Dissertations / Theses: 'HEISENBERG MODEL; SPIN'

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Lozano, Dairon Andrés Jiménez. "Modelo de Heisenberg Antiferromagnético de spin-1/2 na rede triangular com interações competitivas." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-21092016-212043/.

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Nesta dissertação estudamos sistemas de spins em redes de baixa dimensionalidade e em temperatura nula, analisando suas transições de fases quânticas. Mais precisamente, estu- damos as propriedades do estado fundamental e as possíveis transições de fase do modelo de Heisenberg quântico antiferromagnético de spin-1/2, com interações entre os primeiros e segundos vizinhos, em diversas redes, e em particular na rede triangular, que é o foco de nosso estudo. Para a obtenção do estado fundamental aproximado, usamos um método variacional em que a rede é particionada num conjunto de plaquetas de sítios. O estado fundamental é escrito como um produto tensorial dos estados das plaquetas. Para a rede triangular, escolhemos um triângulo como uma plaqueta. Quatro fases foram encontra- das: a fase antiferromagnética de Néel, a colinear, a fase de Néel modificada e aquela que denominamos de ligação covalente ressonante. Obtivemos as energias e as magnetizações de subrede em função da razão entre as interações de primeiros e segundos vizinhos. En- tre as fases de Néel e a colinear, podemos observar a fase de ligação covalente ressonante caracterizada como um singleto quanto ao spin de cada plaqueta. In this thesis we study spin systems in low-dimensional lattices at zero temperature, analyzing their quantum phase transitions. More precisely, we study the properties of the ground state and the possible phase transitions in the antiferromagnetic spin-1/2 quan- tum Heisenberg model with interaction between the first and second neighbors, in several lattices, and in particular in the triangular lattice, which is the focus of our study. To obtain the approximate ground state, we use a variational method in which the lattice is partitioned into a set of plates of sites. The ground state is written as a tensor product of the states of plates. For the triangular lattice, we choose a triangle as a plate. Four phases were found: the antiferromagnetic Néel phase, the collinear, the modified Néel phase and that we call resonating valence bond. We obtained the energy and the magnetization as a function of the ratio of the interactions between the first and second neighbor sites. Between the Néel and collinear phases, we can observe the spin resonating valence bond phase, characterized as a singlet with respect to the spin of each plate.

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Fong, Manson Cheuk-Man. "Heisenberg model with spin anisotropy on the Kagomé lattice /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202008%20ZFONG.

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Rowan, David Glenn. "Theoretical studies of disordered short-range spin models." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299226.

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Szàllàs, Attila. "Heisenberg antiferromagnetic model on 2D quasiperiodic tilings." Paris 11, 2008. http://www.theses.fr/2008PA112174.

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Le pavage de Penrose est une structure quasipériodique bidimensionnelle, utilisée dans la description des composés quasicristallins. Cette structure est parfaitement ordonnée, avec une symétrie de rotation cinq et elle est invariante sous un changement d'échelle par un facteur τ. Nous avons étudié les propriétés d'un modèle d'Heisenberg sur le pavage de Penrose construit à partir de losanges, en utilisant une méthode de développement en ondes de spin. Les énergies et fonctions d'ondes des magnons (quantum d'une onde des spins) ont été étudiées dans le cadre d'une théorie linéarisée. Les propriétés spatiales des modes propres ont été étudiées en détail. A basse énergie, nous trouvons que les états propres sont relativement étendus. Une analyse multifractale montre qu'ils sont de type “critique”, ayant une distribution d'exposants multifractaux. L'énergie de l’état fondamental de cette antiferromagnetique, et la distribution des aimantations locales dans cet état ont été calculés. Des projections dans l’espace perpendiculaire montrent la simplicité sous-jacente de ce état "complexe". Un simple modèle analytique, l’étoile de Heisenberg à deux niveaux, a été présenté pour expliquer de la distribution d'aimantation locales dans ce système antiferromagnétique. Dans une dernière partie, les effets de désordre de type “phason” sont considérés. Nous avons progressivement augmenté le désordre géometrique de la structure originale. Nous montrons, à l'aide d'un développement en ondes des spin ainsi que par QMC, que l'aimantation alternée diminue exponentiellement vers une valeur asymptote en fonction du désordre. La vitesse des ondes des spin augmente avec le désordre The Penrose tiling is a perfectly ordered two dimensional structure with fivefold symmetry and scale invariance. We considered a Heisenberg antiferromagnet on the Penrose rhombus tiling, and showed it has an inhomogeneous Neel-ordered ground state. Spin wave energies and wavefunctions were studied in the linear spin wave approximation. Spatial properties of eigenmodes were characterized in several different ways. At low energies, eigenstates were found to be relatively extended, and appeared to show multifractal scaling. At higher energies, states were found to be more localized, and, depending on the energy, confined to sites of a specified coordination number. The ground state energy of this antiferromagnet, and local staggered magnetizations were calculated. Perpendicular space projections were shown, showing the underlying simplicity of this “complex" ground state. A simple analytical model, the two-tier Heisenberg star, was presented to explain the staggered magnetization distribution in this antiferromagnetic system. The effects of a novel type of disorder in a two dimensional quantum antiferromagnet is considered. The original bipartite structure is geometrically disordered in such a way that no frustration is introduced, and the system retains a Neel ordered ground state. We show, using a linear spin wave expansion and QMC, that the staggered moment decreases exponentially as a function of increasing disorder. The spatial distribution of staggered magnetizations becomes more homogeneous compared to the deterministic tiling, the effective spin wave velocity increases with disorder, and singularities in the magnon spectrum and wavefunctions are partly smoothed

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Oliveira, Ravenna Rodrigues. "Modelo de Heisenberg para cadeia de spins." reponame:Repositório Institucional da UFC, 2016. http://www.repositorio.ufc.br/handle/riufc/19729.

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OLIVEIRA, R. R. Modelo de Heisenberg para cadeia de spins. 2016. 58 f. Dissertação (Mestrado em Física) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016. Submitted by Giordana Silva (giordana.nascimento@gmail.com) on 2016-09-26T18:55:18Z No. of bitstreams: 1 2016_dis_rroliveira.pdf: 2847981 bytes, checksum: edaf4ac09f696a3c00730658e00f0e9c (MD5) Approved for entry into archive by Giordana Silva (giordana.nascimento@gmail.com) on 2016-09-26T18:55:56Z (GMT) No. of bitstreams: 1 2016_dis_rroliveira.pdf: 2847981 bytes, checksum: edaf4ac09f696a3c00730658e00f0e9c (MD5) Made available in DSpace on 2016-09-26T18:55:56Z (GMT). No. of bitstreams: 1 2016_dis_rroliveira.pdf: 2847981 bytes, checksum: edaf4ac09f696a3c00730658e00f0e9c (MD5) Previous issue date: 2016-08-04 Everyday new technological inventions arrives in the world, improving the life of the society as one. For new devices to have improvements, science needs to be improved too. Within science, a subject that stands out is the magnetism properties of the materials, like ferromagnetic materials. Due to the studies about the magnetism properties of the materials become possible the criation of computer hard drive. In this dissertation, we use the Heisenberg model to better understand the spin waves, which commonly appear in magnetic materials. This model considers the exchange interation of spins, together with the Zeeman effect. In this dissertation we use the eisenberg model for spin waves applied to some networks. The study for a two layer network where one of them is displaced in relation to the other was done. The behavior for a network displaced to the left and a network equally dislocated to the right is the same. Due to the helical structure of an RNA molecule we study the Heisenberg model in a network around a cylinder. For this network, we found that case where the network is symmetrically displaced is degenerate, which can be broke by changing the network configuration, so there is no symmetry in the system. Todo dia novas invenções tecnológicas surgem no mundo, melhorando a vida da sociedade como um todo. Para que os novos dispositivos estejam cada vez mais evoluindo, a ciência também precisa estar evoluindo. Dentro da ciência, um assunto que ganha destaque são as propriedades magnéticas dos materiais, tais quais materiais ferromagnéticos. A partir do estudo de materiais magnéticos foi possível a fabricação de dispositivos como o HD de computadores. Nos sistemas ferromagnéticos os spins vizinhos estão acoplados uns aos outros por meio da interação de troca, possuindo modos coletivos chamados de ondas de spin. Para entender as propriedades de ondas de spin utiliza-se o modelo de Heisenberg, que considera o termo de troca, juntamente com o efeito Zeeman. Nesta dissertação utilizamos o modelo de Heisenberg para ondas de spins para algumas redes. O estudo para uma rede de duas camadas onde uma é deslocada em relação à outra foi realizado, observando que o comportamento para uma rede deslocada para a esquerda e uma rede igualmente deslocada para a direita é o mesmo. Motivados pelo formato helicoidal da molécula de RNA, estudamos uma rede ao redor de um cilindro. O caso onde a rede é disposta simetricamente é encontrado degenerescência, que pode ser desfeita alterando a configuração da rede de modo que não haja mais simetria.

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Silva, Wanêssa Façanha da. "Ondas de spin em redes decoradas." reponame:Repositório Institucional da UFC, 2014. http://www.repositorio.ufc.br/handle/riufc/13700.

