Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / Quantum spin models are useful in many areas of physics, such as strongly correlated materials and quantum phase transitions, or, generally, quantum many-body systems. Most of the models of interest are not analytically solvable. Therefore they are often investigated using computational methods. However, spin models with frustrated interactions are not easily simulated numerically with existing methods, and more effective algorithms are needed. In this thesis, I will cover two areas of quantum spin research: 1. studies of several quantum spin models and 2. development of more efficient computational methods. The discussion of the computational methods and new algorithms is integrated with the physical properties of the models and new results obtained. I study the frustrated S=1/2 J1-J2 model Heisenberg model, the J-Q model, the Ising model with a transverse magnetic field, and a two-orbital spin model describing the magnetic properties of iron pnictides. I will discuss several computational algorithms, including a cluster variational method using mean-field boundary conditions, variational quantum Monte Carlo simulation with clusters-based wave functions, as well as a method I call "optilization" -- an algorithm constructed in order to accelerate the process of optimization with a large number of parameters. I apply it to matrix product states. / 2031-01-02

Quantum phenomena in high-Tc superconductors and dimerized quantum Heisenberg antiferromagnets are studied analytically in this thesis. The implications of the Fermi surface consisting of the disjoint pieces, observed in cuprate superconductors, are considered. It is demonstrated that in this case the g-wave superconducting pairing is closely related to d-wave pairing. The superconductivity in this system can be described in terms of two almost degenerate superconducting condensates. As a result a new spatial scale lg, much larger than the superconducting correlation length x, arises and a new collective excitation corresponding to the relative phase oscillation between condensates, the phason, should exist. The Josephson tunneling for such a two-component system has very special properties. It is shown that the presence of g-wave pairing does not contradict the existing SQUID experimental data on tunneling in the ab-plane. Possible ways to experimentally reveal the g-wave component and the phason in a single tunnel junction, as well as in SQUID experiments, are discussed. The dimerized quantum spin models studied in this thesis include double-layer and alternating chain Heisenberg antiferromagnets. To account for strong correlations between the S=1 elementary excitations (triplets) in the dimerized phase; the analytic Brueckner diagram approach based on a description of the excitations as triplets above a strong-coupling singlet ground state; has been applied. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Analytical calculations of physical observables are in excellent agreement with numerical data.Results obtained for double layer antiferromagnet near the (zero temperature) quantum critical point coincide with those previously obtained within the nonlinear s model approach Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets in the Heisenberg chain with frustration.

No description available.

Neste trabalho, estudamos as dualidades entre modelos de spin em redes bidimensionais a partir de uma abordagem tensorial. Nessa abordagem, componentes de tensores são associadas aos vértices e arestas da rede de forma que a função de partição Z é construída a partir da contração dos índices dessas componentes e é, portanto, um escalar por mudanças de base da álgebra de grupo C[G] utilizada para a definição dos tensores. A partir daí, e observando que a forma das componentes fixam o modelo estudado, obtemos um modelo diferente para cada mudança de base proposta. Esses diferentes modelos possuirão, no entanto, a mesma função de partição, já que esta é um invariante sob tais transformações. De fato, haverá uma infinidade de modelos todos duais entre si. Neste ponto, fixamos nossa atenção nos modelos com spin Zn, nos quais estão incluídos o modelo de Ising, o modelo de Potts e o modelo de Ashkin-Teller-Potts. Explorando uma transformação de base específica, fomos capazes de rederivar a dualidade de Kramers e Wanniers para o modelo de Ising. Usando argumentos análogos, mostramos também que os modelos de Potts com n = 3 e 4 são autoduais e que não existe autodualidade para este modelo com n _ 5. O modelo de Ashkin-Teller-Potts foi mostrado ser autodual para todo n 2 N. / In this work, we study the dualities between spin models in two-dimensional lattices from a tensorial approach. In this approach, we associate tensor components to the vertices and links so that the partition function Z is constructed by a contraction of the indices of the tensor components thereby making Z a scalar under change of basis of the group algebra C[G] used to de_ne the tensors. Having obtained this, and noting that the values of the components _x the studied model, we obtain a di_erent model for each basis transformation proposed. These di_erent models, however, have the same partition function since Z is invariant under these transformations. In fact we can obtain several models all dual to each other in this manner. We then focus on Zn spin models, which include the Ising model, the Potts model and Ashkin- Teller-Potts model. Exploring a speci_c basis transformation, we are able to rederive Kramers and Wanniers\' duality for the Ising model. With analogous arguments, we also show that Potts models with n = 3 and n = 4 are self-dual whereas this property is lost for n _ 5. The Ashkin-Teller-Potts model is shown to be self-dual for all n 2 N.

