In this thesis we introduce a new quantity which we call the dynamic fidelity susceptibility (DFS). We show that it is relevant to out-of-equilibrium dynamics in many-particle quantum systems, taking the problem of an impurity in a Bosonic Josephson junction, and the transverse field Ising model, as examples. Both of these systems feature quantum phase transitions in their ground states and understanding the dynamics near such critical points is currently an active area of research. In particular, sweeping a system through a quantum critical point at finite speed leads to non-adiabatic dynamics. A simple theoretical tool for describing such a scenario is the celebrated Kibble-Zurek theory which predicts that the number of excitations is related to the speed of sweep via the phase transition’s critical exponents at equilibrium. Another theoretical tool, useful in describing the static properties of quantum phase transitions, is the fidelity susceptibility. Our DFS generalizes the concept of fidelity susceptibility to nonequilibrium dynamics, reproducing its results in the static limit, whilst also displaying universal scaling properties, akin to those found in Kibble-Zurek theory, in the non-adiabatic regime. Furthermore, we show that the DFS is the same quantity as the time-dependent quantum Fisher information which provides a measure of multi-partite entanglement, as well as being closely related to out-of-time-order correlators (OTOCs). / Thesis / Master of Science (MSc)

In the study of strongly interacting condensed-matter systems controlled microscopic theories hold a key position. Spin-wave theory, large-N expansion, and $epsilon$-expansion are some of the few successful cornerstones. In this doctoral thesis work, we have developed a novel large-$d$ expansion method, $d$ being the spatial dimension, to study model Hamiltonians hosting a quantum phase transition between a paramagnet and a magnetically ordered phase. A highlight of this technique is that it can consistently describe the entire phase diagram of the above mentioned models, including the quantum critical point. Note that most analytical techniques either efficiently describe only one of the phases or suffer from divergences near the critical point. The idea of large-$d$ formalism is that in this limit, non-local fluctuations become unimportant and that a suitable product state delivers exact expectation values for local observables, with corrections being suppressed in powers of $1/d$. It turns out that, due to momentum summation properties of the interaction structure factor, all diagrams are suppressed in powers of $1/d$ leading to an analytic expansion. We have demonstrated this method in two important systems namely, the coupled-dimer magnets and the transverse-field Ising model. Coupled-dimer magnets are Heisenberg spin systems with two spins, coupled by intra-dimer antiferromagnetic interaction, per crystallographic unit cell (dimer). In turn, spins from neighboring dimers interact via some inter-dimer interaction. A quantum paramagnet is realized for a dominant intra-dimer interaction, while a magnetically ordered phase exists for a dominant (or of the same order as intra-dimer interaction) inter-dimer interaction. These two phases are connected by a quantum phase transition, which is in the Heisenberg O(3) universality class. Microscopic analytical theories to study such systems have been restricted to either only one of the phases or involve uncontrolled approximations. Using a non-linear bond-operator theory for spins with S=$1/2$, we have calculated the $1/d$ expansion of static and dynamic observables for coupled dimers on a hypercubic lattice at zero temperature. Analyticity of the $1/d$ expansion, even at the critical point, is ensured by correctly identifying suitable observables using the mean-field critical exponents. This method yields gapless excitation modes in the continuous symmetry broken phase, as required by Goldstone\'s theorem. In appropriate limits, our results match with perturbation expansion in small ratio of inter-dimer and intra-dimer coupling, performed using continuous unitary transformations, as well as the spin-wave theory for spin-$1/2$ in arbitrary dimensions. We also discuss the Brueckner approach, which relies on small quasiparticle density, and derive the same $1/d$ expansion for the dispersion relation in the disordered phase. Another success of our work is in describing the amplitude (Higgs) mode in coupled-dimer magnets. Our novel method establishes the popular bond-operator theory as a controlled approach. In $d=2$, the results from our calculations are in qualitative agreement with the quantum Monte Carlo study of the square-lattice bilayer Heisenberg AF spin-$1/2$ model. In particular, our results are useful to identify the amplitude (Higgs) mode in the QMC data. The ideas of large-$d$ are also successfully applied to the transverse-field Ising model on a hypercubic lattice. Similar to bond operators, we have introduced auxiliary Bosonsic operators to set up our method in this case. We have also discussed briefly the bilayer Kitaev model, constructed by antiferromagnetically coupling two layers of the Kitaev model on a honeycomb lattice. In this case, we investigate the dimer quantum paramagnetic phase, realized in the strong inter-layer coupling limit. Using bond-operator theory, we calculate the mode dispersion in this phase, within the harmonic approximation. We also conjecture a zero-temperature phase diagram for this model.