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SILVA, Wanêssa Façanha. Ondas de spin em redes decoradas. 2014. 62 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-22T20:40:26Z No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-22T20:40:38Z (GMT) No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) Made available in DSpace on 2015-10-22T20:40:38Z (GMT). No. of bitstreams: 1 2014_dis_wfsilva.pdf: 5621741 bytes, checksum: 74eb09424ba24b6a3b1acd4b7df5dee6 (MD5) Previous issue date: 2014 Low-dimensional systems have attracted much attention lately due to systems such as graphene and carbon nanotubes. Such systems have great potential for technological applications. In particular the creation of electronic devices due to their specific electronic properties. In this sense , the study of other systems in low dimension becomes urgent. More specifically , the study of magnetic properties of materials at low dimensionality also brings great new features in the behavior of ferromagnetic systems . The behavior of spin waves in such systems may be important to the study of spintronic and the development of new devices and magnetic memories . Thus in this work we aim to study the behavior of ferromagnetic spin waves in two-dimensional systems . For two-dimensional systems we consider here two-dimensional networks decorated . The decorations are introduced to generate networks with more than one basic atom in the unit cell of the system to study the richness of the spectrum of spin waves due to these changes . At first deal with a superimposition of square networks where the displacement of these networks depends on the control parameters alpha and beta . We also use the superposition of a square on a hexagonal network. Sistema de baixa dimensionalidade têm atraído uma grande atenção ultimamente devido a sistemas como grafeno e nanotubos de carbono. Tais sistemas têm grandes possibilidades de aplicações tecnológicas, em particular na criação de dispositivos eletrônicos, devido às suas propriedades eletrônicas específicas. Nesse sentido, o estudos de outros sistemas em baixa dimensão se torna urgente. Mais especificamente, o estudo de propriedades magnéticas de materiais de materiais em baixa dimensionalidade também trás grandes novidades no comportamento de sistemas ferromagnéticos. O comportamento de ondas de spin em tais sistemas pode ser para o estudo da spintrônica e o desenvolvimento de novos aparelhos e memórias magnéticas. Dessa forma temos como objetivo nesse trabalho estudar o comportamento de ondas de spin em sistemas bidimensionais ferromagnéticos. Por sistemas bidimensionais consideramos aqui redes bidimensionais decoradas. As decorações são introduzidas para gerar redes com mais de um átomo na base da célula unitária da rede para estudarmos a riqueza do espectro das ondas de spin devido a essas modificações. A princípio tratamos com uma superposição de redes quadradas onde o deslocamento dessas redes depende dos parâmetros de controle α e β. Também usamos a superposição de um rede quadrada sobre um hexagonal.

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Souza, Fabiano Caetano de. "Método de diagonalização iterativa para o modelo de Heisenberg." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-13092010-103541/.

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Nesta tese desenvolvemos um método numérico para diagonalizar o Hamiltoniano de Heisenberg iterativamente. O método consiste basicamente em diagonalizar cadeias de spins, cada vez maiores, em que cada passo da diagonalização corresponde à adição de um novo spin à cadeia. A base de vetores para calcular o Hamiltoniano de uma cadeia de N spins, HN, é construída por meio do produto direto dos autovetores do Hamiltoniano Hn-1 da rede diagonalizada no passo anterior, pelos autoestados correspondentes ao N-ésimo spin adicionado. Além de usar a comutação do Hamiltoniano com a componente azimutal do spin total, Sz, prática comum em outros métodos, usufruímos da conservação com o quadrado do spin total, S2. Para uma classe específica de redes também implementamos a simetria de reflexão. Obtemos o espectro completo de energia de cadeias de spins 1/2 com até 20 sítios, para as quais mostramos resultados da dependência com a temperatura da susceptibilidade magnética e do calor específico, para redes com impurezas tipo spin substitucionais, com defeitos nas ligações ou com efeitos de bordas, isto é, para sistemas sem invariância translacional. Usualmente essa restrição impõe enormes dificuldades em métodos tradicionais. Para diagonalizar cadeias com um número maior de sítios, implementamos um procedimento que seleciona os estados de mais baixa energia para serem usados na base de vetores do passo seguinte. Com esse tipo de truncamento de estados, fomos capazes de obter o estado fundamental e alguns estados de baixa energia de cadeias com mais de uma centena de sítios, com precisão de até cinco algarismos significativos. Nossos resultados reproduzem os da literatura para os casos conhecidos, em geral sistemas homogêneos. As aproximações desenvolvidas recentemente no contexto da Teoria do Funcional da Densidade, aplicada ao modelo de Heisenberg, e que também se aplicam a sistemas inomogêneos, estão em conformidade com nossos resultados numericamente exatos. Generalizamos o método para diagonalizar escadas de spins 1/2. Calculamos o estado fundamental e o gap de energia desse sistema, onde variamos a razão entre os acoplamentos ao longo das pernas da escada e ao longo dos degraus da mesma; nossos resultados são comparados com os da literatura. Apresentamos também a implementação do método iterativo no modelo de Hubbard, que descreve um sistema de spins itinerantes. Sabe-se que no regime de alta repulsão Coulombiana entre os spins e densidade um (número de spins igual ao número de sítios da cadeia), esse modelo é mapeado no modelo de Heisenberg, resultado que é verificado numericamente em nosso procedimento por meio do cálculo de energias de ambos os modelos em um regime paramétrico apropriado. In this Thesis we develop a numerical method to diagonalize the Heisenberg model iteratively. In essence, we diagonalize spin chains in steps, each one corresponding to an addition of a spin to a smaller chain. The basis vectors to calculate the Hamiltonian of a N-spin chain, HN, is built by means of the direct product of the eigenvectors of the (N-1)-spin Hamiltonian, diagonalized on the previous step, by the eigenstates of the N-th added spin. Besides the common use of the conservation of the z-component of the total spin, Sz, we also exploit the conservation of the squared total spin, S2. For a specific class of spin systems we also implemented the reflection symmetry. We obtain the entire energy spectrum of spin-1/2 chains up to 20 sites, for which we show the temperature dependence of the magnetic susceptibility and specific heat, for systems with substitutional impurity spins, bond defects, border effects, i.e., for systems without translational invariance. This normally imposes enormous restrictions in many traditional methods. In order to diagonalize chains with a larger number of sites we implemented a procedure that selects lower energy states to be used in the basis vector on the next step. Using this truncation scheme, we are able to obtain low-lying energy states for chains with more than a hundred sites, up to five significant figures of accuracy. Our results reproduce those of the literature for the known cases, in general homogeneous systems. The approaches recently developed in the context of Density Functional Theory to the Heisenberg model, which also apply to inhomogeneous systems, are consistent with our numerical results. We generalize the method to diagonalize spin-1/2 ladders. We calculate the ground-state and the energy gap of this system, for arbitrary ratio of the couplings along the lags or over the rungs of the ladder. We also present the implementation of our iterative method to the Hubbard model, which describes a system of itinerant spins. It is known that in the regime of high Coulomb repulsion between the spins and unitary density (number of spins equal to the number of sites in the chain), this model is mapped onto Heisenberg one, a result which is verified numerically in our procedure by calculating the energy spectrum of both models in na appropriated parametric regime.

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Silva, WanÃssa FaÃanha da. "Ondas de spin em redes decoradas." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12439.

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Sistema de baixa dimensionalidade tÃm atraÃdo uma grande atenÃÃo ultimamente devido a sistemas como grafeno e nanotubos de carbono. Tais sistemas tÃm grandes possibilidades de aplicaÃÃes tecnolÃgicas, em particular na criaÃÃo de dispositivos eletrÃnicos, devido Ãs suas propriedades eletrÃnicas especÃficas. Nesse sentido, o estudos de outros sistemas em baixa dimensÃo se torna urgente. Mais especificamente, o estudo de propriedades magnÃticas de materiais de materiais em baixa dimensionalidade tambÃm trÃs grandes novidades no comportamento de sistemas ferromagnÃticos. O comportamento de ondas de spin em tais sistemas pode ser para o estudo da spintrÃnica e o desenvolvimento de novos aparelhos e memÃrias magnÃticas. Dessa forma temos como objetivo nesse trabalho estudar o comportamento de ondas de spin em sistemas bidimensionais ferromagnÃticos. Por sistemas bidimensionais consideramos aqui redes bidimensionais decoradas. As decoraÃÃes sÃo introduzidas para gerar redes com mais de um Ãtomo na base da cÃlula unitÃria da rede para estudarmos a riqueza do espectro das ondas de spin devido a essas modificaÃÃes. A princÃpio tratamos com uma superposiÃÃo de redes quadradas onde o deslocamento dessas redes depende dos parÃmetros de controle α e β. TambÃm usamos a superposiÃÃo de um rede quadrada sobre um hexagonal Low-dimensional systems have attracted much attention lately due to systems such as graphene and carbon nanotubes. Such systems have great potential for technological applications. In particular the creation of electronic devices due to their specific electronic properties. In this sense , the study of other systems in low dimension becomes urgent. More specifically , the study of magnetic properties of materials at low dimensionality also brings great new features in the behavior of ferromagnetic systems . The behavior of spin waves in such systems may be important to the study of spintronic and the development of new devices and magnetic memories . Thus in this work we aim to study the behavior of ferromagnetic spin waves in two-dimensional systems . For two-dimensional systems we consider here two-dimensional networks decorated . The decorations are introduced to generate networks with more than one basic atom in the unit cell of the system to study the richness of the spectrum of spin waves due to these changes . At first deal with a superimposition of square networks where the displacement of these networks depends on the control parameters alpha and beta . We also use the superposition of a square on a hexagonal network.

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Exler, Matthias. "On classical and quantum mechanical energy spectra of finite Heisenberg spin systems." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980110440.