Les réseaux de nanoaimants à frustration géométrique font l'objet d'investigations depuis maintenant une décennie. Ils permettent de réaliser expérimentalement des modèles de spins théoriques qui n'ont parfois pas d'équivalent naturel. Ces réseaux présentent, entre autres, l'intérêt d'offrir un accès direct aux configurations locales de spin. Le travail présenté dans ce manuscrit vise à réaliser expérimentalement le modèle dit de "glace carrée" dans un réseau nanoaimants. Ce modèle hautement frustré présente un état fondamental massivement dégénéré, à l'origine de son entropie résiduelle à basse température. Dans ce travail, nous allons présenter deux approches permettant de réaliser le modèle de glace carrée.La première consiste à introduire dans le réseau carré conventionnel des nanoaimants supplémentaires. Sous certaines conditions, ceux-ci agissent en modifiant les couplages effectifs entre les aimants du réseau principal. Pour cela, les aimants additionnels doivent se comporter passivement vis à vis du réseau principal. Dans une étude théorique, nous montrerons que l'analyse du hamiltonien dans l'espace réciproque échoue à saisir les propriétés essentielles de ce nouveau modèle. C'est en calculant l'énergie de configurations aléatoires de spins que nous prouverons que notre système présente les caractéristiques recherchées. Nous porterons une attention particulière à l'effet de la portée et de la nature des interactions entre aimants. Grâce à des simulations micromagnétiques par différences finies, nous déterminerons les géométries pertinentes à employer pour une réalisation expérimentale. Grâce aux outils de microfabrication disponibles au laboratoire, nous avons pu fabriquer de tels réseaux. Les aimants sont constitués de permalloy mince, ce qui leur permet d'atteindre un régime superparamagnétique lors d'un recuit thermique. Nous avons observé que les aimants additionnels influencent comme prévu la physique du réseau carré. Un biais expérimental a cependant engendré une aimantation rémanente élevée dans certains réseaux. Cet effet a malheureusement masqué les corrélations caractéristiques attendues dans le modèle de glace carrée. Mais ces travaux ont permis de mettre en évidence un effet inattendu des aimants additionnels. Ceux-ci semblent stimuler les fluctuations thermiques dans les réseaux qui en sont pourvus.La seconde approche consiste à surélever les aimants orientés dans l'une des deux directions du réseau carré. Nous emploierons une méthodologie similaire à celle décrite précédemment pour l'étude de ce nouveau système. Théoriquement, le contrôle de la surélévation permet d'explorer trois modèles de spins différents, dont le modèle de glace carrée. Nous avons fabriqué des réseaux avec plusieurs surélévations, estimées au moyen de simulations micromagnétiques. Pour des raisons techniques, nous avons cette fois travaillé avec des nanoaimants de permalloy épais. Ils présentent la caractéristique d'être athermiques. Les fluctuations sont alors introduites grâce à un champ magnétique tournant et décroissant. Nous montrerons par des simulations que cette dynamique particulière stimule l'apparition de corrélations ferromagnétiques. La désaimantation réduit alors les surélévations nécessaires à la réalisation du modèle de glace carrée. Nous avons observé expérimentalement que l'effet de la surélévation est parfaitement cohérent avec nos prévisions. Les facteurs de structure que nous avons obtenus prouvent que nous avons réussi à réaliser le modèle de glace avec des nanoaimants. Cette approche nous a permis d'observer pour la première fois une phase de Coulomb dans l'espace direct. Ce travail ouvre des perspectives intéressantes pour l'étude des excitations existant dans cette phase, analogues à des monopoles magnétiques classiques. / Since a decade, a big interest has grown about geometrically frustrated nanomagnets arrays. They allow experimental realisation of theoretical spin models, that sometimes have no natural counterpart. In addition to their high flexibility, these networks provide a direct access to local spin configurations. The work presented in this manuscript aims to realise experimentally the so-called "square ice" model, using nanomagnets array. This highly frustrated model has already been theoretically studied. It is found to have a massively degenerated ground state, associated to a residual entropy at low temperature. In this thesis, we present two approaches that should achieve the square ice model.The first one consists to introduce additional magnets in the conventional square nanomagnets array. They can act through an effective coupling between the magnets of the initial network. The condition required is that additional magnets should behave passively against main magnets. We will show in a theoretical study that a reciprocal space analysis of the Hamiltonian fails to grasp the essential properties of the new model. By computing the energy of a number of random spins configurations, we will show that the square ice model can be achieved. A special attention will be paid to the influence of the range and the nature of magnets interactions. Using finite-difference micromagnetic simulations, we will determine the geometries adapted to an experimental realisation. We were able to make such networks using the microfabrication tools available in the laboratory. Our magnets are made of thin permalloy films. This allows the magnets to reach a superparamagnetic regime during a thermal annealing. We observed that additional magnets have the expected influence on square nanomagnets arrays. However, an experimental bias caused a high residual magnetisation in some networks. This effect has unfortunately hided the correlations expected in the square ice model. But this work shown an unexpected effect. Additional magnets appear to enhance thermal fluctuations in the networks.The second approach is to raise the magnets oriented in one of the two directions of the square lattice. For the study of this new system, a methodology similar to that described above will be used. Theoretically, the control of the elevation can explore three different spins models, including the square ice model. We made arrays for different elevations, estimated by micromagnetic calculations. For technical reasons, we worked with thick permalloy nanomagnets. Their thickness makes them insensitive to thermal fluctuations. Fluctuations are then introduced using a decreasing rotating magnetic field. Our simulations show that this particular dynamic stimulates emergence of ferromagnetic correlations. The field demagnetisation then reduce the elevations required for achieving the square ice model. We have experimentally observed that the elevation has an effect perfectly consistent with our previsions. Experimental structure factors show that we succeed to achieve the square ice model with nanomagnets. This approach allowed us to observe, for the first time, a Coulomb phase in the real space. This work opens interesting perspectives for studying the excitations of this phase. It has previously been shown that they are similar to classical magnetic monopoles.