<p>In this work, we study two important themes in the physics of the interacting one-dimensional (1D) electron gas: the transition from one-dimensional to higher dimensional behavior, and the role of inhomogeneity. The interplay between interactions, reduced dimensionality, and inhomogeneity drives a rich variety of phenomena in mesoscopic physics. In 1D, interactions fundamentally alter the nature of the electron gas, and the homogeneous 1D electron gas is described by Luttinger Liquid theory. We use Quantum Monte Carlo methods to study two situations that are beyond Luttinger Liquid theory --- the quantum phase transition from a linear 1D electron system to a quasi-1D zigzag arrangement, and electron localization in quantum point contacts. </p><p>Since the interacting electron gas has fundamentally different behavior in one dimension than in higher dimensions, the transition from 1D to higher dimensional behavior is of both practical and theoretical interest. We study the first stage in such a transition; the quantum phase transition from a 1D linear arrangement of electrons in a quantum wire to a quasi-1D zigzag configuration, and then to a liquid-like phase at higher densities. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal; then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase; and, finally, the electrons form a disordered liquid-like phase. We show that the linear to zigzag phase transition occurs even in narrow wires with strong quantum fluctuations, and that it has characteristics which are qualitatively different from the classical transition.</p><p>Experiments in quantum point contacts (QPC's) show an unexplained feature in the conductance known as the ``0.7 Effect''. The presence of the 0.7 effect is an indication of the rich physics present in inhomogeneous systems, and we study electron localization in quantum point contacts to evaluate several different proposed mechanisms for the 0.7 effect. We show that electrons form a Wigner crystal in a 1D constriction; for sharp constriction potentials the localized electrons are separated from the leads by a gap in the density, while for smoother potentials, the Wigner crystal is smoothly connected to the leads. Isolated bound states can also form in smooth constrictions if they are sufficiently long. We thus show that localization can occur in QPC's for a variety of potential shapes and at a variety of electron densities. These results are consistent with the idea that the 0.7 effect and bound states observed in quantum point contacts are two distinct phenomena.</p> / Dissertation

In this thesis I will outline various quantum phase transitions in 2D models of magnets that are amenable to simulation with quantum Monte Carlo techniques. The key player in this work is the theory of deconfined criticality, which generically allows for zero temperature quantum phase transitions between phases that break distinct global symmetries. I will describe models with different symmetries including SU(N), SO(N), and "easy-plane" SU(N) and I will demonstrate how the presence or absence of continuous transitions in these models fits together with the theory of deconfined criticality.

