We use Monte Carlo simulations in order to investigate the density of states and the two-time density autocorrelation function for the two- and three-dimensional Coulomb glass as well as the Bose glass phase of flux lines in type-II superconductors. We find a very fast forming gap in the density of states and explore the dependence of temperature and filling fraction. By studying two scaling methods, we find that the nonequilibrium relaxation properties can be described sufficiently by a full-aging scaling analysis. The scaling exponents depend on both temperature and filling fraction, and are thus non-universal. We look at the trends of these exponents and found that as either the temperature decreases or the filling fraction deviates more from half-filling, the exponents reflect slower relaxation kinetics. With two separate interaction potentials, a comparison of relaxation rates and the gap in the density of states is made. / Ph. D.

Estudamos transições de fases quânticas em gases bosônicos ultrafrios aprisionados em redes óticas. A física desses sistemas é capturada por um modelo do tipo Bose-Hubbard que, no caso de um sistema sem desordem, em que os átomos têm interação de curto alcance e o tunelamento é apenas entre sítios primeiros vizinhos, prevê a transição de fases quântica superfluido-isolante de Mott (SF-MI) quando a profundidade do potencial da rede ótica é variado. Num primeiro estudo, verificamos como o diagrama de fases dessa transição muda quando passamos de uma rede quadrada para uma hexagonal. Num segundo, investigamos como a desordem modifica essa transição. No estudo com rede hexagonal, apresentamos o diagrama de fases da transição SF-MI e uma estimativa para o ponto crítico do primeiro lobo de Mott. Esses resultados foram obtidos usando o algoritmo de Monte Carlo quântico denominado Worm. Comparamos nossos resultados com os obtidos a partir de uma aproximação de campo médio e com os de um sistema com uma rede ótica quadrada. Ao introduzir desordem no sistema, uma nova fase emerge no diagrama de fases do estado fundamental intermediando a fase superfluida e a isolante de Mott. Essa nova fase é conhecida como vidro de Bose (BG) e a transição de fases quântica SF-BG que ocorre nesse sistema gerou muitas controvérsias desde seus primeiros estudos iniciados no fim dos anos 80. Apesar dos avanços em direção ao entendimento completo desta transição, a caracterização básica das suas propriedades críticas ainda é debatida. O que motivou nosso estudo, foi a publicação de resultados experimentais e numéricos em sistemas tridimensionais [Yu et al. Nature 489, 379 (2012), Yu et al. PRB 86, 134421 (2012)] que violam a lei de escala $\\phi= u z$, em que $\\phi$ é o expoente da temperatura crítica, $z$ é o expoente crítico dinâmico e $ u$ é o expoente do comprimento de correlação. Abordamos essa controvérsia numericamente fazendo uma análise de escalonamento finito usando o algoritmo Worm nas suas versões quântica e clássica. Nossos resultados demonstram que trabalhos anteriores sobre a dependência da temperatura de transição superfluido-líquido normal com o potencial químico (ou campo magnético, em sistemas de spin), $T_c \\propto (\\mu-\\mu_c)^\\phi$, estavam equivocados na interpretação de um comportamento transiente na aproximação da região crítica genuína. Quando os parâmetros do modelo são modificados de maneira a ampliar a região crítica quântica, simulações com ambos os modelos clássico e quântico revelam que a lei de escala $\\phi= u z$ [com $\\phi=2.7(2)$, $z=3$ e $ u = 0.88(5)$] é válida. Também estimamos o expoente crítico do parâmetro de ordem, encontrando $\\beta=1.5(2)$. / In this thesis, we have studied phase transitions in ultracold atoms trapped in optical lattices. The physics of these systems is captured by Bose-Hubbard-like models, which predicts a quantum phase transition (the so called superfluid-Mott insulator, or SF-MI) when varying the potential depth of the optical lattice in a system without disorder, where atoms have short range interactions, and tunneling is allowed only between nearest neighbors. Our studies followed two directions, one is concerned with the influence of the geometry of the lattice namely, we study the changes in the phase diagram of the SF-MI phase transition when the optical lattice is hexagonal. A second direction is to include disorder in the original system. In our study of the hexagonal lattice, we obtain the phase diagram for the SF-MI transition and give an approximation for the critical point of the first Mott lobe, using a quantum Monte Carlo algorithm called Worm. We also compare our results with the ones from the squared lattice and obtained using mean-field approximation. When disorder is included in the system, a new phase emerge in the ground-state phase diagram intermediating the superfluid and Mott-insulator phases. This new phase is called Bose-glass (BG) and the quantum phase transition SF-BG was the subject of many controversies since its first studies in the late 80s. Though many progress towards its thorough understanding were made, basics characterization of critical proprieties are still under debate. Our study was motivated by the publication of recent experimental and numerical studies in three-dimensional systems [Yu et al. Nature 489, 379 (2012), Yu et al. PRB 86, 134421 (2012)] reporting strong violations of the key quantum critical relation, $\\phi= u z$, where $\\phi$ is the critical-temperature exponent, $z$ and $ u$ are the dynamic and correlation length critical exponents, respectively. We addressed this controversy numerically performing finite-size scaling analysis using the Worm algorithm, both in its quantum and classical scheme. Our results demonstrate that previous work on the superfluid-to-normal fluid transition-temperature dependence on chemical potential (or magnetic field, in spin systems), $T_c \\propto (\\mu-\\mu_c)^\\phi$, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the $\\phi= u z$ law [with $\\phi=2.7(2)$, $z=3$, and $ u = 0.88(5)$] holds true. We also estimate the order parameter exponent, finding $\\beta=1.5(2)$.