Neste trabalho, estudamos as dualidades entre modelos de spin em redes bidimensionais a partir de uma abordagem tensorial. Nessa abordagem, componentes de tensores são associadas aos vértices e arestas da rede de forma que a função de partição Z é construída a partir da contração dos índices dessas componentes e é, portanto, um escalar por mudanças de base da álgebra de grupo C[G] utilizada para a definição dos tensores. A partir daí, e observando que a forma das componentes fixam o modelo estudado, obtemos um modelo diferente para cada mudança de base proposta. Esses diferentes modelos possuirão, no entanto, a mesma função de partição, já que esta é um invariante sob tais transformações. De fato, haverá uma infinidade de modelos todos duais entre si. Neste ponto, fixamos nossa atenção nos modelos com spin Zn, nos quais estão incluídos o modelo de Ising, o modelo de Potts e o modelo de Ashkin-Teller-Potts. Explorando uma transformação de base específica, fomos capazes de rederivar a dualidade de Kramers e Wanniers para o modelo de Ising. Usando argumentos análogos, mostramos também que os modelos de Potts com n = 3 e 4 são autoduais e que não existe autodualidade para este modelo com n _ 5. O modelo de Ashkin-Teller-Potts foi mostrado ser autodual para todo n 2 N. / In this work, we study the dualities between spin models in two-dimensional lattices from a tensorial approach. In this approach, we associate tensor components to the vertices and links so that the partition function Z is constructed by a contraction of the indices of the tensor components thereby making Z a scalar under change of basis of the group algebra C[G] used to de_ne the tensors. Having obtained this, and noting that the values of the components _x the studied model, we obtain a di_erent model for each basis transformation proposed. These di_erent models, however, have the same partition function since Z is invariant under these transformations. In fact we can obtain several models all dual to each other in this manner. We then focus on Zn spin models, which include the Ising model, the Potts model and Ashkin- Teller-Potts model. Exploring a speci_c basis transformation, we are able to rederive Kramers and Wanniers\' duality for the Ising model. With analogous arguments, we also show that Potts models with n = 3 and n = 4 are self-dual whereas this property is lost for n _ 5. The Ashkin-Teller-Potts model is shown to be self-dual for all n 2 N.