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Szallas, Attila. "Heisenberg antiferromagnetique model sur le pavage quasicrystaux bidimensionnelle." Phd thesis, Université Paris Sud - Paris XI, 2008. http://tel.archives-ouvertes.fr/tel-00358251.

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Le pavage de Penrose est une structure quasipériodique bidimensionnelle, utilisée dans la description des composés quasicristallins. Cette structure est parfaitement ordonnée, avec une symétrie de rotation cinq et elle est invariante sous un changement d'échelle par un facteur $\tau$ (le nombre d'or). On s'attend à ce que les propriétés d'un modèle d'antiferromagnétisme dans un tel système diffèrent nettement de celles des antiferromagnétiques périodiques. Nous avons étudié les propriétés d'un modèle d'Heisenberg sur le pavage de Penrose construit à partir de losanges, en utilisant une méthode de développement en ondes de spin. Les énergies et fonctions d'ondes des magnons (quantum d'une onde des spins) ont été étudiées dans le cadre d'une théorie linéarisée. A basse énergie, on trouve une loi de dispersion linéaire, comme dans d'autres antiferromagnetiques bipartites, avec une vitesse effective de l'onde de spin inférieure à celle d'un réseau carré équivalent. Les propriétés spatiales des modes propres ont été étudiées en détail. A basse énergie, nous trouvons que les états propres sont relativement étendus. Une analyse multifractale montre qu'ils sont de type “critique”, ayant une distribution d'exposants multifractaux. Aux énergies plus élevées, les états deviennent plus localisés, et, en fonction de l'énergie, l'amplitude de la fonction d'onde est non-nulle autour d'un sous-ensemble de sites d'une valeur de coordinence donnée. L'énergie de l'état fondamental de cette antiferromagnetique, et la distribution des aimantations locales dans cet état ont été calculés. Des projections dans l'espace perpendiculaire montrent la simplicité sous-jacente de ce état "complexe". Un simple modèle analytique, l'étoile de Heisenberg à deux niveaux, a été présenté pour expliquer de la distribution d'aimantation locales dans ce système antiferromagnétique. Dans une dernière partie, les effets de désordre de type “phason” sont considérés. Nous avons progressivement augmenté le désordre géometrique de la structure originale. Nous avons trouvé que l'etat fondamental conserve son ordre de Néel, mais que la forme de la distribution ainsi que la norme des aimantations sont modifiés. Nous montrons, à l'aide d'un développement en ondes des spin ainsi que par Quantum Monte Carlo, que l'aimantation alternée diminue exponentiellement vers une valeur asymptote en fonction du désordre. La distribution spatiale de magnetizations locales devient plus homogène par rapport à pavage parfait. La vitesse des ondes des spin augmente avec le désordre, et les singularités dans le spectre et les functions d'onde sont en partie lissées. Ces résultats sont comparés avec des résultats connus dans des systèmes désordonnés.

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Belo, Leandro Ribeiro Andrade. "Modelo de Heisenberg em um espaço com curvatura negativa: excitações topológicas de spin na pseudo-esfera." Universidade Federal de Viçosa, 2007. http://locus.ufv.br/handle/123456789/4263.

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Made available in DSpace on 2015-03-26T13:35:20Z (GMT). No. of bitstreams: 1 texto completo.pdf: 763296 bytes, checksum: 67a8dbb32f0cc3ff0e3104d5ec7126e0 (MD5) Previous issue date: 2007-03-01 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Heisenberg-like spins lying on the pseudosphere (a 2- dimensional infinite space with constant negative curvature) cannot give rise to stable soliton solutions. Only fractional solutions can be stabilized on this surface provided that at least one hole is incorporated. We also address the issue of in-plane vortices, in the XY regime. Interestingly, the energy of a single vortex no longer blows up as the excitation spreads to infinity. This yields a non-confining potential between a vortex and a antivortex at large distances so that the pair may dissociate at arbitrarily low temperature. Spins de Heisenberg que se encontram na pseudo-esfera (um espaço infinito 2- dimensional com curvatura constante e negativa) não podem gerar soluções solitônicas estáveis. Apenas soluções fracionárias podem ser estabilizadas nessa superfície desde que um furo seja feito. Dirigimo-nos também à introdução de vórtices no plano no regime XY. Interessantemente, a energia de um único vórtice não diverge quando o sistema tende ao infinito. Isso leva a um potencial não-confinante entre um vórtice e um anti-vórtice a grandes distâncias, de modo que o par possa dissociar-se a uma baixa e arbitraria temperatura.

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Fernandes, Walney Reis. "Modelos de emparelhamento integráveis." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-21102010-121332/.

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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 first 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.

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Shinjo, Kazuya. "Density-matrix renormalization group study of quantum spin systems with Kitaev-type anisotropic interaction." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215292.

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Janson, Oleg. "DFT-based microscopic magnetic modeling for low-dimensional spin systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-91976.

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In the vast realm of inorganic materials, the Cu2+-containing cuprates form one of the richest classes. Due to the combined effect of crystal-field, covalency and strong correlations, all undoped cuprates are magnetic insulators with well-localized spins S=1/2, whereas the charge and orbital degrees of freedom are frozen out. The combination of the spin-only nature of their magnetism with the unique structural diversity renders cuprates as excellent model systems. The experimental studies, boosted by the discovery of high-temperature superconductivity in doped La2CuO4, revealed a fascinating variety of magnetic behaviors observed in cuprates. A digest of prominent examples should include the spin-Peierls transition in CuGeO3, the Bose-Einstein condensation of magnons in BaCuSi2O6, and the quantum critical behavior of Li2ZrCuO4. The magnetism of cuprates originates from short-range (typically, well below 1 nm) exchange interactions between pairs of spins Si and Sj, localized on Cu atoms i and j. Especially in low-dimensional compounds, these interactions are strongly anisotropic: even for similar interatomic distances |Rij|, the respective magnetic couplings Jij can vary by several orders of magnitude. On the other hand, there is an empirical evidence for the isotropic nature of this interaction in the spin space: different components of Si are coupled equally strong. Thus, the magnetism of cuprates is mostly described by a Heisenberg model, comprised of Jij(Si*Sj) terms. Although the applicability of this approach to cuprates is settled, the model parameters Jij are specific to a certain material, or more precisely, to a particular arrangement of the constituent atoms, i.e. the crystal structure. Typically, among the infinite number of Jij terms, only several are physically relevant. These leading exchange couplings constitute the (minimal) microscopic magnetic model. Already at the early stages of real material studies, it became gradually evident that the assignment of model parameters is a highly nontrivial task. In general, the problem can be solved experimentally, using elaborate measurements, such as inelastic neutron scattering on large single crystals, yielding the magnetic excitation spectrum. The measured dispersion is fitted using theoretical models, and in this way, the model parameters are refined. Despite excellent accuracy of this method, the measurements require high-quality samples and can be carried out only at special large-scale facilities. Therefore, less demanding (especially, regarding the sample requirements), yet reliable and accurate procedures are desirable. An alternative way to conjecture a magnetic model is the empirical approach, which typically relies on the Goodenough-Kanamori rules. This approach links the magnetic exchange couplings to the relevant structural parameters, such as bond angles. Despite the unbeatable performance of this approach, it is not universally applicable. Moreover, in certain cases the resulting tentative models are erroneous. The recent developments of computational facilities and techniques, especially for strongly correlated systems, turned density-functional theory (DFT) band structure calculations into an appealing alternative, complementary to the experiment. At present, the state-of-the-art computational methods yield accurate numerical estimates for the leading microscopic exchange couplings Jij (error bars typically do not exceed 10-15%). Although this computational approach is often regarded as ab initio, the actual procedure is not parameter-free. Moreover, the numerical results are dependent on the parameterization of the exchange and correlation potential, the type of the double-counting correction, the Hubbard repulsion U etc., thus an accurate choice of these crucial parameters is a prerequisite. In this work, the optimal parameters for cuprates are carefully evaluated based on extensive band structure calculations and subsequent model simulations. Considering the diversity of crystal structures, and consequently, magnetic behaviors, the evaluation of a microscopic model should be carried out in a systematic way. To this end, a multi-step computational approach is developed. The starting point of this procedure is a consideration of the experimental structural data, used as an input for DFT calculations. Next, a minimal DFT-based microscopic magnetic model is evaluated. This part of the study comprises band structure calculations, the analysis of the relevant bands, supercell calculations, and finally, the evaluation of a microscopic magnetic model. The ground state and the magnetic excitation spectrum of the evaluated model are analyzed using various simulation techniques, such as quantum Monte Carlo, exact diagonalization and density-matrix renormalization groups, while the choice of a particular technique is governed by the dimensionality of the model, and the presence or absence of magnetic frustration. To illustrate the performance of the approach and tune the free parameters, the computational scheme is applied to cuprates featuring rather simple, yet diverse magnetic behaviors: spin chains in CuSe2O5, [NO]Cu(NO3)3, and CaCu2(SeO3)2Cl2; quasi-two-dimensional lattices with dimer-like couplings in alpha-Cu2P2O7 and CdCu2(BO3)2, as well as the 3D magnetic model with pronounced 1D correlations in Cu6Si6O18*6H2O. Finally, the approach is applied to spin liquid candidates --- intricate materials featuring kagome-lattice arrangement of the constituent spins. Based on the DFT calculations, microscopic magnetic models are evaluated for herbertsmithite Cu3(Zn0.85Cu0.15)(OH)6Cl2, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, as well as for volborthite Cu3[V2O7](OH)2*2H2O. The results of the DFT calculations and model simulations are compared to and challenged with the available experimental data. The advantages of the developed approach should be briefly discussed. First, it allows to distinguish between different microscopic models that yield similar macroscopic behavior. One of the most remarkable example is volborthite Cu3[V2O7](OH)2*2H2O, initially described as an anisotropic kagome lattice. The DFT calculations reveal that this compound features strongly coupled frustrated spin chains, thus a completely different type of magnetic frustration is realized. Second, the developed approach is capable of providing accurate estimates for the leading magnetic couplings, and consequently, reliably parameterize the microscopic Hamiltonian. Dioptase Cu6Si6O18*6H2O is an instructive example showing that the microscopic theoretical approach eliminates possible ambiguity and reliably yields the correct parameterization. Third, DFT calculations yield even better accuracy for the ratios of magnetic exchange couplings. This holds also for small interchain or interplane couplings that can be substantially smaller than the leading exchange. Hence, band structure calculations provide a unique possibility to address the interchain or interplane coupling regime, essential for the magnetic ground state, but hardly perceptible in the experiment due to the different energy scales. Finally, an important advantage specific to magnetically frustrated systems should be mentioned. Numerous theoretical and numerical studies evidence that low-dimensionality and frustration effects are typically entwined, and their disentanglement in the experiment is at best challenging. In contrast, the computational procedure allows to distinguish between these two effects, as demonstrated by studying the long-range magnetic ordering transition in quasi-1D spin chain systems. The computational approach presented in the thesis is a powerful tool that can be directly applied to numerous S=1/2 Heisenberg materials. Moreover, with minor modifications, it can be largely extended to other metallates with higher value of spin. Besides the excellent performance of the computational approach, its relevance should be underscored: for all the systems investigated in this work, the DFT-based studies not only reproduced the experimental data, but instead delivered new valuable information on the magnetic properties for each particular compound. Beyond any doubt, further computational studies will yield new surprising results for known as well as for new, yet unexplored compounds. Such "surprising" outcomes can involve the ferromagnetic nature of the couplings that were previously considered antiferromagnetic, unexpected long-range couplings, or the subtle balance of antiferromagnetic and ferromagnetic contributions that "switches off" the respective magnetic exchange. In this way, dozens of potentially interesting systems can acquire quantitative microscopic magnetic models. The results of this work evidence that elaborate experimental methods and the DFT-based modeling are of comparable reliability and complement each other. In this way, the advantageous combination of theory and experiment can largely advance the research in the field of low-dimensional quantum magnetism. For practical applications, the excellent predictive power of the computational approach can largely alleviate designing materials with specific properties.

