation theory in the interaction, U, to self-consistently deduce the exact low-energy forms of both the self-energies and propagators in each of the distinct phases of the model. We analyse the behaviour of the model approaching the QPT from each phase, focusing on the scaling of the zero-field single-particle dynamics using both analytical arguments and detailed numerical renormalization group (NRG) calculations. We also apply two `conserving' approximations to the PAIM. First, second-order self-consistent perturbation theory and second, the fluctuation exchange approximation (FLEX). Within the FLEX approximation we develop a numerical algorithm capable of self-consistently and coherently describing the QPT coming from both distinct phases. Finally, we consider a range of static spin susceptibilities that each probe the underlying QPT in response to coupling to a magnetic field.

Durant cette thèse, je me suis intéressé à deux thématiques générales qui peuvent être explorées dans des systèmes d’atomes froids : d’une part, la dynamique hors-équilibre d’un système quantique isolé, et d’autre part l’influence du désordre sur un système fortement corrélé à basse température. Dans un premier temps, nous avons développé une méthode de champ moyen, qui permet de résoudre la dynamique unitaire dans un modèle à géométrie particulière, le réseau complètement connecté. Cette approche permet d’établir une correspondance entre la dynamique unitaire du système quantique et des équations du mouvement classique. Nous avons mis à profit cette méthode pour étudier le phénomène de transition dynamique qui se signale, dans des modèles de champ moyen, par une singularité des observables aux temps longs, en fonction des paramètres initiaux ou finaux de la trempe. Nous avons montré l’existence d’une transition dynamique quantique dans les modèle de Bose-Hubbard, d’Ising en champ transverse et le modèle de Jaynes-Cummings. Ces résultats confirment l’existence d’un lien fort entre la présence d’une transition de phase quantique et d’une transition dynamique.Dans un second temps, nous avons étudié un modèle de théorie des champs relativiste avec symétrie O(N) afin de comprendre l’influence des fluctuations sur ces singularités. À l’ordre dominant en grand N, nous avons montré que la transition dynamique s’apparente à un phénomène critique. En effet, à la transition dynamique, les fonctions de corrélations suivent une loi d’échelle à temps égaux et à temps arbitraires. Il existe également une longueur caractéristique qui diverge à l’approche du point de transition. D’autre part, il apparaît que le point fixe admet une interprétation en terme de particules sans masse se propageant librement. Enfin, nous avons montré que la dynamique asymptotique au niveau du point fixe s’apparente à celle d’une trempe d’un état symétrique dans la phase de symétrie brisée. Le troisième volet de cette thèse apporte des éléments nouveaux pour la compréhension du diagramme des phases du modèle de Bose-Hubbard en présence de désordre. Pour ce faire,nous avons utilisé et étendu la méthode de la cavité quantique en champ moyen de Ioffe et Mézard, qui doit être utilisée avec la méthode des répliques. De cette manière, il est possible d’obtenir des résultats analytiques pour les exposants des lois de probabilité de la susceptibilité.Nos résultats indiquent que dans les différents régimes de la transition de phase de superfluide vers isolant, les lois d’échelle conventionnelles sont tantôt applicables, tantôt remplacées par une loi d’activation. Enfin, les exposants critiques varient continûment à la transition conventionnelle. / The fast progress of cold atoms experiments in the last decade has allowed to explore new aspects of strongly correlated systems. This thesis deals with two such general themes: the out of equilibrium dynamics of closed quantum systems, and the impact of disorder on strongly correlated bosons at zero temperature. Among the different questions about out of equilibrium dynamics, the phenomenon of dynamical transition is still lacking a complete understanding. The transition is typically signalled, in mean-field, by a singular behaviour of observables as a function of the parameters of the quench. In this thesis, a mean field method is developed to give evidence of a strong link between the quantum phase transition at zero temperature and the dynamical transition. We then study using field theory techniques a relativistic O($N$) model, and show that the dynamical transition bears similarities with a critical phenomenon. In this context, the dynamical transition also appears to be formally related to the dynamics of symmetry breaking. The second part of this thesis is about the disordered Bose-Hubbard model and the nature of its phase transitions. We use and extend the cavity mean field method, introduced by Ioffe and Mezard to obtain analytical results from the quantum cavity method and the replica trick. We find that the conventional transition, with power law scaling, is changed into an activated scaling in some regions of the phase diagram. Furthermore, the critical exponents are continuously varying along the conventional transition. These intriguing properties call for further investigations using different methods.

