Made available in DSpace on 2016-06-02T20:15:26Z (GMT). No. of bitstreams: 1 4780.pdf: 9997745 bytes, checksum: 24a1f1c6cc3ce4ef4b6ac0cc5009255c (MD5) Previous issue date: 2013-01-11 / Universidade Federal de Sao Carlos / In this thesis, we study the behavior of Quantum Discord in the contexts of open quantum systems and spin chains. Furthermore, we investigate the thermalization process of a spin chain due to interaction with the environment. First, we present a review on the concept of quantum correlation, beginning with the first ideas on non-locality, and leading to the measure of quantum correlations called Quantum Discord. Afterwards, we study the dynamics of the quantum correlations between two non-interacting qubits coupled to Markovian and non- Markovian thermal reservoirs. In the context of spin chains, we investigate the behavior of quantum correlations at finite temperatures, starting with a system composed of two interacting spins, described by XYZ model, in order to generalize this study to the case of infinite unidimensional spin chains, described by XY and XXZ models. In this context, we investigate the relationship between quantum correlations and quantum phase transitions present in these two models. We conclude this thesis with a study of the thermalization process of two interacting spins weakly coupled to independent bosonic thermal reservoirs, or to a single collective reservoir, besides presenting some results for larger systems, composed of an arbitrary number of spins. / Nesta tese estudamos o comportamento da Discórdia Quântica nos contextos de sistemas quânticos abertos e cadeias de spins. Além disso, investigamos também o processo de termalização de uma cadeia de spins sujeita a interação com o meio-ambiente. Primeiramente, apresentamos uma revisão do conceito de correlação quântica, partindo das ideias iniciais sobre não-localidade e tendo como ponto final a medida de correlações quânticas denominada Discórdia Quântica. Posteriormente, estudamos a dinâmica das correlações quânticas entre dois qubits não-interagentes acoplados a reservatórios térmicos markovianos e não-markovianos. No contexto de cadeias de spins, investigamos o comportamento das correlações quânticas a temperaturas finitas, começando com um sistema formado por dois spins interagentes, descrito pelo modelo XYZ para, em seguida, generalizar este estudo para o caso de cadeias de spins unidimensionais infinitas, descritas pelos modelos XY e XXZ. Neste contexto, investigamos a relação entre as correlações quânticas e as transições de fase quânticas presentes nestes dois modelos. Finalizamos esta tese com um estudo sobre o processo de termalização de dois spins interagentes fracamente acoplados a reservatórios térmicos bosônicos independentes ou um único reservatório coletivo, além de apresentar alguns resultados referentes a sistemas maiores, formados por um número arbitrário de spins.

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.

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>The development of ultracold atom physics enables people to study fundamental questions in quantum mechanics within this highly-tunable platform. This dissertation focuses on several topics of the dynamical evolution of quantum systems.</p><p>Chapter 2 and 3 talk about Loschmidt echo, a simple quantity that reveals many hidden properties of a system’s time evolution. Chapter 2 looks for vanishing Loschmidt echo in the complex plane of time and the corresponding dynamical quantum phase transitions (DQPT) in the thermodynamic limit. For a two-site Bose-Hubbard model consisting of weakly interacting particles, DQPTs reside at the time scale inversely proportional to the interaction, where highly entangled pair condensates also show up. Chapter 3 discusses the revival of Loschmidt echo in a discrete time crystal, a Floquet system whose discrete temporal transition symmetry is spontaneously broken. We propose a new design and demonstrate its robustness against the fluctuations in the driving field. It can also be used in precision measurement to go beyond the Heisenberg limit. Experimental schemes are presented.</p><p>Out-of-time-order correlator (OTOC) is a more complicated variant of Loschmidt echo. Experimentally it requires reversing the time evolution. In Chapter 4, by exploiting the SU(1,1) symmetry of a weakly interacting BEC and connecting its quantum dynamics to a hyperbolic space, we obtain a geometric framework that enables experimentalists to manipulate the evolution with great freedom. Backward evolution is then realized effectively to measure OTOC of such SU(1,1) systems.</p><p>Chapter 5 discusses the decoherence of a spin impurity immersed in a spinor BEC. Our calculations show that by looking at the dynamics of the impurity’s reduced density matrix, the phase of the spinor BEC can be detected.</p>

No description available.