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15

Antini, Alessandro. "Non-local order parameters in one-dimensional spin systems." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18043/.

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Per molti anni si è creduto che la teoria di Landau sulla rottura spontanea di simmetria esaurisse la descrizione di tutte le fasi in cui è possibile osservare la materia. Ogni transizione di fase si riteneva dunque dover essere sempre accompagnata da un cambiamento della simmetria del sistema. È da diversi decenni ormai che però siamo consapevoli dell'esistenza di fasi della materia distinte che posseggono esattamente la stessa simmetria. A queste fasi è stato dato il nome di fasi topologiche, e chiaramente non possono essere descritte e previste dalla teoria di Landau. In sistemi unidimensionali è possibile osservare fasi topologicamente non banali in presenza di alcune simmetrie. L'esempio più importante in questo contesto è fornito dalla fase in cui si trova la catena di Heisenberg di spin 1 antiferromagnetica, la cosiddetta fase di Haldane. Essa risulta una dei primi esempi di fase topologica, e presenta già diverse caratteristiche proprie di queste fasi, come la presenza di stati di bordo e di ordini di stringa nascosti. Infatti una delle peculiarità delle fasi topologiche è quella di essere rilevate da parametri d'ordine non locali, che a differenza dai comuni parametri d'ordine che caratterizzano le diverse fasi associate a rotture spontanee di simmetria, sono forniti da valori di aspettazione di operatori non locali. In questa tesi vengono introdotti nuovi parametri d'ordine non locali, diversi rispetto a quelli comunemente utilizzati, ma ugualmente efficaci nella rilevazione delle diverse fasi massive in cui è possibile trovare il nostro modello di spin 1 di riferimento, ovvero il cosiddetto modello bilineare-biquadratico. Questi parametri d'ordine non locali sono stati valutati sia numericamente che analiticamente laddove fosse disponibile una rappresentazione esatta dello stato fondamentale del sistema.

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16

Sauerwein, Ricardo Andreas. "Método de Monte Carlo para Sistemas Quânticos." Universidade de São Paulo, 1995. http://www.teses.usp.br/teses/disponiveis/43/43133/tde-13122013-180031/.

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As propriedades do estado fundamental do modelo de Heisenberg antiferroinagnético quântico de spin-1/2 na rede quadrada e na rede cúbica espacialmente anisotrópica são investigadas através de um novo método de Monte Carlo, baseado na estimativa do maior autovalor de uma matriz de elementos não negativos. A energia do estado fundamental e a magnetização \"staggered\" destes sistemas são calculadas em redes relativamente grandes com até 24 x 24 sítios para o caso de redes quadradas e 8 x 8 x 8 sítios para o caso de redes cúbicas. O método desenvolvido também pode ser usado como um novo algoritmo para a determinação direta da entropia de sistemas de spins de Ising através de simulações usuais de Monte Carlo. Usando este método, calculamos a entropia do antiferromagneto de Ising na presença de um campo magnético externo nas redes triangular e cúbica de face centrada. The ground state properties of the antiferromagnetic quantum Heisenberg model with spin-112 defined on a square lattice and on a cubic lattice with spatial anisotropy are investigated through a new Monte Carlo method, based on the estimation of the largest eigenvalue of a matrix with nonnegative elements. The ground state energy and the staggered magnetization of these systems are calculated in relatively large lattices with up to 24 x 24 sites for the square lattices and 8 x 8 x 8 sites for cubic lattices. The method developped can also be used as a new algorithm for the direct determination of the entropy of Ising spin systems through ordinary Monte Car10 simulations. By using this method we calculate the entropy of the Ising antiferromagnetic in the presence of a magnetic field in the triangular and face centered cubic lattices.

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17

Allalen, Mohammed. "Magnetic properties and proton spin-lattice relaxation in molecular clusters." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=979984777.

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18

Schäpers, Markus. "Exploring the Frustrated Spin-Chain Compound Linarite by NMR and Thermodynamic Investigations." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-153947.

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Within the last decades low-dimensional frustrated quantum spin systems have attracted great interest in the field of modern research. In these systems a competition of various magnetic interactions takes place, leading to an energetically degenerated magnetic ground state, and thus to the occurrence of exotic, unconventional physical properties at low temperatures. This thesis focuses on the quasi one-dimensional frustrated spin chain system linarite, PbCuSO4(OH)2. In this compound the basic building blocks are CuO4 plaquettes which are connected to each other along one crystallographic direction, analogue to a chain. The frustration in linarite is established due to the competition between the magnetic interactions. The nearest-neighbor magnetic spins are coupled ferromagnetically along the chain via a coupling constant J1, while the next-nearest neighbors are coupled antiferromagnetically via a coupling constant J2. For this configuration it is not possible to satisfy all magnetic couplings simultaneously, hence the system is magnetically frustrated. In this work, comprehensive thermodynamic and nuclear magnetic resonance (NMR) studies demonstrate that linarite is one of the richest and most fascinating compounds in the class of low-dimensional frustrated magnets. By means of susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements a rich magnetic phase diagram could be mapped out below a temperature of 2.8 K. The phase diagram contains five different magnetic regions/phases for an external magnetic field pointing along the chain direction. Based on the thermodynamic studies it was possible to calculate the exchange integrals within the frustrated J1-J2 model and extensions of it by using various theoretical approaches. The magnetic microscopic nature of the different long-range magnetic phases present in linarite were investigated by NMR measurements and by collaborative neutron scattering experiments. The ground state (phase I) is identified as an incommensurate elliptical helical structure. Via a theoretical modelling the 1H-NMR spectrum of the ground state could be explained, revealing a rearrangement of the zero-field structure in an external magnetic field of 2.0 T used for the NMR studies. By further increasing the external field the system undergoes a complex spin flop transition in two steps (phase I - phase III - phase IV). In phase III a phase separation takes place where one part of the spins form a circular spiral structure while the remaining fraction form a simple antiferromagnetic structure. In phase IV the remaining circular spiral structure vanishes, so that all spins collectively form the antiferromagnetic collinear phase. The most peculiar physical properties studied in this thesis take place in region V at high fields, showing only tiny features in the thermodynamic properties. The magnetic spins in region V form a sine-wave modulated spin-density structure as identified via NMR and neutron investigations. It is discussed whether region V is related to a multipolar phase or if the spin-density wave structure could possibly coexist with such a phase.

