This work presents macroscopic and microscopic experiments of the disordered hexagonal double perovskite BaTi1/2Mn1/2O3, in order to characterize its electronic, magnetic and structural properties to support the possibility that this system hosts a spin liquid phase. Such assumption is based on the absence of a transition to a magnetically ordered phase in the magnetic and thermodynamic measurements, which points to a strong magnetic frustration in this material. In addition, it is observed the formation of a correlated spin state. To characterize this correlation, we resorted to Muon Spin Resonance (µSR) experiments to measure the low temperature spin dynamics. The zero field µSR relaxation regime displays dynamic magnetism down to T = 0.019 K and longitudinal field experiments support as well that dynamic magnetism persists at low temperatures, a behavior expected for a spin liquid system. The magnetic behavior of BaTi1/2Mn1/2O3 consists in the high temperature physics being dominated by the presence of magnetic trimers, magnetic dimers, and orphan spins. At lower temperatures, the effective magnetic degrees of freedom, composed by orphan spins and magnetic trimers, are correlated but no phase transition is detected down to T = 0.1 K, despite the effective exchange couplings between magnetic trimers and orphan spins being -8.5 K, resulting in a magnetic frustration parameter of at least 85. The possibility that disorder is responsible for the spin liquid ground state is discussed, however, other scenarios are not totally discarded. For example, the possibility that the measured state is not the true ground state, which could lie at even lowers temperatures or the possible formation of a spin glass state. This work raises questions that are not easy to answer. Ultimately, the growth of a single crystal is necessary to continue the characterization of BaTi1/2Mn1/2O3. Besides, theoretical and experimental developments in this field of research are needed to find a more direct and conclusive way to characterize the magnetic phases in this complex material. / Neste trabalho apresento dados experimentais macroscópicos e microscópicos da peroviskita hexagonal dupla BaTi1/2Mn1/2O3, a fim de caracterizar sua estrutura eletrônica, magnética e cristalina para embasar a possibilidade deste sistema apresentar uma fase de líquido de spin. Esta hipótese está baseada na ausência de transição para uma fase magneticamente ordenada nas medidas magnéticas e termodinâmicas, que apontam para uma forte frustração magnética neste material. Além disso, é observada a formação de um estado de spins correlacionados. Para caracterizar esta correlação, recorremos para experimentos de ressonância de múons (µSR) para medir a dinâmica de spins em baixas temperaturas. Dados de µSR para campo magnético nulo mostram em seu regime de relaxamento um magnetismo dinâmico para temperaturas tão baixas quanto T = 0.019 K, adicionalmente, experimentos com campo magnético longitudinal aplicado apontam também que o magnetismo dinâmico persiste em baixas temperaturas, um comportamento esperado para um sistema de líquido de spin. O comportamento magnético do BaTi1/2Mn1/2O3 consiste na física de altas temperaturas sendo dominada pela presença de trimers magnéticos, dimers magnéticos e spins órfãos. Para temperaturas mais baixas, os graus de liberdade magnéticos são efetivamente compostos por spins órfãos e trimers magnéticos, que estão correlacionados mas nenhuma transição de fase é detectada para temperaturas tão baixas quanto T = 0.1 K, mesmo que a constante de interação efetiva entre os spins órfãos e os trimers magnéticos seja -8.5 K, resultando num fator de frustração magnética de ao menos 85. A possibilidade da desordem ser responsável pelo estado fundamental de líquido de spin é discutida, no entanto, outros cenários não estão totalmente descartados, por exemplo, a possibilidade de que o estado medido não seja o verdadeiro estado fundamental, e que este estaria em temperaturas ainda mais baixas ou a possível formação de um estado de vidro de spin. Este trabalho levanta questões que não são fáceis de responder. Por fim, o crescimento de uma amostra monocristalina é necessário para continuar a caracterização do BaTi1/2Mn1/2O3. Ademais, desenvolvimentos de cunho teórico e experimental neste campo de pesquisa são necessários para encontrar um método mais direto e conclusivo para caracterizar a fase magnética neste material complexo.