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.

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>

Orientador: Eduardo Miranda / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física "Gleb Wataghin" / Made available in DSpace on 2018-09-24T13:52:11Z (GMT). No. of bitstreams: 1 HerazoWarnes_JesusMaria_D.pdf: 4836710 bytes, checksum: 5b7290f1db20bc31b153f3e7202fff39 (MD5) Previous issue date: 2011 / Resumo: A questão da natureza das transições de fases de sistemas de redes de bósons tem se tornado cada vez mais urgente à vista da capacidade de carregamento de átomos ultrafrios em redes ópticas. Nesta tese, tentamos avançar este conhecimento através do estudo de 3 modelos básicos de redes de bósons interagentes. Inicialmente, determinamos o diagrama de fases c as propriedades físicas do modelo bosônico de impureza única de Anderson. Este modelo é interessante tanto em si mesmo quanto por causa de sua relação com outras abordagens teóricas tais como a teoria dinâmica de campo médio bosônica. Usamos como estratégia a inclusão de um pequeno campo externo acoplado ao parâmetro de ordem superfluido, que quebra a simetria global de calibre do modelo. Desta forma, foi possível estudar a transição de condensação de Base-Einstein através do critério de quebra espontânea de simetria global de calibre. Outras quantidades como a ocupação da impureza, o desvio padrão da ocupação e a susceptibilidade com respeito ao campo externo também foram calculadas, caracterizando a transição de fase do modelo. Alguns desses resultados foram comparados com aqueles já obtidos na literatura através do grupo de renormalização numérico. Encontramos bom acordo entre os dois métodos. O segundo estudo realizado nesta tese refere-se ao comportamento crítico do modelo de Bose-Hubbard desordenado através da chamada teoria de campo médio estocástica. O objeto central dessa teoria de campo médio é a distribuição de parâmetros de ordem P(?). Estudos numéricos estabelecem que perto da linha crítica que separa as fases superfluida e vidro de Base do modelo, essa distribuição exibe uma grande região com comportamento de lei de potência P(?) ~ ? ^-(1+ß_c), onde ß_c < 1. Usando esse comportamento como tentativa, obtivemos analiticamente tanto a fronteira de fases quanto o valor do expoente crítico da lei de potência ß_c , encontrando um razoável acordo com os resultados numéricos e avançando o entendimento da natureza da transição de fase específica ao modelo desordenado. Finalmente, o modelo de Bose-Hubbard desordenado para partículas de spin-1 foi estudado dentro da teoria de campo médio estocástica. As distribuições de probabilidade de várias quantidades físicas como o parâmetro de ordem superfluido, o desvio padrão da ocupação por sítio, a fração do condensado, o quadrado do operador de spin, bem como seus valores médios, foram determinados para as três fases do modelo, a saber, o superfluido polar, o isolante de Mott e o vidro de Bose. Uma completa caracterização das propriedades físicas dessas fases e das transições de fase entre elas foi estabelecida / Abstract: The question of the nature of phase transitions of systems of lattice bosons has become increasingly more pressing in view of the capability of loading ultracold atoms in opticallattices. In this thesis we try to advance this understanding through the study of 3 basic models of interacting lattice bosons. Initially, we determined the phase diagram and physical properties of the bosonic singleimpurity Anderson model. This model is interesting both in its own right and because of its relation to other theoretical approaches such as the bosonic dynamical field theory method. We used as strategy the inclusion of a small external field coupled to the superfluid order parameter, which breaks the global gauge symmetry of the model. Thus, it was possible to study the Base-Einstein condensation transition through the criterion of the onset of spontaneous broken global gauge symmetry. Other quantities such as the occupation of the impurity, the standard deviation of the occupation and the susceptibility with respect to the external! Field were calculated characterizing the phase transition in the model. Some of the results were compared with those already reported in the literature, obtained with tic numerical renormalization group. We found good agreement between the two methods. The second study carried out in this thesis concerned the critical behavior of the disordered Bose-Hubbard model within the so-called stochastic mean-field theory. The central object of this mean-field theory is the distribution of order parameters P(?). Numerical studies establish that near the critical line separating the superfluid and Bose glass phases of this model, this distribution shows a wide region of power-law behavior P(?) ~ ? ^-(1+ß_c), where ß_c < 1. Using this behavior as an Ansatz, we obtained analytically both the phase boundary and the value of the critical power-law exponent ß_c, finding a reasonably good agreement with the numerical results and thus shedding new light on the nature of this phase transition specific to disordered model. Finally, the disordered Bose-Hubbard model for spin-1 particles was studied within the stochastic mean-field theory. The probability distributions of various physical quantities, such as the superfluid order parameter, the standard deviation of the occupation per site, the condensate fraction, the square of the spin operator, as well as their average values, were determined for the three phases of the model, namely, the polar superfluid, the Mott insulating and the Bose glass phases. A complete characterization of the physical properties of these phases and the phase transitions between them was then established / Doutorado / Física da Matéria Condensada / Doutor em Ciências