Estudamos transições de fases quânticas em gases bosônicos ultrafrios aprisionados em redes óticas. A física desses sistemas é capturada por um modelo do tipo Bose-Hubbard que, no caso de um sistema sem desordem, em que os átomos têm interação de curto alcance e o tunelamento é apenas entre sítios primeiros vizinhos, prevê a transição de fases quântica superfluido-isolante de Mott (SF-MI) quando a profundidade do potencial da rede ótica é variado. Num primeiro estudo, verificamos como o diagrama de fases dessa transição muda quando passamos de uma rede quadrada para uma hexagonal. Num segundo, investigamos como a desordem modifica essa transição. No estudo com rede hexagonal, apresentamos o diagrama de fases da transição SF-MI e uma estimativa para o ponto crítico do primeiro lobo de Mott. Esses resultados foram obtidos usando o algoritmo de Monte Carlo quântico denominado Worm. Comparamos nossos resultados com os obtidos a partir de uma aproximação de campo médio e com os de um sistema com uma rede ótica quadrada. Ao introduzir desordem no sistema, uma nova fase emerge no diagrama de fases do estado fundamental intermediando a fase superfluida e a isolante de Mott. Essa nova fase é conhecida como vidro de Bose (BG) e a transição de fases quântica SF-BG que ocorre nesse sistema gerou muitas controvérsias desde seus primeiros estudos iniciados no fim dos anos 80. Apesar dos avanços em direção ao entendimento completo desta transição, a caracterização básica das suas propriedades críticas ainda é debatida. O que motivou nosso estudo, foi a publicação de resultados experimentais e numéricos em sistemas tridimensionais [Yu et al. Nature 489, 379 (2012), Yu et al. PRB 86, 134421 (2012)] que violam a lei de escala $\\phi= u z$, em que $\\phi$ é o expoente da temperatura crítica, $z$ é o expoente crítico dinâmico e $ u$ é o expoente do comprimento de correlação. Abordamos essa controvérsia numericamente fazendo uma análise de escalonamento finito usando o algoritmo Worm nas suas versões quântica e clássica. Nossos resultados demonstram que trabalhos anteriores sobre a dependência da temperatura de transição superfluido-líquido normal com o potencial químico (ou campo magnético, em sistemas de spin), $T_c \\propto (\\mu-\\mu_c)^\\phi$, estavam equivocados na interpretação de um comportamento transiente na aproximação da região crítica genuína. Quando os parâmetros do modelo são modificados de maneira a ampliar a região crítica quântica, simulações com ambos os modelos clássico e quântico revelam que a lei de escala $\\phi= u z$ [com $\\phi=2.7(2)$, $z=3$ e $ u = 0.88(5)$] é válida. Também estimamos o expoente crítico do parâmetro de ordem, encontrando $\\beta=1.5(2)$. / In this thesis, we have studied phase transitions in ultracold atoms trapped in optical lattices. The physics of these systems is captured by Bose-Hubbard-like models, which predicts a quantum phase transition (the so called superfluid-Mott insulator, or SF-MI) when varying the potential depth of the optical lattice in a system without disorder, where atoms have short range interactions, and tunneling is allowed only between nearest neighbors. Our studies followed two directions, one is concerned with the influence of the geometry of the lattice namely, we study the changes in the phase diagram of the SF-MI phase transition when the optical lattice is hexagonal. A second direction is to include disorder in the original system. In our study of the hexagonal lattice, we obtain the phase diagram for the SF-MI transition and give an approximation for the critical point of the first Mott lobe, using a quantum Monte Carlo algorithm called Worm. We also compare our results with the ones from the squared lattice and obtained using mean-field approximation. When disorder is included in the system, a new phase emerge in the ground-state phase diagram intermediating the superfluid and Mott-insulator phases. This new phase is called Bose-glass (BG) and the quantum phase transition SF-BG was the subject of many controversies since its first studies in the late 80s. Though many progress towards its thorough understanding were made, basics characterization of critical proprieties are still under