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19

Freire, MÃrcio de Melo. "Teoria de funÃÃes de Green para uma impureza isolada localizada intersticialmente em sistemas ferromagnÃticos." Universidade Federal do CearÃ, 2017. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=18807.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico Um formalismo da funÃÃo de Green Ã usado para calcular o espectro de excitaÃÃes associadas com uma impureza magnÃtica localizada intersticialmente em diferentes estruturas ferromagnÃticas descritas pelo modelo de Ising e de Heisenberg. No capÃtulo 3, descrevemos um ferromagneto de rede cÃbica simples semi-infinita atravÃs do modelo de Ising. Neste caso, as excitaÃÃes nÃo-ressonantes (isto Ã, os modos de defeito fora da regiÃo das ondas de spin de volume e de superfÃcie) e as excitaÃÃes ressonantes (os modos de defeito dentro da regiÃo das ondas de spin de volume) sÃo calculadas numericamente para a fase de alta-temperatura. Duas situaÃÃes sÃo analisadas, dependendo da posiÃÃo da impureza em relaÃÃo a seus vizinhos: a impureza estÃ na superfÃcie; a impureza estÃ na regiÃo de volume. Nos demais capÃtulos, usamos o modelo de Heisenberg/Ising (onde passamos do modelo de Heisenberg para o de Ising atravÃs do controle de um parÃmetro) para descrever os seguintes sistemas: ferromagneto de rede quadrada infinita (capÃtulo 4), ferromagneto de rede quadrada centrada infinita (capÃtulo 5), ferromagneto de rede cÃbica de corpo centrado infinita (capÃtulo 6) e rede favo de mel infinita (capÃtulo 7), todos contendo uma impureza magnÃtica localizada intersticialmente. Nos trÃs primeiros casos, sÃo calculados apenas os modos de defeito acima da banda de volume do material puro (modos Ãpticos). No capÃtulo 7, sÃo analisados apenas os modos de defeito abaixo da banda de volume do material puro (modos acÃsticos).

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20

Canals, Benjamin. "Contribution à l'étude des propriétés de quelques systèmes magnétiques frustrés." Université Joseph Fourier (Grenoble ; 1971-2015), 1997. http://www.theses.fr/1997GRE10142.

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Nous etudions trois reseaux frustres geometriquement. En utilisant l'hamiltonien de heisenberg quantique antiferromagnetique sur le reseau pyrochlore, nous donnons des arguments qui caracterisent ce systeme comme un liquide de spins ou le gap est tres faible. Les delafossites dopes (la,y)cuo#2#. #6#6 sont interpretes comme des reseaux kagome. En considerant differents modeles (xy, hubbard, t-j), nous concluons que le compose au lanthane est certainement metallique alors que celui a l'yttrium doit etre isolant. Nous caracterisons dans les deux cas (la ou y) les proprietes magnetiques. Enfin, le compose uni#4b est decrit comme un reseau de anderson triangulaire. En derivant un modele effectif, nous reproduisons son etat fondamental et prevoyons son comportement sous champ.

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21

Chaboussant, Grégory. "Étude expérimentale d'une échelle de spin-1/2 antiferromagnétique : Cu2(C5H12N2)2Cl4." Université Joseph Fourier (Grenoble ; 1971-2015), 1997. http://www.theses.fr/1997GRE10007.

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Ce memoire presente une etude experimentale d'un compose organique isolant ayant des proprietes magnetiques unidimensionnelles (1d): cu#2(c#5h#1#2n#2)#2cl#4. C'est un systeme antiferromagnetique de heisenberg s=1/2 en echelle de spins. Les interactions d'echanges entre les electrons non apparies des ions cu#2#+ forment une structure magnetique en echelle que l'on peut decrire par deux parametres d'echanges, j entre les barreaux et j le long des deux chaines. Comme toutes les echelles de spin-1/2 ayant un nombre pair de chaines couplees, ce systeme a un gap d'energie dans le spectre des excitations. Les proprietes de l'etat fondamental et, dans une certaine limite des etats excites, sont alors similaires a celles des chaines de haldane (s=1). A contrario les echelles comportant un nombre impair de chaines sont critiques (sans gap) et appartiennent a la meme classe d'universalite que les chaines de spin-1/2 dont la solution est donnee par l'ansatz de bethe. Cette these presente une etude assez complete des proprietes thermodynamiques et dynamiques de ce compose. Les mesures thermodynamiques ou statiques reposent sur l'utilisation de magnetometres squid ou, pour les champs magnetiques intenses, d'oscillateurs torsionnels a haute resolution. Les techniques de resonance electronique de spin (rpe) dans la gamme micro-ondes et de resonance magnetique nucleaire sur le proton ont ete utilisees pour etudier les proprietes dynamiques liees aux fonctions de correlations telle que la largeur de raie rpe ou le temps de relaxation nucleaire spin-reseau t#1. Nous avons determine l'ensemble des parametres essentiels lies au magnetisme de ce compose: cu#2(c#5h#1#2n#2)#2cl#4 est decrit par un hamiltonien de heisenberg dont les interactions d'echanges forment une echelle de spins dans la limite de couplage fort: j 13. 2k et j 2. 5k. Le gap d'energie entre l'etat fondamental non-magnetique s=0 et les etats excites triplets (s=1) est 10. 5k

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22

Grechnyev, Oleksiy. "Theoretical Studies of Two-Dimensional Magnetism and Chemical Bonding." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4815.

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23

Labouze, Xavier. "Etude par résonances nucléaires des propriétés magnétiques des cuprates supraconducteurs dans leurs phases isolantes." Grenoble 1, 1994. http://www.theses.fr/1994GRE10042.

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Cette these porte sur l'etude des proprietes magnetiques des cuprates supraconducteurs dans leurs phases isolantes. Les techniques experimentales utilisees sont la resonance nucleaire, magnetique (rmn) et quadrupolaire (rqn). La premiere partie presente une revue des proprietes essentielles des cuprates supraconducteurs. La deuxieme explique particulierement comment utiliser la rqn. L'etude des composes au plomb type ybco (partie iii) montre que le magnetisme des cuprates doit etre quasi-2d quasi-heisenberg. La partie iv traite des composes ybco substitues au calcium. L'etude statique par mesures de largeurs de raie rqn a permis de determiner les temperatures de transition des composes intermediaires. Un modele de l'influence des porteurs de charges a ete construit. Une etude dynamique par mesures du temps de relaxation spin/reseau a aussi ete menee. On compare ces resultats avec ceux des composes monoplans lsco

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24

Beaujouan, David. "Simulation des matériaux magnétiques à base Cobalt par Dynamique Moléculaire Magnétique." Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00760645.

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Les propriétés magnétiques des matériaux sont fortement connectées à leur structure cristallographique. Nous proposons un modèle atomique de la dynamique d'aimantation capable de rendre compte de cette magnétoélasticité. Bien que ce travail s'inscrive dans une thématique générale de l'étude des matériaux magnétiques en température, nous la particularisons à un seul élément, le Cobalt. Dans ce modèle effectif, les atomes sont décrits par 3 vecteurs classiques qui sont position, impulsion et spin. Ils interagissent entre eux via un potentiel magnéto-mécanique ad hoc. On s'intéresse tout d'abord à la dynamique de spin atomique. Cette méthode permet d'aborder simplement l'écriture des équations d'évolution d'un système atomique de spins dans lequel la position et l'impulsion des atomes sont gelées. Il est toutefois possible de définir une température de spin permettant de développer naturellement une connexion avec un bain thermique. Montrant les limites d'une approche stochastique, nous développons une nouvelle formulation déterministe du contrôle de la température d'un système à spins.Dans un second temps, nous développons et analysons les intégrateurs géométriques nécessaires au couplage temporel de la dynamique moléculaire avec cette dynamique de spin atomique. La liaison des spins avec le réseau est assurée par un potentiel magnétique dépendant des positions des atomes. La nouveauté de ce potentiel réside dans la manière de paramétrer l'anisotropie magnétique qui est la manifestation d'un couplage spin-orbite. L'écriture d'un modèle de paires étendu de l'anisotropie permet de restituer les constantes de magnétostriction expérimentales du hcp-Co. En considérant un système canonique, où pression et température sont contrôlées, nous avons mis en évidence la transition de retournement de spin si particulière au Co vers 695K.Nous finissons par l'étude des retournements d'aimantation super-paramagnétiques de nanoplots de Co permettant de comparer ce couplage spin-réseau aux mesures récentes.

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25

Rosner, Helge. "Electronic structure and exchange integrals of low-dimensional cuprates." [S.l. : s.n.], 1999. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9470690.

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26

Collins, Alexander Rory Physics Faculty of Science UNSW. "Quantum lattice models." Publisher:University of New South Wales. Physics, 2008. http://handle.unsw.edu.au/1959.4/43408.

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This thesis presents studies of the low energy properties of nseveral frustrated spin-1/2 Heisenberg antiferromagnets using various analytic and computational methods. The models studied include the union jack model, the alternating Heisenberg chain, the Heisenberg bilayer model, and the spin-Peierls model. The union jack model is a Heisenberg antiferromagnetic spin model with frustration, and is analyzed using spin-wave theory. For small values of the frustrating coupling $\alpha$, the system is N{\' e}el ordered, while for large $\alpha$ the frustration is found to induce a canted phase. Spin wave theory with second order corrections finds the critical coupling at $\alpha \simeq 0.645$,which agrees quantitatively with series expansion results. No intermediate spin-liquid phase is found to exist between the two phases. The alternating Heisenberg chain is studied using an alternative triplet-wave expansion formalism for dimerized spin systems, modification of the ??bond operator?? formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace, rather than constraint equations. Comparisons are made with the results of dimer series expansions and exact diagonalization. The S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the S=0 and S=1 channels, and antibound states in the S=2 channel, is predicted with triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N{\' e}el phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series expansion methods and found to conform with theoretical expectations. The Heisenberg spin-Peierls model with dispersive, gapless phonons is studied with Density Matrix Renormalization Group methods. We investigate the zero temperature properties of the model using the crossover method. The calculations were found to converge poorly and no conclusive results could be found using this method. An analysis of the convergence problems and the discovery of an anomalous triplet ground state is presented in this chapter.