La synthèse du graphène par traitement thermique d’un substrat de carbure de silicium (SiC) est une technique prometteuse pour l’intégration de ce nouveau matériau dans l’industrie, notamment dans les dispositifs électroniques. L’avantage de cette méthode réside dans la croissance de films minces de graphène de taille macroscopique directement sur substrat isolant. Toutefois, avant d’intégrer ce matériau, il convient d’en contrôler la synthèse et d’en moduler les propriétés. Dans ce travail de thèse, nous étudions les propriétés structurales et électroniques du graphène obtenu par la graphitisation des polytypes 3C-, 4H- et 6H-SiC. A partir de diverses méthodes de caractérisation, telles que la diffraction des électrons lents (LEED) ou la microscopie et spectroscopie à effet tunnel (STM/STS), nous avons vérifié, dans un premier temps, que le caractère discontinu du graphène sur les bords de marches peut introduire un confinement latéral supplémentaire des électrons dans le graphène. Dans un second temps, l’observation des singularités de Van Hove nous a permis de démontrer l’effet de confinement unidimensionnel dans les régions d’accumulations de marches du SiC. Enfin, l’introduction de désordre dans nos couches de graphène induit une réduction de la densité de porteurs de charges dans les couches. De même, ce désordre conduit à une transition de phase quantique entre le régime localisé et le régime d’effet Hall quantique. / The synthesis of graphene by thermal decomposition of silicon carbide (SiC) is a promising technique for the integration of this new material in the industry, especially in electronic devices. The advantage of this method lies in the growth of macroscopic graphene films directly on an insulator substrate. However, before using this material in electronic devices, it is advisable to control its synthesis and modulate its properties. In this thesis, we present the structural and electronic properties of graphene obtained by graphitization of 3C- , 4H - and 6H- SiC polytypes. Various characterization methods were used, including low energy electron diffraction (LEED) and microscopy and scanning tunneling spectroscopy (STM / STS). Based on STM / STS measurements, we show that the discontinuity of epitaxial graphene at the step edges may introduce an additional lateral confinement of electrons in graphene. The observation of Van Hove singularities in the STS spectra confirmed the one dimensional confinement of graphene in step bunching regions of SiC.Finally, we show that when disorder is introduced on our graphene samples, the charge carrier density is reduced. This disorder lead to the observation of a quantum phase transition from a localized regime to a quantum Hall effect regime.

Les interactions entre particules dans les gaz quantiques ultrafroids peuvent être contrôlées à l'aide de résonances de Fano-Feshbach. Ces résonances de diffusion se produisent lors de collisions à basse énergie entre deux atomes et sont généralement obtenues à l'aide d'un champ magnétique statique externe. Elles font des gaz atomiques ultrafroids un terrain d'exploration pour la recherche de nouvelles phases dans lesquelles la physique quantique joue un rôle clef.Le travail présenté dans ce mémoire s'inscrit dans le cadre de la recherche de telles phases.Ce manuscrit comporte deux parties. La première est consacrée à l'étude de bosons composites obtenus dans des gaz de Fermi hétéronucléaires 2D. Nous étudions le diagramme de phase de ce système à T = 0 et nous mettons en évidence une transition de phase gaz-cristal. Nos résultats sont prometteurs en vue d'expériences futures avec le mélange 6Li-40K.Dans la seconde partie, nous proposons un nouveau type de résonance de Fano-Feshbach. Le couplage à l'origine de cette résonance est obtenu à l'aide d'un champ magnétique micro-onde.Notre méthode s'applique à n'importe quelle espèce atomique dont l'état fondamental est clivé par l'interaction hyperfine. Elle ne nécessite pas l'utilisation d'un champ magnétique statique.Nous décrivons d'abord ces résonances à l'aide d'un modèle simple à deux niveaux. Ensuite, nous les caractérisons numériquement à l'aide de notre propre programme implémentant l'approche multi-canaux des collisions atomiques. Nos résultats ouvrent des perspectives optimistes en vue de l'observation des résonances de Feshbach induites par un champ micro-onde avec les atomes alcalins bosoniques suivants : 23Na, 41K, 87Rb et 133Cs. / The interparticle interactions in ultracold atomic gases can be tuned using Fano-Feshbach scattering resonances, which occur in low-energy collisions between two atoms. These resonances are usually obtained using an external static magnetic field. They turn ultracold atomic gases into an experimental playground for the investigation of novel phases in which Quantum Physics plays a key role. The work presented in this memoir is part of the theoretical effort towards the search for yet unexplored quantum phases.This manuscript is organised in two parts. The first one is devoted to composite bosons formed in a 2D heteronuclear Fermi gas. We characterise the zero-temperature phase diagram and show the gas-crystal phase transition in this system. Our results are promising in view of future experiments with the 6Li-40K mixture.In the second part, we propose an alternative to static-field Fano-Feshbach resonances. The idea is to achieve the coupling by using a resonant microwave magnetic field. Our scheme applies to any atomic species whose ground state is split by the hyperfine interaction. It does not require the use of a static magnetic field. First, these resonances are presented using a simple two-channel model. We then characterise them numerically using our own full-edged implementation of the coupled-channel approach. Our results yield optimistic prospects for the observation of microwave-induced Fano-Feshbach resonances with the bosonic alkali atoms 23Na, 41K, 87Rb, and 133Cs.