debate. Our study was motivated by the publication of recent experimental and numerical studies in three-dimensional systems [Yu et al. Nature 489, 379 (2012), Yu et al. PRB 86, 134421 (2012)] reporting strong violations of the key quantum critical relation, $\\phi= u z$, where $\\phi$ is the critical-temperature exponent, $z$ and $ u$ are the dynamic and correlation length critical exponents, respectively. We addressed this controversy numerically performing finite-size scaling analysis using the Worm algorithm, both in its quantum and classical scheme. Our results demonstrate that previous work on the superfluid-to-normal fluid transition-temperature dependence on chemical potential (or magnetic field, in spin systems), $T_c \\propto (\\mu-\\mu_c)^\\phi$, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the $\\phi= u z$ law [with $\\phi=2.7(2)$, $z=3$, and $ u = 0.88(5)$] holds true. We also estimate the order parameter exponent, finding $\\beta=1.5(2)$.

Condensed matter systems undergoing phase transitions rarely allow exact solutions. The presence of disorder renders the situation  even worse but collective Monte Carlo methods and parallel algorithms allow numerical descriptions. This thesis considers classical phase transitions in disordered spin systems in general and in effective models of superfluids with disorder and novel interactions in particular. Quantum phase transitions are considered via a quantum to classical mapping. Central questions are if the presence of defects changes universal properties and what qualitative implications follow for experiments. Common to the cases considered is that the disorder maps out correlated structures. All results are obtained using large-scale Monte Carlo simulations of effective models capturing the relevant degrees of freedom at the transition. Considering a model system for superflow aided by a defect network, we find that the onset properties are significantly altered compared to the $\lambda$-transition in $^{4}$He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario. For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent $z=1.8 \pm 0.05$ contradicting the long standing result $z=d$. Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role. Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations. / <p>QC 20150306</p>

This thesis contains four studies of the effects of disorder and randomness on strongly correlated quantum phases of matter. Starting with an itinerant ferromagnet, I first use an order-by-disorder approach to show that adding quenched charged disorder to the model generates new quantum fluctuations in the vicinity of the quantum critical point which lead to the formation of a novel magnetic phase known as a helical glass. Switching to bosons, I then employ a momentum-shell renormalisation group analysis of disordered lattice gases of bosons where I show that disorder breaks ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This work was carried out in the context of ultracold atomic gases, however the same physics can be realised in dimerised quantum antiferromagnets. By mapping the antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show the importance of the non-ergodic effects to the thermodynamics of the model and find evidence for an unusual glassy phase known as a Mott glass not previously thought to exist in this model. Finally, I use a mean-field numerical approach to simulate current generation quantum gas microscopes and demonstrate the feasibility of a novel measurement scheme designed to measure the Edwards-Anderson order parameter, a quantity which describes the degree of ergodicity breaking and which has never before been experimentally measured in any strongly correlated quantum system. Together, these works show that the addition of disorder into strongly interacting quantum systems can lead to qualitatively new behaviour, triggering the formation of new phases and new physics, rather than simply leading to small quantitative changes to the physics of the clean system. They provide new insights into the underlying physics of the models and make direct connection with experimental systems which can be used to test the results presented here.