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Nunes, Wagner Antonio da Silva. "Comportamento multicrítico no modelo de Heisenberg frustrado: transições de fases clássica e quântica." Universidade Federal de São Carlos, 2011. https://repositorio.ufscar.br/handle/ufscar/4970.

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Made available in DSpace on 2016-06-02T20:15:30Z (GMT). No. of bitstreams: 1 5740.pdf: 4504584 bytes, checksum: 51970950add8aab7bab613ecfd4117ee (MD5) Previous issue date: 2011-09-01 In this work we study the critical behavior of systems described by the Anysotropic- Heisenberg model of spin 1/2 with competitive interactions (J1-J2 Model) on planes, and interplane nearest-neighbor interactions. We applied Effective-Field techniques for finite clusters with two (EFT2) and four (EFT4) central sites, as well as Linear Spin-Waves Theory (LSWT). We define α=J2/J1, as the frustration parameter, which together with the the anysotropy exchange and the spatial one lambda, we obtain the respective phase diagrams. Classic phase transitions are studied at finite temperatures, as well as the quantum ones at T=0. We observed the presence of two ferromagnetic (antiferromagnetic) states, a quantum paramagnetic, colinear ferromagnetic (CF) and antiferromagnetic (CAF) at T=0 for J1 < 0 and J1 > 0. We characterized the type of transition (continuous or discontinuous) existing in them. For T > 0, the same phases are found, with the exception of the quantum and the normal paramagnetic ones. The CAF a CF states are characterized in three dimensions in the following way: spin lines with the same orientation adjacent to lines in the opposite sense, and spin planes with the same orientation adjacent to spin planes with opposite sense. In the two dimensions these two states are equivalent. We analyze the classical and quantum limits of the model through the phase destruction of PQ in the ferromagnetic and antiferromagnetic case under the influence of anisotropies. We also applied to the frustated model in the plane and the λ interaction between planes the Theory of Linear Spin Waves and compared their results with those found for the Effective Field Theory. Neste trabalho estudamos o comportamento multicrítico de sistemas descritos pelo modelo de Heisenberg anisotrópico de spin 1/2 com interações competitivas (modelo J1 J2) no plano e interação de primeiros vizinhos entre planos acoplados pelo parâmetro λ na rede cúbica simples. Aplicamos as técnicas de Teoria de Campo Efetivo, em aglomerados finitos com dois (EFT-2) e quatro (EFT-4) sítios, e Teoria de Ondas de Spin Linear (LSWT). Designamos por α = J2/J1 o parâmetro de frustração, fenômeno este característico do modelo e construimos diagramas de fases em função deste, do parâmetro de anisotropia de exchange Δ e espacial λ. Pela Teoria de Campo Efetivo estudamos as transições de fase apresentadas pelo modelo nos regimes de temperaturas não nula (transição de fases clássica) e no estado fundamental T = 0 (transição de fases quânticas). Analisamos os casos com interação de primeiros vizinhos ferromagnéticas ou antiferromagnéticas. Observamos a presença dos estados ferromagnético (antiferromagnético) (F(AF)), paramagnético quântico (PQ), colinear ferromagnético (CF) e colinear antiferromagnético (CAF)) no estado fundamental para J1 < 0 e J1 > 0 e caracterizamos o tipo de transição (contínua ou descontínua) existente entre eles. Da mesma forma para T > 0, onde os estados que se apresentaram são os mesmos estados anteriores (exceto a PQ) e o estado paramagnético normal (P). Os estados CAF e CF são caracterizados em três dimensões da seguinte maneira: linhas de spins com a mesma orientação adjacentes a linhas com orientações opostas (CAF) e planos de spins com mesma orientação adjacentes com planos de orientação oposta (CF). Em duas dimensões estes dois estados são equivalentes. Fizemos a análise dos limites clássicos e quânticos do modelo através da destruição da fase PQ nos casos ferromagnético e antiferromagnético sob a influências das anisotropias. Aplicamos também ao modelo frustrado no plano e interação λ entre planos a Teoria de Ondas de Spin Linear e comparamos os seus resultados com aqueles encontrados pela Teoria de Campo Efetivo.

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Goomanee, Salvish. "Rigorous Approach to Quantum Integrable Models at Finite Temperature." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEN039/document.

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Cette thèse développe un cadre rigoureux qui permet de démontrer des représentations exactes associées à divers observables de la chaîne XXZ de Heisenberg de spin 1/2 à température finie. Il a était argumenté dans la littérature que l’énergie libre par site ou les longueurs de corrélations admettent des représentations intégrales où les intégrandes sont exprimées en termes de solutions d’équations intégrales non-linéaires. Les dérivations de ces représentations reposaient sur divers conjectures telles que l’existence d’une valeur propre de la matrice de transfert quantique, real, non-dégénérée, de module maximale, de l’échangeabilitée de la limite du volume infinie et du nombre de Trotter à l’infinie, de l’existence et de l’unicité des solutions des equation intégrales non-linéaires auxiliaires et finalement de l’identification des valeurs propers de la matrice de transfert quantiques avec les solutions de l’équations intégrales non-linéaires. Nous démontrons toutes ces conjectures dans le regime de haute température. Nôtre analyse nous permet aussi de démontrer que pour ces température suffisamment élevées, il est possible d’avoir une description d’un certain sous-ensemble de valeurs propres sous-dominante de la matrice de transfert quantique décrite en terme de solutions d’une chaîne de spin-1 de taille finie This thesis develops a rigorous framework allowing one to prove the exact representations for various observables in the XXZ Heisenberg spin-1/2 chain at finite temperature. Previously it has been argued in the literature that the per-site free energy or the correlation lengths admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations relied on various conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the exchangeability of the infinite volume limit and the Trotter number limits, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations and finally the identification of the quantum transfer matrix’s Eigenvalues with solutions to the non-linear integral equation. We rigorously prove all these conjectures in the high temperature regime. Our analysis also allows us to prove that for temperatures high enough, one may describe a certain subset of sub-dominant Eigenvalues of the quantum transfer matrix described in terms of solutions to a spin-1 chain of finite length

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Litaiff, Fabian Cardoso. "Modelos de spins geometricamente frustrados: transição de fase e estruturas de platores." Universidade Federal de São Carlos, 2013. https://repositorio.ufscar.br/handle/ufscar/4963.

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Made available in DSpace on 2016-06-02T20:15:29Z (GMT). No. of bitstreams: 1 5202.pdf: 3904832 bytes, checksum: c623a581c3cdb03d9cc81fc16ecef935 (MD5) Previous issue date: 2013-04-08 Universidade Federal de Minas Gerais This thesis presents a study of the magnetization plateau and the phenomenon of geometrical frustration in spin systems applied to lattices with triangular structure, as well as the results achieved by applying the differential operator technique of the Ising and Heisenberg models with external magnetic field applied to the easy magnetization axis z, their phase diagrams, behavior plateaus observed and analyzed according to the Haldane conjecture and appearance of plateaus presented by Oshikawa, Yamanaka and Affleck, and also to study the behavior of the magnetic susceptibility in order to verify the behavior of frustrated systems using the frustration factor f= θWC/TN to verify frustration encountered at various stages of the study models Este trabalho apresenta um estudo da magnetização de platô e do fenômeno de frustração geométrica em sistemas de spins, aplicados às redes com estrutura triangular, bem como os resultados alcançados aplicando-se a técnica do operador diferencial a modelos de Ising e Heisenberg com campo magnético externo aplicado sobre o eixo fácil de magnetização z, seus diagramas de fases e comportamento de platôs observados e analisados segundo a conjectura de Haldane e a condição de aparecimento de platôs apresentada por Oshikawa, Yamanaka e Affleck, e ainda, o estudo do comportamento da susceptibilidade magnética com o objetivo de verificar o comportamento dos sistemas frustrados utilizando-se o fator de frustração f= θWC/TN para verificar a frustração nas diversas fases encontradas ao longo do estudo dos modelos.

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Favaro, Ana Paula. "Energia do estado fundamental de modelo de Heisenberg para cadeias de spin com ligações alternadas e com defeitos locais." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-25082015-114253/.