This thesis presents a comprehensive study of the magnetic properties and of quantum phase transitions (QPTs) of two different systems which have been investigated by means of low-temperature magnetization measurements. The systems are the heavy-fermion Yb(Rh1-xCox)2Si2 (metallic) and the quantum magnet NiCl2-4SC(NH2)2 (insulator). Although they are very different materials, they share two common properties: magnetism and QPTs. Magnetism originates in Yb(Rh1-xCox)2Si2 from the trivalent state of the Yb3+ ions with effective spin S = 1=2. In NiCl2-4SC(NH2)2, the magnetic Ni2+ ions have spin S = 1. These magnetic ions are located on a body-centered tetragonal lattice in both systems and, in this study, the QPTs are induced by an external magnetic field. In Yb(Rh1-xCox)2Si2 the evolution of magnetism from itinerant in slightly Co-doped YbRh2Si2 to local in YbCo2Si2 is examined analyzing the magnetic moment versus chemical pressure x phase diagram in high-quality single crystals, which indicates a continuous change of dominating energy scale from the Kondo to the RKKY one. The physics of the antiferromagnet YbCo2Si2 can be completely understood. On the other hand, the physics of pure and slightly Co-containing YbRh2Si2 is much more complex, due to the itinerant character of magnetism and the vicinity of the system to an unconventional quantum critical point (QCP). The field-induced AFM QCP in Yb(Rh0.93Co0.07)2Si2 and in pure YbRh2Si2 under a pressure of 1.5GPa is characterized by means of the magnetic Grüneisen ratio. The final part of this thesis describes quantum criticality near the field-induced QCP in NiCl2-4SC(NH2)2 . These results will be compared to the theory of QPTs in Ising and XY antiferromagnets. Since the XY -AFM ordering can be described as BEC of magnons by mapping the spin-1 system into a gas of hardcore bosons, the temperature dependence of the magnetization for a BEC is analytically derived and compared to the results just below the critical field. The remarkable agreement between the BEC theory and experiments in this quantum magnet is one of the most prominent examples of the concept of universality.

Im Rahmen dieser Arbeit wurden die Kondo-Gitter YbT2Si2 (T = Rh, Ir, Co) und CeTPO (T = Ru, Os, Fe, Co) untersucht. In diesen Systemen treten starke ferromagnetische Korrelationen der 4f-Momente zusammen mit ausgeprägter Kondo-Wechselwirkung auf, deren theoretische Beschreibung bislang sehr kontrovers diskutiert wird. Diese Arbeit liefert damit einen essentiellen experimentellen Beitrag zur Physik von ferromagnetischen Kondo-Gittern. So konnten qualitativ hochwertige Einkristalle von YbRh2Si2 hergestellt und erstmalig an einem Schwere-Fermion-System deren kritische Fluktuationen um den magnetischen Phasenübergang analysiert werden. Weiterhin konnte das bis dahin unverstandene Auftreten einer Elektron-Spin-Resonanz (ESR)-Linie in YbT2Si2 auf ferromagnetische Korrelationen zurückgeführt werden. Außerdem wurde mit CeFePO ein neues Schwere-Fermion-System mit starken ferromagnetischen Korrelationen entdeckt sowie mit dem isoelektronischen CeRuPO der seltene Fall eines ferromagnetisch geordneten Kondo-Gitters realisiert. / Within the context of this thesis the Kondo lattices YbT2Si2 (T = Rh, Ir, Co) and CeTPO (T = Ru, Os, Fe, Co) were investigated. In these systems strong ferromagnetic correlations of the 4f-moments together with pronounced Kondo interactions are present, whose theoretical description are pres-ently controversial discussed. Therefore, this work gives an essential experimental contribution to the physics of ferromagnetic Kondo lattices. The main results include the growth of high-quality single crystals of YbRh2Si2 and the first analysis of the critical fluctuations around the magnetic phase transition in a heavy fermion system. Furthermore, the unexpected observation of an electron spin resonance in YbT2Si2 could be ascribed to ferromagnetic correlations. Moreover, a new heavy fermion system CeFePO with strong ferromagnetic correlations was found and with the isoelec-tronic CeRuPO the rare case of a ferromagnetic Kondo-lattice discovered.