<p>In Part I, the relationship between the topology of the Fermi surface and the entanglement entropy S is examined. Spinless fermionic systems on one and two dimensional lattices at fixed chemical potential are considered. The lattice is partitioned into sub-system of length L and environment, and the entanglement of the subsystem with the environment is calculated via the correlation matrix. S is plotted as a function of the next-nearest or next-next nearest neighbor hopping parameter, t. In 1 dimension, the entanglement entropy jumps at lifshitz transitions where the number of Fermi points changes. In 2 dimensions, a neck-collapsing transition is accompanied by a cusp in S, while the formation of electron or hole-like pockets coincides with a kink in the S as a function of the hopping parameter. The entanglement entropy as a function of subsystem length L is also examined. The leading order coefficient of the LlnL term in 2 dimensions was seen to agree well with the Widom conjecture. Of interest is the difference this coefficient and the coefficient of the term linear in L near the neck-collapsing point. The leading order term changes like |t-t_c|^1/2 whereas the first sub-leading term varies like |t-t_c|^1/3, where t_c is the critical value of the hopping parameter at the transition.</p> <p>In Part II, we study the statistics of fractionalized excitations in a bosonic model which describes strongly interacting excitons in a N-band insulator. The elementary excitations of this system are strings, in a large N limit. A string is made of a series of bosons whose flavors are correlated such that the end points of a string carries a fractionalized flavor quantum number. When the tension of a string vanishes, the end points are deconfined. We determine the statistics of the fractionalized particles described by the end points of strings. We show that either bosons or Fermions can arise depending on the microscopic coupling constants. In the presence of the cubic interaction in the Hamiltonian as the only higher order interaction term, it was shown that bosons are emergent. In the presence of the quartic interaction with a positive coupling constant, it was revealed that the elementary excitations of the system possess Fermion statistics.</p> / Master of Science (MSc)

<p>The following dissertation presents neutron scattering studies on three specific magnetic insulating oxide materials whose lattice is based on triangular structural motifs. Each of the three materials studied, LuCoGaO₄, Co₃V₂O₈ and Tb₂Ti₂O₇, displays an interesting disordered ground state that is reached by different mechanisms: site disorder, geometric frustration, and quantum fluctuations induced by a transverse magnetic field. The main focus of this work is the characterization of the resulting magnetic ground states and magnetic excitations within these systems.</p> <p>Chapters 3, 4 and 5 contain original work in the form of six research articles that have either been published or have been prepared for publication in peer-reviewed journals.</p> <p>Chapter 3 describes studies of the quasi two-dimensional triangular layered antiferromagnet LuCoGaO₄. This material is found to exhibit a spin glass ground state as a result of geometrical frustration and site disorder inherent in this system. Below the freezing temperature, this system exhibits static, two-dimensional correlations consistent with frozen short-range correlated regions in the plane of the bilayers that extend over roughly five unit cells. The dynamic correlations reveal typical spin glass behavior upon cooling. Furthermore, a resonant gapped spin-wave-like excitation is observed, that can be related to the anisotropy in the system. Such an excitation is relatively uncommon in spin glasses and has been studied for the first time in such detail.</p> <p>Chapter 4 is concerned with the study of the kagome staircase system Co₃V₂O₈. While prone to geometrical frustration due to its underlying kagome structural motif, this material is characterized by predominantly ferromagnetic interactions that lead to an unfrustrated, ferromagnetic ground state. In this chapter, departures from this conventional ground state by different disordering mechanisms are investigated. The first part focuses on the effects of site disorder by introducing quenched nonmagnetic impurities into the system. The growth of single crystals of (Co_1-xMg_x)₃V₂O₈ is reported. These crystals reveal that the ferromagnetic ground state is very sensitive to doping, and show that a low doping concentration of 19% leads to a suppression of the ferromagnetic ground state below 1.5 K. This could be understood as percolation problem on the quasi two-dimensional kagome lattice including site and bond percolation. The second part focuses on the influence of a transverse magnetic field on the ground state of Ising spins, introducing quantum fluctuations that lead to quantum phase transitions at ~6.25, 7 and 13 T. The observed quantum phase transitions are characterized by distinct changes in the magnetic structure and their associated spin excitation spectra.</p> <p>Chapter 5 presents studies on the pyrochlore antiferromagnet Tb₂Ti₂O₇, which is a proposed spin liquid candidate but whose actual ground state is still the topic of current debate. The ground state of Tb₂Ti₂O₇ was revisited by neutron scattering measurements, revealing a new phase in the low temperature low field phase diagram that can be described as a frozen antiferromagnetic spin ice that exhibits distinct elastic and inelastic scattering features.</p> / Doctor of Philosophy (PhD)

Neste trabalho realizo uma adaptação do método de Ma, Dasgupta e Hu para o estudo e caracterização das transições de fase quânticas, induzidas por um campo transverso, em cadeias XY de spins 1/2, unidimensionais e aperiódicas, no espírito da adaptação correspondente para cadeias XXZ. O presente trabalho determina de forma analítica uma série de expoentes críticos associados às transições ferro-paramagnéticas do sistema, e dá pistas quanto à natureza das estruturas presentes no estado fundamental. Os resultados são então testados pelo emprego da técnica de férmions livres, da análise de nite size scaling e, no limite de Ising, de resultados extraídos do mapeamento do problema em uma caminhada aleatória. / We employ an adaptation of the Ma, Dasgupta, Hu method in order to analyze the quantum phase transition, induced by a transversal magnetic eld, at spin-1/2 aperiodic XY chains, in analogy to the corresponding adaptation for XXZ chains. We derive analytical expressions for some cri tical exponents related with the ferro-paramagnetic transitions, and shed light onto the nature of the ground state structures. The main results obtained by this approach were tested by the free-fermion method, nite-size scaling analyses and, at the Ising limit of the model, by using results derived from a mapping to a random-walk problem.