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Estudamos modelos de materiais magnéticos não uniformes, ou seja, sem simetria translacional. Esta simetria pode ser quebrada pela bordas do sistema, e pela presença de impurezas ou defeitos, ou reduzida por modulações periódicas nas ligações. Como ferramenta nessas investigações utilizamos a formulação da Teoria do Funcional da Densidade para o modelo de Heisenberg. Baseados nos conceitos dessa formulação, propomos a aproximação de ligação local. com o intuito de prover uma forma viável para calcular a energia do estado fundamental de uma cadeia de spins com defeitos ou com modulações nas ligações. Submetemos os funcionais gerados pela aproximação de ligação local a testes de verificação, variando as condições de contorno. a dimensionalidade. e as parametrizações do sistema homogêneo. Com auxílio da aproximação proposta foi possível estudar como a energia do estado fundamental se comporta diante de hordas. e de defeitos locais ferromagnéticos e antiferromagnéticos. Verificamos a existência de urna lei de escala nas cadeias alternadas, e analisamos a dimerização de urna cadeia com modulações FM-AFM. Por Último, estudamos o comportamento crítico de uma cadeia alternada AFM-AFM no limite em que se torna homogênea, com o intuito de verificar conjecturas sobre este comportamento apresentadas recentemente na literatura We investigate models of spatially inhomogeneous magnetic materials. Translational invariance is broken due to the presence of boundaries, impurities or defects, or reduced by periodic modulation of the bonds between neighbouring sites. As computational tool, we use density-functional theory, in its recently proposed formulation for inhomogeneous Heisenberg models. We use concepts of this formulation to propose a local approximation for the ground-state energy of Heisenberg models with nonuniform distribution of exchange couplings J. This local-bond approximation(LBA) is tested in diverse circumstances, by varying boundary conditions, dimensionality, and parametrizations of the uniform reference system. As a result, we obtain a clear picture of when and how local approximations can be used to calculate the energy of Heisenberg models with defects or with periodic modulations. Based on this knowledge, we verify the existence of a scaling law in modulated spin chain, and analyse the dimerization of a chains. that alternates FM and AFM couplings. Finally, we investigate the critical behavior or chains alternating two types of AFM couplings, in the limit in which they approach homogeneous chains

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Caprara, Leandro Peres. "Ondas de spin em paredes de domínio unidimensionais em monocamadas magnéticas." Universidade Federal de São Carlos, 2012. https://repositorio.ufscar.br/handle/ufscar/5043.

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Made available in DSpace on 2016-06-02T20:16:49Z (GMT). No. of bitstreams: 1 4517.pdf: 1547785 bytes, checksum: 6effb94c4a1e222fb3264328e57ccfc6 (MD5) Previous issue date: 2012-08-16 Financiadora de Estudos e Projetos Recent investigations on ferromagnetic monolayers predict the existence of spinwave modes without gap in the spectrum, even in the presence of anisotropy. These excitations propagate within the domain walls that exist in the monolayer, hence in quasione- dimensional structures. They are different from the known bulk-modes whose spectrum presents anisotropy gap and whose propagation may cover all the monolayer's extension. Moreover, since they do not have gap in the spectrum, the predicted modes are not associated to an activation temperature and must influence low-temperature observable physical properties. In the present work, a theoretical study is presented for a single ferromagnetic monolayer with domain walls and the response toan oscillating magnetic field. Gapless spin-wave modes' resonances are studied in the results. Investigações recentes em monocamadas ferromagnéticas prevêem a existência de modos de onda de spin sem gap no espectro, mesmo na presença de anisotropia. Estas excitações propagam-se no interior das paredes de domínio existentes na monocamada, portanto em estruturas quase unidimensionais. Elas distinguem-se dos modos já conhecidos cujo espectro possui gap de anisotropia e cuja propagação pode cobrir toda extensão da monocamada. Além disso, por não terem gap no espectro, os modos previstos não associam uma temperatura de ativação e devem influenciar as propriedades físicas observáveis a baixas temperaturas. Este trabalho apresenta um estudo teórico de uma monocamada ferromagnética com paredes de domínio e a resposta a um campo magnético oscilante. As ressonâncias dos modos de onda de spin sem gap são estudadas como resultado.

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Santos, Marcelo Meireles dos. "A evolução temporal de sistemas de spins 1/2 congelados no espaço e descritos pelo modelo de Heisenberg." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-27032013-120632/.

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Este projeto se destina ao estudo de sistemas quânticos não relativísticos de dois, quatro e oito níveis de energia que descrevem partículas com spin s=1/2 sujeitas à ação de campos externos e interagentes entre si. São apresentadas soluções exatas para as equações que regem esses sistemas. Tais sistemas possuem uma vasta aplicação em diversas áreas da física, dentre as quais é possível destacar a computação quântica. Possíveis aplicações dos resultados são a construção de portas lógicas quânticas universais. Estas portas lógicas quânticas representam um elemento essencial no desenvolvimento dos chamados computadores quânticos. A análise e a implementação destes computadores quânticos exige a manipulação de sistemas de vários níveis, sujeitos a campos externos dependentes do tempo. Neste trabalho é apresentada a solução para o assim chamado Problema de Rabi, um particular problema de dois níveis. Um exemplo de solução para o sistema de quatro níveis, aqui relativo a um problema de dois spins também é discutido. Foram obtidas soluções exatas para sistemas de oito níveis cuja possível aplicação é a Correção Quântica de Erros. This project aims to study the non-relativistic quantum systems of two, four and eight energy levels that describe particles with spin s=1/2 in external .elds and interacting with each other. We find exact analitical solutions for these systems. Such systems have extensive applications in various areas of physics, among which its possible to highlight quantum computing. Possible applications of the results are the construction of quantum universal logic gates.These quantum logic gates are an essential element in the development of so-called quantum computers. The analysis and implementation of quantum computers requires handling systems of various levels, subject to time-dependent external fields. This work presents a solution to the so-called Rabi problem, a particular problem at two levels. An example of a solution to the system of four levels, related to two spins problem is also investigated. We obtained exact solutions for systems of eight levels with possible application to the Quantum Error Correction.

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Campos, Alessandra Matos. "Implementações sequencial e paralela de um novo algoritmo para a simulação de elementos e compostos magnéticos." Universidade Federal de Juiz de Fora (UFJF), 2011. https://repositorio.ufjf.br/jspui/handle/ufjf/3543.

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Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-03T19:15:39Z No. of bitstreams: 1 alessandramatoscampos.pdf: 1960550 bytes, checksum: 14e573eea1f29d2dacca4a586c4d7035 (MD5) Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-06T20:18:34Z (GMT) No. of bitstreams: 1 alessandramatoscampos.pdf: 1960550 bytes, checksum: 14e573eea1f29d2dacca4a586c4d7035 (MD5) Made available in DSpace on 2017-03-06T20:18:34Z (GMT). No. of bitstreams: 1 alessandramatoscampos.pdf: 1960550 bytes, checksum: 14e573eea1f29d2dacca4a586c4d7035 (MD5) Previous issue date: 2011-02-25 CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior O fenômeno magnético é amplamente utilizado nos mais diversos dispositivos eletrônicos, de armazenamento de dados e de telecomunicações, dentre outros. O entendimento deste fenômeno é portanto de grande importância para dar suporte ao aperfeiçoamento e desenvolvimento de novas tecnologias. Uma das formas de melhorar a compreensão do fenômeno magnético é estudá-lo em escala atômica. Quando os átomos magnéticos se aproximam, interagem magneticamente, mesmo que submetidos a um campo magnético externo, e podem formar estruturas em escala nanométrica. Programas computacionais podem ser desenvolvidos com o objetivo de simular o comportamento de tais estruturas. Tais simuladores podem facilitar o estudo do magnetismo em escala nanométrica porque podem prover informações detalhadas sobre este fenômeno. Cientistas podem usar um simulador para criar e/ou modificar diferentes propriedades físicas de um sistema magnético; dados numéricos e visuais gerados pelo simulador podem ajudar na compreensão dos processos físicos associados com os fenômenos magnéticos. Entretanto, a execução de tais simulações é computacionalmente cara. A interação entre átomos ocorre de forma similar ao problema dos N corpos. Sua complexidade nos algoritmos tradicionais é O(N2), onde N é o número de spins, ou átomos, sendo simulados no sistema. Neste trabalho propomos um novo algoritmo capaz de reduzir substancialmente este custo computacional, o que permite que uma grande quantidade de spins possa ser simulada. Adicionalmente ferramentas e ambientes de computação paralela são empregados para que os custos em termos de tempo de computação possam ser ainda mais reduzidos. The magnetic phenomena are widely used in many devices, such as electronic, data storage and telecommunications devices. The understanding of this phenomenon is therefore of great interest to support the improvement and development of new technologies. To better understand the magnetic phenomena, it is essential to study interactions at nano scale. When magnetic atoms are brought together they interact magnetically, even with an external magnetic field, and can form structures at nanoscale. Special design computer programs can be developed to simulate this interaction. Such simulators can facilitate the study of magnetism in nanometer scale because they can provide detailed information about this phenomenon. Scientists may use a simulator to create and/or modify different physical properties of a magnetic system; visual and numerical data generated by the simulator can help to understand the physical processes associated with the magnetic phenomenon. However, there is a natural high complexity in the numerical solution of physical models. The interaction between spins occurs in a similar way to the classical n-body problem. The complexity of this problem is O(N2), where N is the number of spins or atoms in the system. In this work we propose a new algorithm that can substantially reduce the computational cost, and allows the simulation of a large number of spins. Besides, tools and environments for high-performance computing are used so that the costs of computation time may be further reduced.

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Freire, Márcio de Melo. "Teoria de funções de Green para uma impureza isolada localizada intersticialmente em sistemas ferromagnéticos." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/22443.