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.

The thesis is divided in two parts, corresponding to the two main subjects on which I have worked during my PhD. In the first Part, we introduce many-body long-range interacting systems, such as plasma and self-gravitating systems. We first review the well known properties of isolated systems, which show peculiar behaviors both for what concern the equilibrium and the relaxation to equilibrium. We then consider long-range systems driven away from equilibrium and we show how the techniques developed for isolated systems can be extended to describe these situations. Generalizations to describe simplified models relevant for geophysical flows and two-dimensional turbulence are also discussed. Our work stands at the edge between the study of long-range interacting systems and the study of non-equilibrium systems.The second part of the thesis is devoted to the study of equilibrium properties of Hamiltonian systems with energy landscape techniques. A number of recent results is reviewed and applied to long and short-range interacting systems. One of the scope of my work was to study models whose energy landscape is much more complicated than what previously done. In the case of ferromagnetic short-range O(n) models on hypercubic lattices, our analysis unveiled a striking similarity between the critical energies of the Ising model and the O(n) models defined on the same lattice with the same interaction matrix. Generalizations of the Stillinger and Weber formalism are discussed as preliminary results and future perspectives.

Orientador: Jacques Wainer / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-16T22:50:12Z (GMT). No. of bitstreams: 1 Andre_AmauryBosso_M.pdf: 698462 bytes, checksum: 3a97278e3328845adbb26c7cb448204b (MD5) Previous issue date: 2010 / Resumo: O gerenciamento de workflows é uma realidade atualmente, mas os sistemas atuais carecem de suporte à verificação de correção em modelos de workflow. Este trabalho visa a realização de verificações em processos, objetivando a detecção de erros sintáticos, como a existência de atividades mal modeladas, ou seja, sem condições de entrada ou de saída. É objetivo deste trabalho também a definição de verificações de ordem estrutural, como detectar se o processo de workflow não possui deadlocks (estado em que o processo trava sem possibilidade de progredir), ou verificar se existem atividades mortas no processo (atividades impossíveis de serem executadas), ou se há terminações incompletas, ou seja, transições pendentes após o processo ter atingido seus objetivos. Além de verificações sintáticas e estruturais, é necessário também a realização de verificações semânticas do modelo, ou seja, é importante que os processos possam ser validados quanto a características que dizem respeito à sua organização lógica, a um nível um pouco mais alto de informação do que simplesmente estrutural. Por exemplo, é diretamente impactante na qualidade do modelo de um processo, definir se este possui conflitos ao acesso de recursos. Dessa forma, um processo estruturalmente correto, pode ficar travado em um deadlock, devido à concorrência quanto ao acesso de um recurso comum entre atividades distintas. Além disso, verificações de restrições de custo, por exemplo, também podem inviabilizar um processo. Todas essas verificações são importantes para decidir se um processo de workflow é correto. A maior contribuição deste trabalho, é então a definição de uma modelagem de processos de workflow que possibilite a verificação de problemas sintáticos, estruturais e semânticos, todos em uma única ferramenta, que se mostra escalável para processos reais, além de possibilitar a verificação de questões ad-hoc, específicas de cada instância, como verificar ordenações entre atividades específicas, etc / Abstract: Workflow management is a reality nowadays, but today's systems give very little support to verify correctness in workflow models. This