Nous présentons l'étude par Résonance Magnétique Nucléaire (RMN) du composé NiCl2-4SC(NH2)2, dit DTN, constitué de chaînes de spins 1 faiblement couplées suivant les directions transverses aux chaînes. A basse température et dans un champ magnétique compris entre les deux valeurs critiques Hc1 et Hc2, ce système s'ordonne dans un état de type Condensat de Bose-Einstein (CBE). Dans cette phase, nous décrivons d'une part la détermination expérimentale du paramètre d'ordre (aimantation transverse), dont l'amplitude est bien décrite par la théorie mais dont la phase (orientation) semble fixée par un terme d'anisotropie. D'autre part nous avons étudié les fluctuations des spins électroniques à basse énergie, par la mesure du taux de relaxation RMN 1/T1, et montré que celui-ci obéit à la loi de puissance 1/T1 propto T^5. Ce comportement peut être associé au processus de 2ème ordre lié à des excitations ayant une dispersion linéaire, tels que les quasiparticules de Bogoliubov, mais sa nature n'est pas encore bien comprise. En dehors de la phase CBE, nous décrivons l'étude des fluctuations de spin dans le régime critique quantique (H ~ Hc2), dans lequel nous établissons une loi d'échelle sur 1/T1, identique à celle que l'on a observé dans un autre composé de description équivalente (échelle de spins BPCB), prouvant ainsi l'universalité de ce régime [S. Mukhopadhyay et al., Phys. Rev. Lett. 109, 177206 (2012)]. Nous avons aussi étudié les effets du désordre induit par la substitution Br-Cl dans le composé Ni(Cl1−xBrx)2-4SC(NH2)2, pour lequel des mesures par des techniques macroscopiques ont suggéré l'existence d'une phase "verre de Bose" [R. Yu et al., Nature 489, 379 (2012)]. Cette phase est caractérisée, pour différentes concentrations du dopage x = 4%, 9%, 13%, par un pic de relaxation RMN 1/T1 au champ Hp = 13.5 T, marquant un regain des fluctuations longitudinales et présentant une forte distribution des valeurs de 1/T1 - probablement due à l'aspect vitreux du système. L'indépendance du Hp en fonction de x démontre que la physique y est dominée par les effets locaux liés aux dopants. / We present a Nuclear Magnetic Resonance (NMR) study of the NiCl2-4SC(NH2)2 compound, called DTN, consisting of spin-1 chains that are weakly coupled along the transverse directions. At low temperatures and for magnetic field values between the two critical fields Hc1 and Hc2, this system enters an ordered phase of the Bose-Einstein Condensate (BEC) type. Within this phase, we first describe the experimental determination of the order parameter (transverse magnetization), the amplitude of which is found to be well described by theory while its phase (orientation) seems to be fixed by an anisotropy term. Second, by NMR relaxation rate 1/T1 we have studied the low-energy fluctuations of the electronic spins and found that they obey the power law 1/T1 ~ T 5. Such a behaviour points to a 2nd order process involving linearly dispersing excitations, such as Bogoliubov quasiparticles, but its nature is not yet well understood. Outside the BEC phase, we report a study of the spin fluctuations in the quantum critical regime (H ~ Hc2), demonstrating a scaling law on 1/T1 similar to the one that has already been observed in another equivalent compound, BPCB spin-ladder, thus proving the universality of this regime [S. Mukhopadhyay et al., Phys. Rev. Lett. 109, 177206 (2012)]. We have also studied the effect of disorder induced by the Br-Cl substitution in the compound Ni(Cl1-xBrx)2-4SC(NH2)2 (doped DTN), for which measurements using macroscopic techniques have suggested the existence of a "Bose glass" phase [R. Yu et al., Nature 489, 379 (2012)]. This phase is characterized, for all studied doping concentrations x = 4%, 9%, 13%, by a peak in the NMR relaxation rate 1/T1 at the field value Hp ~ 13.5 T, evidencing an upsurge of the longitudinal <SzSz> spin fluctuations, and presenting strong inhomogeneity of the 1/T1 values – probably reflecting the glassy character of the system. The observed doping-independence of Hp demonstrates that the corresponding physics is dominated by local effects due to the dopants.