Ce manuscrit présente l’étude de transitions de phase quantiques dans l’oxyde BaCo2V2O8, un système antiferromagnétique quasi-unidimensionnel constitué de chaînes d’ions cobalt portant un spin effectif S = 1/2 caractérisé par une forte anisotropie de type Ising. Lors de ce travail, nous avons étudié les propriétés statiques et dynamiques de BaCo2V2O8 sous l’effet de différents paramètres physiques.Notre première étude a porté sur l’effet d’un champ magnétique transverse, i.e. appliqué perpendiculairement à l’axe Ising. Il a été proposé que lors de l’application d’un tel champ, un champ magnétique alterné effectif est induit perpendiculairement à l’axe d’anisotropie et au champ uniforme appliqué. La comparaison d'expériences de diffusion (élastique et inélastique) de neutrons et de calculs numériques nous a permis de montrer que ce champ alterné entre en compétition avec l’anisotropie. Ceci aboutit à une transition de phase originale, dite topologique, que l'on peut modéliser par une théorie quantique des champs nommée « modèle de double sine-Gordon » qui décrit la compétition entre deux excitations topologiques duales. Nous avons pu montrer que BaCo2V2O8 sous champ magnétique transverse était la première réalisation d'une telle théorie.La seconde étude était consacrée à BaCo2V2O8 sous champ magnétique longitudinal, i.e. un champ appliqué parallèlement à l’axe Ising. La dynamique de spins a été sondée grâce à la diffusion inélastique de neutrons et nous avons montré qu’au-dessus d’un champ critique de 4 T, celle-ci semble en accord avec le spectre des fluctuations de spin attendu pour un liquide de Tomonaga Luttinger (TLL). De plus, les calculs numériques ont confirmé que, du fait de l’anisotropie de type Ising dans ce système, la majorité du poids spectral du spectre en énergie est porté par les fluctuations de spins de type longitudinales. Ce résultat est la signature d'un comportement quantique sans analogue classique avec des fluctuations de basses énergies essentiellement longitudinales pilotant la physique du système. Enfin, c’est la première fois que la dynamique de spin dans des chaînes de type Ising a pu être sondée dans cette phase TLL.Les deux dernières études sont préliminaires. Le diagramme de phase de BaCo2V2O8 a été sondé par des mesures calorimétriques sous l’application d’une pression hydrostatique et d’un champ magnétique longitudinal. Afin d’obtenir des pressions allant jusqu’à 10 GPa, nous avons utilisé une cellule à enclumes de diamant. Nous avons effectué des mesures de chaleur spécifique qui nous ont permis de sonder l'effet de la pression sur le Hamiltonien de BaCo2V2O8 au travers de son diagramme de phase $(H, P, T)$. Enfin, nous avons étudié l’effet de la substitution des ions magnétiques Co2+ par des impuretés non-magnétiques Mg2+. Les expériences de diffraction neutronique sous champ longitudinal ont montré que la température et le champ critiques diminuent proportionnellement à la concentration en impuretés. La dynamique de spins à champ magnétique nul a aussi été sondée et révèle l’apparition de modes non-dispersifs, provenant possiblement de l’effet de segmentation des chaînes par les impuretés.En conclusion, nos études expérimentales couplées à des calculs numériques nous ont permis de dévoiler une physique extrêmement riche dans ce composé modèle pour l'étude du magnétisme quantique et des transitions de phase quantiques. / This manuscript is devoted to the study of quantum phase transitions in the BaCo2V2O8 oxide, a quasi-one dimensional antiferromagnet consisting of spin chains of cobalt magnetic ions carrying an effective spin S = 1/2 showing a strong Ising-like anisotropy. To achieve this, we have studied BaCo2V2O8 under the effect of different physical parameters.Our first study concerned the effect of a transverse magnetic field, i.e. applied perpendicularly to the Ising axis. It has been shown that when BaCo2V2O8 is subjected to such a field, an effective staggered magnetic field is induced perpendicularly to both the Ising-axis and the uniform applied field. Using neutron scattering experiments (both elastic and inelastic) compared to numerical calculations, we have proved that this staggered field competes with the Ising-like anisotropy. This leads to a very original quantum phase transition. Our