This work presents macroscopic and microscopic experiments of the disordered hexagonal double perovskite BaTi1/2Mn1/2O3, in order to characterize its electronic, magnetic and structural properties to support the possibility that this system hosts a spin liquid phase. Such assumption is based on the absence of a transition to a magnetically ordered phase in the magnetic and thermodynamic measurements, which points to a strong magnetic frustration in this material. In addition, it is observed the formation of a correlated spin state. To characterize this correlation, we resorted to Muon Spin Resonance (µSR) experiments to measure the low temperature spin dynamics. The zero field µSR relaxation regime displays dynamic magnetism down to T = 0.019 K and longitudinal field experiments support as well that dynamic magnetism persists at low temperatures, a behavior expected for a spin liquid system. The magnetic behavior of BaTi1/2Mn1/2O3 consists in the high temperature physics being dominated by the presence of magnetic trimers, magnetic dimers, and orphan spins. At lower temperatures, the effective magnetic degrees of freedom, composed by orphan spins and magnetic trimers, are correlated but no phase transition is detected down to T = 0.1 K, despite the effective exchange couplings between magnetic trimers and orphan spins being -8.5 K, resulting in a magnetic frustration parameter of at least 85. The possibility that disorder is responsible for the spin liquid ground state is discussed, however, other scenarios are not totally discarded. For example, the possibility that the measured state is not the true ground state, which could lie at even lowers temperatures or the possible formation of a spin glass state. This work raises questions that are not easy to answer. Ultimately, the growth of a single crystal is necessary to continue the characterization of BaTi1/2Mn1/2O3. Besides, theoretical and experimental developments in this field of research are needed to find a more direct and conclusive way to characterize the magnetic phases in this complex material. / Neste trabalho apresento dados experimentais macroscópicos e microscópicos da peroviskita hexagonal dupla BaTi1/2Mn1/2O3, a fim de caracterizar sua estrutura eletrônica, magnética e cristalina para embasar a possibilidade deste sistema apresentar uma fase de líquido de spin. Esta hipótese está baseada na ausência de transição para uma fase magneticamente ordenada nas medidas magnéticas e termodinâmicas, que apontam para uma forte frustração magnética neste material. Além disso, é observada a formação de um estado de spins correlacionados. Para caracterizar esta correlação, recorremos para experimentos de ressonância de múons (µSR) para medir a dinâmica de spins em baixas temperaturas. Dados de µSR para campo magnético nulo mostram em seu regime de relaxamento um magnetismo dinâmico para temperaturas tão baixas quanto T = 0.019 K, adicionalmente, experimentos com campo magnético longitudinal aplicado apontam também que o magnetismo dinâmico persiste em baixas temperaturas, um comportamento esperado para um sistema de líquido de spin. O comportamento magnético do BaTi1/2Mn1/2O3 consiste na física de altas temperaturas sendo dominada pela presença de trimers magnéticos, dimers magnéticos e spins órfãos. Para temperaturas mais baixas, os graus de liberdade magnéticos são efetivamente compostos por spins órfãos e trimers magnéticos, que estão correlacionados mas nenhuma transição de fase é detectada para temperaturas tão baixas quanto T = 0.1 K, mesmo que a constante de interação efetiva entre os spins órfãos e os trimers magnéticos seja -8.5 K, resultando num fator de frustração magnética de ao menos 85. A possibilidade da desordem ser responsável pelo estado fundamental de líquido de spin é discutida, no entanto, outros cenários não estão totalmente descartados, por exemplo, a possibilidade de que o estado medido não seja o verdadeiro estado fundamental, e que este estaria em temperaturas ainda mais baixas ou a possível formação de um estado de vidro de spin. Este trabalho levanta questões que não são fáceis de responder. Por fim, o crescimento de uma amostra monocristalina é necessário para continuar a caracterização do BaTi1/2Mn1/2O3. Ademais, desenvolvimentos de cunho teórico e experimental neste campo de pesquisa são necessários para encontrar um método mais direto e conclusivo para caracterizar a fase magnética neste material complexo.