<p>In high-temperature superconductors a large region of the magnetic phase diagram is occupied by a vortex phase that displays a number of exciting phenomena. At low temperatures, vortices form a truly superconducting solid phase which at high temperatures turns into a dissipative vortex liquid. The character of the transition between these two phases depends on the amount and type of disorder present in the system. For weak point disorder the vortex solid-to-liquid transition is a first-order melting. In the presence of strong point disorder the solid is thought to be a vortex-glass and the transition into the liquid is instead of second order. When the disorder is correlated, like twin boundaries or artificially introduced columnar defects, the transition is also second order, but has essentially different properties. In this work, the transition between the solid and liquid phases of the vortex state has been studied by resistive transport measurements in mainly YBa2Cu3O7-[delta](YBCO) single crystals with different types of disorder.</p><p>The vortex-glass transition has been investigated in an extended model for the vortex-liquid resistivity close to the transition that takes into account both the temperature and magnetic field dependence of the transition line. The resistivity of samples with different properties was measured with various contact configurations at several magnetic fields and analyzed within this model. For each sample, attempts were made to scale the transition curves to one curve according to a suitable scaling variable predicted by the model. Good scaling was found in a number of different situations. The influence of increasing anisotropy and angular dependence of the magnetic field in the model were also considered.</p><p>The vortex solid-to-liquid transition was also studied in heavy-ion irradiated YBCO single crystals. The ions create columnar defects in the sample that act as correlated disorder. A magnetic field was applied at a tilt angle with respect to the direction of the columns. At the transition the resistance disappears as a power law with different exponents in the three orthogonal directions considered. This provides evidence for a new type of critical behavior with fully anisotropic critical scaling properties not previously found in any physical system.</p><p>The effect on the vortex solid-to-liquid transition of high magnetic fields applied parallel to the superconducting layers of underdoped YBCO single crystals was also studied. Some novel features were observed: a sharp kink appearing close to Tc at high magnetic fields and a triple dip in the angular dependence of the resistivity close to B||ab in some regions of the phase diagram.</p> / <p>I högtemperatursupraledare består en stor del av det magnetiska fasdiagrammet av en vortexfas som uppvisar ett flertal spännande fenomen. Vid låga temperaturer bildar vortexarna en fast vortexfas utan elektriskt motstånd. Vid högre temperatur övergår denna fas till en dissipativ vortexvätska. Egenskaperna hos denna fasövergång beror på oordningen i form av defekter. Vid svag punktoordning är fasomvandlingen mellan det fasta och flytande vortextillståndet en första ordningens smältövergång. Vid stark punktoordning anses den fasta fasen vara ett vortexglas och övergången till vortexvätskan är istället av andra ordningen. När oordningen är korrelerad, som för tvillinggränser eller artificiellt skapade kolumndefekter, är övergången också av andra ordningen men med väsentligt annorlunda egenskaper. I detta arbete har övergången mellan det fasta och det flytande vortextillståndet studerats med resistiva transportmätningar i framförallt enkristaller av YBa2Cu3O7-[delta] (YBCO) med olika typer av oordning.</p><p>Vortexglasövergången har undersökts i en utvidgad modell för resistansen i vortexvätskan nära fasövergången där hänsyn tas till såväl temperatur- som fältberoendet. Resistansen hos prover med olika egenskaper mättes i varierande magnetfält och i flera kontaktkonfigurationer och analyserades inom denna modell. Övergångskurvorna skalades till en kurva med en skalningsvariabel som givits av modellen. God skalning uppnåddes i flera olika fall. Effekten av ökande anisotropi och vinkelberoendet i modellen undersöktes också.</p><p>Vortexövergången mellan det fasta och det flytande vortextillståndet undersöktes även i enkristaller av YBCO bestrålade med tunga joner. Jonerna skapade kolumndefekter som fungerar som korrelerad oordning. Vinkeln mellan pålagt magnetfält och dessa kolumndefekter varierades. Vid fasövergången avtar resistansen som en potenslag med olika exponenter i de tre undersökta ortogonala riktningarna. Detta ger experimentell belägg för en ny typ av kritiskt beteende med fullständigt anisotropa kritiska skalningsegenskaper.</p><p>Egenskaparna hos på vortexövergången mellan fast och flytande fas vid höga magnetfält parallella med de supraledande lagren hos underdopade YBCO enkristaller undersöktes också. Några nya effekter observerades: en skarp knyck uppstod nära Tc vid höga magnetfält och en tredubbel dipp i den vinkelberoende resistiviteten nära B||ab i några regioner av fasdiagrammet.</p>