system can actually be mapped onto a quantum field theory called “double sine-Gordon model”, describing the competition between two dual topological excitations. We have thus shown that BaCo2V2O8 under a transverse magnetic field is the first experimental realization of such a theory.The second study was devoted to the effect of a longitudinal magnetic field, i.e. a field applied parallel to the Ising-axis. The spin-dynamics have been investigated by means of inelastic neutron scattering experiments and it has been shown that above a critical field of 4 T, it corresponds to the one expected for a Tomonaga Luttinger liquid phase (TLL). Moreover, numerical calculations have shown that, because of the Ising-like anisotropy in this system, the majority of the spectral weight in the energy spectrum is carried by longitudinal spin fluctuations. This result is the signature of a quantum behavior without classical analogous with low energy longitudinal fluctuations driving the physics of the system. Finally, this is the first time that the dispersion spectrum for an Ising-like spin 1/2 chain could be probed in this TLL phase.The last two studies are preliminary work. The phase diagram of BaCo2V2O8 has been probed by calorimetric measurements under pressure and under a longitudinal magnetic field. Pressures up to 10 GPa have been obtained using a diamond anvil cell. We have then performed specific heat measurements allowing us to investigate the effect of pressure on the Hamiltonian of BaCo2V2O8 through its (H, P, T) phase diagram. Finally, we have also started to study the effect of the substitution of magnetic ions Co2+ by non-magnetic impurities Mg2+. The neutron diffraction experiments under a longitudinal magnetic field have shown that the critical temperature and critical field decrease proportionally to the concentration of impurities. The spin-dynamics at zero-field has also been investigated and reveals the appearance of non-dispersive magnetic modes, which possibly comes from the finite size effect of the spin chains segmented by the non-magnetic impurities.In conclusion, our experimental studies associated to numerical calculations allowed us to unveil a very rich physics in this model compound for the study of quantum magnetism and quantum phase transitions.

Orientador: Marcos Cesar de Oliveira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-09-24T17:07:35Z (GMT). No. of bitstreams: 1 Oliveira_ThiagoRodriguesde_D.pdf: 2410853 bytes, checksum: 48f52d2d48ef1be2ecb155881b8e16df (MD5) Previous issue date: 2008 / Resumo: Esta dissertação tenta contribuir ao entendimento das possíveis interconexões entre a Teoria de Informação Quântica e Matéria Condensada, um novo campo de pesquisa em amplo desenvolvimento. Mais especificamente, investigamos o papel do emaranhamento, ou correlações quânticas, em transições de fase quânticas contínuas. Enquanto o papel do primeiro na Teoria de Informação dispensa apresentação, as últimas são de grande interesse por exibir um comportamento universal, o qual se origina na divergência de um comprimento de correlação. É esta origem mútua em correlações de ambos os fenômenos que cria uma expectativa de uma possível relação entre estes. Nosso trabalho, embasado no estudo do modelo XY unidimensional em um campo transverso, aponta evidências de um favorecimento do emaranhamento multipartite em detrimento do bipartite na transição, e assim da importância do primeiro no estabelecimento de correlações de longo alcance. Nessa tarefa, acabamos por definir uma classe de medidas de emaranhamento multipartite, generalizando o Emaranhamento Global introduzido por Meyer e Wallach em2002. Mostramos que algumas destas classes provêem informações adicionais à do Emaranhamento Global, além de serem escritas de forma simples em termos de funções de correlação. Tal simplicidade permite o estabelecimento de uma relação formal entre uma dessas classes e transições de fase sinalizadas por divergências na energia. Ao final estudamos o papel da quebra de simetria no emaranhamento bipartite e multipartite, evidenciando, uma vez mais, a maior importância do último em relação ao primeiro. Em uma segunda parte, examinamos o uso de estados de produtos de matrizes na aproximação de estados fundamentais de sistemas críticos. Estes