work aims to perform formal verification, with the goal of detecting syntactic errors, like the existence of activities poorly modeled, in other words, activities with no precondition or effect. It is a goal too, the definition of workflows structural verification, as to detect if the process does not have deadlocks (state in which the process is stuck with no possibility of getting any further), or verifying if there are dead activities in the process (activities impossible to be reached), or if exist incomplete terminations, ie, pending transitions after the process reached its objectives. Besides syntactic and structural verifications, it is necessary too, to perform semantic verifications in the process, in other words, it is important to validate the processes in respect to characteristics of its logical organization, in a higher level of information than simply structural verification. For example, it is directly impacting in the quality of the process model the definition if it has resource access conflicts. In this way, a process that is structurally correct, can be stuck in a deadlock, due to the concurrency in the access of a common resource of distinct activities. Besides that, verifications of costs restrictions, for example, can spoil a process. All these verifications are important to decide if a workflow model is correct. The main contribution of this work is the definition of workflow processes modeling that makes it possible to perform syntactic, structural and semantic verifications, all in a unique tool, that is showed to be scalable for real process, and even possible to verify ad-hoc questions, specific to the model, as checking activities ordering, for example / Mestrado / Inteligência Artificial, Verificação e Validação / Mestre em Ciência da Computação

O objetivo deste trabalho foi o estudo do Ansatz de Bethe Algébrico (ABA), que é uma técnica utilizada na obtenção dos auto-estados do hamiltoniano de inúmeros modelos da Mecânica Estatística e da Teoria Quântica de Campos. Aplicamos este procedimento na diagonalização de três modelos de spins: o modelo de Heisenberg, o modelo de Heisenberg-Sklyanin e o modelo de Heisenberg-Cherednik. Na diagonalização do primeiro modelo, não foi possível encontrar todos os auto-estados do hamiltoniano através do ABA e, durante o procedimento de obtenção das expressões analíticas, nos deparamos com um conjunto de identidades inédito na literatura. A matriz de borda do modelo de Heisenberg-Sklyanin acopla o último e o primeiro sítios, generalizando o modelo anterior, e permite estabelecer uma relação limite com outros modelos integráveis. Neste caso também não conseguimos obter todos os auto-estados utilizando a técnica do ABA. Diferentemente do que ocorreu para os primeiros modelos, o de Heisenberg-Cherednik, com acoplamentos que alternam a intensidade ao longo da cadeia de spin, apresentou um conjunto completo de auto-estados quando diagonalizado pelo ABA. / The goal of this work was to study the Algebraic Bethe ansatz (ABA), which is a technique used to obtain the eigenstates of Hamiltonian of many models of Statistical Mechanics and Quantum Field Theory. We apply this procedure to diagonalize three types of spin models: the Heisenberg model, the Heisenberg-Sklyanin model and the Heisenberg-Cherednik model. On diagonalization of the …rst model, we could not …nd all the eigenstates of Hamiltonian through ABA, and during the procedure for obtaining the analytical expressions, we face an unprecedented set of identities in literature. The Sklyanin´s boundary matrix couples the fi…rst and last sites, generalizing the previous model, and provides a limit for other integrable models. In this case also did not get all eigenstates using the technique of ABA. Unlike what happened with the …rst models, the Heisenberg-Cherednik model, with alternating couplings the intensity along the spin chain, presented a complete set of eigenstates when diagonalized by ABA.