In high-temperature superconductors a large region of the magnetic phase diagram is occupied by a vortex phase that displays a number of exciting phenomena. At low temperatures, vortices form a truly superconducting solid phase which at high temperatures turns into a dissipative vortex liquid. The character of the transition between these two phases depends on the amount and type of disorder present in the system. For weak point disorder the vortex solid-to-liquid transition is a first-order melting. In the presence of strong point disorder the solid is thought to be a vortex-glass and the transition into the liquid is instead of second order. When the disorder is correlated, like twin boundaries or artificially introduced columnar defects, the transition is also second order, but has essentially different properties. In this work, the transition between the solid and liquid phases of the vortex state has been studied by resistive transport measurements in mainly YBa2Cu3O7-[delta](YBCO) single crystals with different types of disorder. The vortex-glass transition has been investigated in an extended model for the vortex-liquid resistivity close to the transition that takes into account both the temperature and magnetic field dependence of the transition line. The resistivity of samples with different properties was measured with various contact configurations at several magnetic fields and analyzed within this model. For each sample, attempts were made to scale the transition curves to one curve according to a suitable scaling variable predicted by the model. Good scaling was found in a number of different situations. The influence of increasing anisotropy and angular dependence of the magnetic field in the model were also considered. The vortex solid-to-liquid transition was also studied in heavy-ion irradiated YBCO single crystals. The ions create columnar defects in the sample that act as correlated disorder. A magnetic field was applied at a tilt angle with respect to the direction of the columns. At the transition the resistance disappears as a power law with different exponents in the three orthogonal directions considered. This provides evidence for a new type of critical behavior with fully anisotropic critical scaling properties not previously found in any physical system. The effect on the vortex solid-to-liquid transition of high magnetic fields applied parallel to the superconducting layers of underdoped YBCO single crystals was also studied. Some novel features were observed: a sharp kink appearing close to Tc at high magnetic fields and a triple dip in the angular dependence of the resistivity close to B||ab in some regions of the phase diagram. / I högtemperatursupraledare består en stor del av det magnetiska fasdiagrammet av en vortexfas som uppvisar ett flertal spännande fenomen. Vid låga temperaturer bildar vortexarna en fast vortexfas utan elektriskt motstånd. Vid högre temperatur övergår denna fas till en dissipativ vortexvätska. Egenskaperna hos denna fasövergång beror på oordningen i form av defekter. Vid svag punktoordning är fasomvandlingen mellan det fasta och flytande vortextillståndet en första ordningens smältövergång. Vid stark punktoordning anses den fasta fasen vara ett vortexglas och övergången till vortexvätskan är istället av andra ordningen. När oordningen är korrelerad, som för tvillinggränser eller artificiellt skapade kolumndefekter, är övergången också av andra ordningen men med väsentligt annorlunda egenskaper. I detta arbete har övergången mellan det fasta och det flytande vortextillståndet studerats med resistiva transportmätningar i framförallt enkristaller av YBa2Cu3O7-[delta] (YBCO) med olika typer av oordning. Vortexglasövergången har undersökts i en utvidgad modell för resistansen i vortexvätskan nära fasövergången där hänsyn tas till såväl temperatur- som fältberoendet. Resistansen hos prover med olika egenskaper mättes i varierande magnetfält och i flera kontaktkonfigurationer och analyserades inom denna modell. Övergångskurvorna skalades till en kurva med en skalningsvariabel som givits av modellen. God skalning uppnåddes i flera olika fall. Effekten av ökande anisotropi och vinkelberoendet i modellen undersöktes också. Vortexövergången mellan det fasta och det flytande vortextillståndet undersöktes även i enkristaller av YBCO bestrålade med tunga joner. Jonerna skapade kolumndefekter som fungerar som korrelerad oordning. Vinkeln mellan pålagt magnetfält och dessa kolumndefekter varierades. Vid fasövergången avtar resistansen som en potenslag med olika exponenter i de tre undersökta ortogonala riktningarna. Detta ger experimentell belägg för en ny typ av kritiskt beteende med fullständigt anisotropa kritiska skalningsegenskaper. Egenskaparna hos på vortexövergången mellan fast och flytande fas vid höga magnetfält parallella med de supraledande lagren hos underdopade YBCO enkristaller undersöktes också. Några nya effekter observerades: en skarp knyck uppstod nära Tc vid höga magnetfält och en tredubbel dipp i den vinkelberoende resistiviteten nära B||ab i några regioner av fasdiagrammet. / QC 20110125

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.