estados podem ser vistos como o ansatz utilizado no Grupo de Renormalização de Matriz Densidade (DMRG), quando este é encarado como um método variacional. Analisando o poder de aproximação de tais estados, agora no modelo de Ising, descobrimos que a "dimensão" do ansatz (ou número de graus de liberdade renormalizados) é uma variável relevante do grupo de renormalização de maneira análoga ao tamanho finito do sistema. Isto possibilita uma análise de escala em relação a essa "dimensão" dos estados de produto de matrizes, com uma possível obtenção de propriedades críticas a baixo custo computacional / Abstract: This thesis attempts to contribute to the understanding of possible connections between Quantum Information and Condensed Matter theories, a new field of research in broad development. Specifically, we investigated the role of entanglement, or quantumcorrelations, in continuous quantum phase transitions. While the importance of the first in the theory of Quantum Information is well known dispense presentation, the latter are of great interest as they exhibit a universal behavior, which descent fromthe divergence of the correlation length. This mutual origin of both in correlations is what creates an expectation of a possible link between them. Our work, based on the study of XY dimensional model in a transverse field, brings evidence of multipartite entanglement being favored, in detriment of bipartite in the transition, and thus in the importance of the first in the establishment of long-range correlations. During our journey, we define a class of measures of multipartite entanglement, generalising the Global Entanglement introduced by Meyer and Wallach in 2002. We show that some of these classes provide additional information to the Global Entanglement, as well as being written in a simple way in terms of correlation functions . This simplicity allows the establishment of a formal relationship between those classes and phases transitions marked by non-analycities in the energy. At the end, we studied the role of spontaneous symmetry breaking in the bipartite and multipartite entanglement, demonstrating once again a major role of the last over the first. In a second part, we examine the use of Matrix Product States to approximate ground states of critical systems. This class of states can be seen as the ansatz used in the Density Matrix Renormalization Group (DMRG), when this one is understood as a variational method. Analyzing the power of approximation of these states, now in Ising model, we found that the "dimension" of the ansatz (or number of renormalized degrees of freedom) is a relevant variable in the renormalization group, in a analogous way to the finite size of the system. This enables an analysis of scaling regarding the "size" of Matrix Product States, with a possible acquisition of critical properties at low computation cost / Doutorado / Física da Matéria Condensada / Doutor em Ciências

The vacuum of quantum field theory is not empty space but filled with quantum vacuum fluctuations, which give rise to many intriguing effects. The first part of this Thesis addresses cosmic inflation, where the quantum fluctuations of the inflaton field freeze and get amplified in the expanding universe. Afterwards, we turn our attention towards Bose-Einstein condensates, a laboratory system. Since most of our calculations are performed using a mean-field expansion, we will study the accuracy of a finite-range interaction potential onto such an expansion. Exploiting the universality of quantum fluctuations, several aspects of cosmic inflation will be identified in ballistically expanding Bose-Einstein condensates. The effective action technique for calculating the quantum backreaction will be scrutinized. Finally, we consider dynamic quantum phase transitions in the last part of this Thesis. To this end two specific scenarios will be investigated: firstly, the structure formation during the superfluid to Mott-insulator transition in the Bose-Hubbard model; and secondly, the formation of spin domains as a two-dimensional spin-one Bose gas is quenched from the (polar) paramagnetic to the (planar) ferromagnetic phase. During this quench, the symmetry of the ground state is spontaneously broken and vortices (topological defects) form.