Die Betrachtung von Schwere-Fermionen-Systemen stellt ein wichtiges Themengebiet im Bereich der Festkörperphysik dar. Das Verhalten von Schwere-Fermionen-Systemen wird durch die starken Korrelationen der magnetischen Momente der ungepaarten Spins der f-Elektronen bestimmt. Experimentell zugängliche Messgrößen sind dadurch bei tiefen Temperaturen stark erhöht, so dass sich diese Systeme besonders gut zur Untersuchung von Grundzustandseigenschaften eignen. Zentrales Thema dieser Arbeit ist die Untersuchung zweier intermetallischer Seltenerd-Verbindungen in Bezug auf Quantenphasenübergänge. Diese treten am absoluten Nullpunkt der Temperatur als Funktion eines anderen Parameters wie Magnetfeld, Druck oder chemischer Substitution auf und sind bei endlicher Temperatur durch Abweichungen physikalischer Messgrößen von der durch L. D. Landau aufgestellten Theorie der Fermi-Flüssigkeiten nachzuweisen. Zu diesem Zweck wurden Tieftemperaturexperimente bis hinab zu 20mK und in Magnetfeldern bis zu 18T durchgeführt. Es wurden elektrischer Widerstand, magnetische Wechselfeldsuszeptibilität, Magnetostriktion und thermische Ausdehnung gemessen. / The investigation of heavy-fermion systems marks an important subject in the research field of solid state physics. The behaviour of heavy-fermion systems is dominated by the strong correlations of the magnetic moments of the unpaired f-electron spins. At low temperatures, experimentally accessible variables are strongly enhanced so that these systems are especially suited to analyse ground state properties. The central topic of this thesis is the investigation of two intermetallic rare-earth compounds with regard to quantum phase transitions. The latter occur at zero temperature as a function of parameters such as magnetic field, pressure or chemical substitution. They are traceable at finite temperature due to deviations of physical variables from the theory of Fermi liquids established by L. D. Landau. For this purpose, low-temperature experiments were performed down to 20mK and in magnetic fields up to 18T. Electrical resistivity, magnetic ac susceptibility, magnetostriction and thermal expansion were measured.

This Thesis focuses on different aspects of quantum computation theory: adiabatic quantum algorithms, decoherence during the adiabatic evolution and quantum simulators. After an overview on the area of quantum computation and setting up the formal ground for the rest of the Thesis we derive a general error estimate for adiabatic quantum computing. We demonstrate that the first-order correction, which has frequently been used as a condition for adiabatic quantum computation, does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections and shows that the computational error can be made exponentially small – which facilitates significantly shorter evolution times than the first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time of order of the inverse minimum energy gap is sufficient and necessary. Furthermore, exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grover’s search algorithm. It turns out that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins/qubits), which might limit the scalability of the system. Finally, we propose the use of electron systems to construct laboratory systems based on present-day technology which reproduce and thereby simulate the quantum dynamics of the Ising model and the O(3) nonlinear sigma model.