Nesta dissertação estudamos uma probabilidade obtida a partir de conceitos da Mecânica Estatística Quântica do ponto de vista da Teoria Ergódica. A probabilidade é obtida a partir de um estado KMS sobre um lattice unidimensional de spins quânticos. Mostramos que esta probabilidade é mixing para o shift. Além disso, mostramos que vale um princípio dos grandes desvios para uma certa classe de funções e exploramos algumas propriedades do Jacobiano. Iremos considerar o estado KMS associado a um certo Hamiltoniano específico agindo sobre o lattice de spins quânticos. Nas seções iniciais vamos apresentar alguns conceitos e prerequisitos básicos (como operadores densidade, produto tensorial, C*-algebras e estados KMS) para o entendimento do resultado principal / In this dissertation we study a probability derived from Quantum Statistical Mechanics through the viewpoint of Ergodic Theory. The probability is obtained from a KMS state acting on a one dimensional lattice of quantum spins. We show that this probability is mixing for the shift map. Moreover, we show that a large deviation principle is true for a certain class of functions and we explore some properties of the Jacobian. We will consider the KMS state associated to a certain specific Hamiltonian acting on the quantum spin lattice. In the initial sections we will present some concepts and prerequisites (such as density operators, tensor product, C*-algebras and KMS states) for the understanding of our main results.

This thesis, divided into two parts, is concerned with the analysis of spectral and dynamical characteristics of certain quantum spin systems in the presence of either I) quenched disorder, or II) dynamical noise. In the first part, the quantum random energy model (QREM), a mean-field spin glass model with a many-body localisation transition, is studied. In Chapter 2, we attempt a diagrammatic perturbative analysis of the QREM from the ergodic side, proceeding by analogy to the single-particle theory of weak localisation. Whilst we are able to describe diffusion, the analogy breaks down and a description of the onset of localisation in terms of quantum corrections quickly becomes intractable. Some progress is possible by deriving a quantum kinetic equation, namely the relaxation of the one-spin reduced density matrix is determined, but this affords little insight and extension to two-spin quantities is difficult. We change our approach in Chapter 3, studying instead a stroboscopic version of the model using the formalism of quantum graphs. Here, an analytic evaluation of the form factor in the diagonal approximation is possible, which we find to be consistent with the universal random matrix theory (RMT) result in the ergodic regime. In Chapter 4, we replace the QREM's transverse field with a random kinetic term and present a diagrammatic calculation of the average density of states, exact in the large-N limit, and interpret the result in terms of the addition of freely independent random variables. In the second part, we turn our attention to noisy quantum spins. Chapter 5 is concerned with noninteracting spins coupled to a common stochastic field; correlations arising from the common noise relax only due to the spins' differing precession frequencies. Our key result is a mapping of the equation of motion of n-spin correlators onto the (integrable) non-Hermitian Richardson-Gaudin model, enabling exact calculation of the relaxation rate of correlations. The second problem, addressed in Chapter 6, is that of the dynamics of operator moments in a noisy Heisenberg model; qualitatively different behaviour is found depending on whether or not the noise conserves a component of spin. In the case of nonconserving noise, we report that the evolution of the second moment maps onto the Fredrickson-Andersen model - a kinetically constrained model originally introduced to describe the glass transition. This facilitates a rigorous study of operator spreading in a continuous-time model, providing a complementary viewpoint to recent investigations of random unitary circuits.

No description available.

In this thesis we present results from quantum Monte Carlo for the fully-frustrated honeycomb lattice. The XXZ model is of interest in the classical limit, as there is a mapping between the classical fully-frustrated honeycomb Ising model groundstates and the classical hard-core dimer model groundstate. The aim of this work is to explore the effect of quantum fluctuations on the fully-frustrated honeycomb model to see what sort of interesting physics arises. One might expect unusual physics due to the quantum hard-core dimer model, where interesting physics are known to exist. This is because there is a duality mapping between the classical dimer model and the classical fully-frustrated honeycomb Ising model. Indeed, by studying the fully-frustrated honeycomb XXZ model we find that in some cases the system orders into crystal-like structures, a case of order-by-disorder. The most interesting case, when the frustrating bonds are chosen randomly, reveals to us a novel state without any discernible order while at the same time avoiding the freezing one would expect of a glass. This state is a featureless system lacking low temperature magnetic susceptibility---a candidate ``quantum spin liquid''. Future work that might more easily measure quantum spin liquid criteria is suggested.

No description available.

In this thesis we present results from quantum Monte Carlo for the fully-frustrated honeycomb lattice. The XXZ model is of interest in the classical limit, as there is a mapping between the classical fully-frustrated honeycomb Ising model groundstates and the classical hard-core dimer model groundstate. The aim of this work is to explore the effect of quantum fluctuations on the fully-frustrated honeycomb model to see what sort of interesting physics arises. One might expect unusual physics due to the quantum hard-core dimer model, where interesting physics are known to exist. This is because there is a duality mapping between the classical dimer model and the classical fully-frustrated honeycomb Ising model. Indeed, by studying the fully-frustrated honeycomb XXZ model we find that in some cases the system orders into crystal-like structures, a case of order-by-disorder. The most interesting case, when the frustrating bonds are chosen randomly, reveals to us a novel state without any discernible order while at the same time avoiding the freezing one would expect of a glass. This state is a featureless system lacking low temperature magnetic susceptibility---a candidate ``quantum spin liquid''. Future work that might more easily measure quantum spin liquid criteria is suggested.

Quantum spin models play an important role in theoretical condensed matter physics and quantum information theory. One numerical technique that is frequently used in studies of quantum spin systems is exact diagonalization. In this approach, numerical methods are used to find the lowest eigenvalues and associated eigenvectors of the Hamilton matrix of the quantum system. The computational problem is thus to determine the lowest eigenpairs of an extremely large, sparse matrix. Although many sophisticated iterative techniques for the determination of a small number of lowest eigenpairs can be found in the literature, most exact diagonalization studies of quantum spin systems have employed the Lanczos algorithm. In contrast to this, other methods have been applied very successfully to the similar problem of electronic structure calculations. The well known VASP code for example uses a Block Davidson method as well as the residual-minimization - direct inversion of the iterative subspace algorithm (RMM-DIIS). The Davidson algorithm is closely related to the Lanczos method but usually needs less iterations. The RMM-DIIS method was originally proposed by Pulay and later modified by Wood and Zunger. The RMM-DIIS method is particularly interesting if more than one eigenpair is sought since it does not require orthogonalization of the trial vectors at each step. In this work I study the efficiency of the Lanczos, Block Davidson and RMM-DIIS method when applied to basic quantum spin models like the spin-1/2 Heisenberg chain, ladder and dimerized ladder. I have implemented all three methods and are currently applying the methods to the different models. In our presentation I will compare the three algorithms based on the number of iterations to achieve convergence, the required computational time. An Intel's Many-Integrated Core architecture with Intel Xeon Phi coprocessor 5110P integrates 60 cores with 4 hardware threads per core was used for RMM-DIIS method, the achieved parallel speedups were compared with those obtained on a conventional multi-core system.

Nesta dissertação estudamos uma probabilidade obtida a partir de conceitos da Mecânica Estatística Quântica do ponto de vista da Teoria Ergódica. A probabilidade é obtida a partir de um estado KMS sobre um lattice unidimensional de spins quânticos. Mostramos que esta probabilidade é mixing para o shift. Além disso, mostramos que vale um princípio dos grandes desvios para uma certa classe de funções e exploramos algumas propriedades do Jacobiano. Iremos considerar o estado KMS associado a um certo Hamiltoniano específico agindo sobre o lattice de spins quânticos. Nas seções iniciais vamos apresentar alguns conceitos e prerequisitos básicos (como operadores densidade, produto tensorial, C*-algebras e estados KMS) para o entendimento do resultado principal / In this dissertation we study a probability derived from Quantum Statistical Mechanics through the viewpoint of Ergodic Theory. The probability is obtained from a KMS state acting on a one dimensional lattice of quantum spins. We show that this probability is mixing for the shift map. Moreover, we show that a large deviation principle is true for a certain class of functions and we explore some properties of the Jacobian. We will consider the KMS state associated to a certain specific Hamiltonian acting on the quantum spin lattice. In the initial sections we will present some concepts and prerequisites (such as density operators, tensor product, C*-algebras and KMS states) for the understanding of our main results.