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FREIRE, M. de M. Teoria de funções de Green para uma impureza isolada localizada intersticialmente em sistemas ferromagnéticos. 2017. 140 f. Tese (Doutorado em Física) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. Submitted by Giordana Silva (giordana.nascimento@gmail.com) on 2017-04-03T22:07:25Z No. of bitstreams: 1 2017_tese_mdmfreire.pdf: 7628225 bytes, checksum: e3a2dea720868776f72333124b7437b6 (MD5) Approved for entry into archive by Giordana Silva (giordana.nascimento@gmail.com) on 2017-04-03T22:08:00Z (GMT) No. of bitstreams: 1 2017_tese_mdmfreire.pdf: 7628225 bytes, checksum: e3a2dea720868776f72333124b7437b6 (MD5) Made available in DSpace on 2017-04-03T22:08:00Z (GMT). No. of bitstreams: 1 2017_tese_mdmfreire.pdf: 7628225 bytes, checksum: e3a2dea720868776f72333124b7437b6 (MD5) Previous issue date: 2017 A Green’s function formalism is used to calculate the expectrum of excitations associated with an interstitial magnetic impurity in different ferromagnetic structures described by the Ising and Heisenberg models. In the chapter 3 the non-resonant excitations of the system due to impurity (i.e, the defect modes outside the region of the bulk and surface spin waves) and the resonant excitations (the defect modes inside the region of the bulk and surface spin waves) are calculated numerically for the high-temperature phase. Two situations are analysed, depending on the position of the impurity: the impurity is on the surface (N = 1) and the impurity is in the bulk region (N ≥ 2). In the others chapters we use the model Ising/Heisenberg (where we can go from Heisenberg model to Ising model, by controlling the value of a parameter λ) to describe the following systems: ferromagnet with an infinite square lattice (Chap. 4), ferromagnet with an infinite face-centered square lattice (Chap. 5), ferromagnet with an infinite body-centered cubic lattice (Chap. 6) and ferromagnet with an infinite honey-comb lattice (Chap. 7), all the systems with a magnetic interstitial impurity. For the first tree cases, only the optical defect modes are calculated, and for the last one, only the acoustic modes are calculated. Um formalismo da função de Green é usado para calcular o espectro de excitações associadas com uma impureza magnética localizada intersticialmente em diferentes estruturas ferromagnéticas descritas pelo modelo de Ising e de Heisenberg. No capítulo 3, descrevemos um ferromagneto de rede cúbica simples semi-infinita através do modelo de Ising. Neste caso, as excitações não-ressonantes (isto é, os modos de defeito fora da região das ondas de spin de volume e de superfície) e as excitações ressonantes (os modos de defeito dentro da região das ondas de spin de volume) são calculadas numericamente para a fase de alta-temperatura. Duas situações são analisadas, dependendo da posição da impureza em relação a seus vizinhos: a impureza está na superfície; a impureza está na região de volume. Nos demais capítulos, usamos o modelo de Heisenberg/Ising (onde passamos do modelo de Heisenberg para o de Ising através do controle de um parâmetro) para descrever os seguintes sistemas: ferromagneto de rede quadrada infinita (capítulo 4), ferromagneto de rede quadrada centrada infinita (capítulo 5), ferromagneto de rede cúbica de corpo centrado infinita (capítulo 6) e rede favo de mel infinita (capítulo 7), todos contendo uma impureza magnética localizada intersticialmente. Nos três primeiros casos, são calculados apenas os modos de defeito acima da banda de volume do material puro (modos ópticos). No capítulo 7, são analisados apenas os modos de defeito abaixo da banda de volume do material puro (modos acústicos).

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Mei, Zhongtao. "Wave Functions of Integrable Models." University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1530880774625297.

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Abreu, Anne Beatriz Rocha. "Teoria quântica de campos aplicada em Modelos de Spins Frustrados." Universidade Federal do Amazonas, 2013. http://tede.ufam.edu.br/handle/tede/4548.

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No. of bitstreams: 1 Dissertação - Anne Beatriz Rocha Abreu.pdf: 1366448 bytes, checksum: 47c7b96a4f310e46ae8f497afc56d8cb (MD5) Previous issue date: 2013-10-02 CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior In this work we study the antiferromagnetic anisotropic Heisenberg spin-1 model with interactions between nearest neighbors (J1 along the rows and J01 along the columns) and between the next nearest neighbors (J2 along the diagonals) on a square lattice. We apply initially the method of linear spin wave theory (LSWT) to study the behavior of the quantum phase transition (T=0) and compare the results with qualitative values obtained for the model J1􀀀J01 􀀀J2, where we explore the two cases of spin-1/2 and spin-1. We analyse the phase diagram in the plane ( J01=J1) versus ( J2=J1). In the case of spin-1/2 the results are not satisfactory in the region of small value of , where disordered region is present for any value of in contradiction with other results available in the literature that present the disordered phase for > 1, whereas for < 1 we have absence of disordered phase with a phase transition of rst order direct between the phases antiferromagnetic (AF) e collinear antiferromagnetic (CAF). The AF state (Néelstate) is characterized by spins oriented antiparallel over all the square lattice. In the CAF state, the spins are oriented parallel in columns and alternated in opposite senses between a horizontal chains. The literature provides only one result in the case of spin-1, which was obtained years ago by Bishop et al. using the cluster coupled method (CCM), in which they demonstrate that no longer exists disordered intermediate phase, not even to = 1, featuring only rst order transitions ( < 1) and second order ( > 1) with presence of a tricritical point. On the other hand, our results for spin waves shows a phase diagram qualitatively similar to those obtained by other methods in the case of spin-1/2. Facing these controversy results found in spin-1, using CCM and LSWT, we will apply the technique of Sachdev operators (bond operators). Our results indicate that we have intermediate desordered phase for any value of > 0. Neste trabalho estudamos o Modelo de Heisenberg Antiferromagnéico Anisotrópico de spin-1 com interações entre primeiros (J1 ao longo das linhas e J01 ao longo das colunas) e segundos vizinhos (J2 ao longo das diagonais) numa rede quadrada. Aplicamos inicial- mente o método da teoria de ondas de spin linear (LSWT) para estudar o comportamento da transição de fase quântica (T=0) e comparamos os resultados qualitativos com os valores obtidos para o modelo J1 􀀀 J01 􀀀 J2, onde exploramos os dois casos de spin-1/2 e spin-1. Analisamos o diagrama de fase no plano ( J01 =J1) versus ( J2=J1). No caso de spin-1/2 os resultados não são satisfatórios na região de pequeno valor de , onde a região desordenada está presente para qualquer valor de em contradição com outros resultados disponíveis na literatura que apresenta a fase desordenada para > 1, enquanto que para < 1 temos ausência desta fase desordenada com uma transição de fase direta de primeira ordem entre as fases antiferromagnética (AF) e colinear antifer-romagnética (CAF). O estado AF (estado de Néel) é caracterizado por spins orientados antiparalelamente sobre toda a rede quadrada. No caso do estado CAF, os spins estão orientados paralelamente em colunas e alternados em sentidos opostos entre cadeias na horizontal. No caso de spin-1 apenas disponibilizamos de um resultado na literatura, que foi obtido anos atrás por Bishop e colaboradores usando o método do cluster acoplado (CCM), no qual demonstram não existir a fase desordenada intermediária, nem mesmo para = 1, apresentando apenas transições de primeira ordem ( < 1) e segunda ordem ( > 1) com presença de um ponto tricrítico. Por outro lado, nossos resultados de ondas de spin mostram um diagrama de fase qualitativamente similar aos encontrados por outros métodos no caso de spin-1/2. Diante desta controvérsia dos resultados encontrados no spin-1, usando CCM e ondas de spin linear, iremos aplicar a técnica dos operadores de Sachdev (operadores de enlace). Nossos resultados indicam que temos a fase desordenada intermediária para qualquer valor de > 0.

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Dillenschneider, Raoul. "Effets d'une contrainte d'occupation strictedans la description de systemes de spins quantiquesa temperature finie." Phd thesis, Université Louis Pasteur - Strasbourg I, 2006. http://tel.archives-ouvertes.fr/tel-00129129.

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Nous etudions des systemes de spin quantiques a temperature finie avec une contrainte d'occupation stricte des sites au moyen d'une procedure introduite par V. N. Popov et S. A. Fedotov. Nous montrons que cette contrainte modifie le comportement d'observables physiques par rapport au cas ou cette contrainte est fixee de facon moyenne par la methode des multiplicateurs de Lagrange. La pertinence de l'etat de Neel est etudiee en presence de la contrainte stricte d'occupation des sites du reseau de spin. La temperature de transition des parametres d'ordre antiferromagnetique de Neel et d'etat de liquide de spins sont doubles par rapport a ceux obtenu par la methode moyenne des multiplicateurs de Lagrange. Nous considerons l'Hamiltonien de basse energie d'ecrit par un Lagrangien de QED3 pour les spinons. Dans ce contexte la masse generee dynamiquement est comparee a celle obtenue par la methode d'occupation moyenne de site.

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Keller-Marxer, Peter. "The antiferromagnetic square-lattice O(3) quantum Heisenberg model for spins S = 1/2 - 5/2 at low temperatures : confirmation of field-theoretical predictions by quantum Monte Carlo simulation /." [Bern] : [s.n.], 1999. http://www.ub.unibe.ch/content/bibliotheken_sammlungen/sondersammlungen/dissen_bestellformular/index_ger.html.

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Mondelli, Claudia. "Fluctuations, frustration and dilution in the SrCrxGa(12-x)O19 compounds : neutron scattering investigation in a broad dynamical range." Université Joseph Fourier (Grenoble), 2000. http://www.theses.fr/2000GRE10250.

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Le compose srcr xga 1 2 xo 1 9 (scgo) represente un bon exemple de systeme magnetique a basse dimensionalite et haute fluctuation. Scgo est un antiferromagnetique de type heisenberg avec de fortes interactions entre premiers voisins ( c w 500k) mais sans ordre a grande distance jusqu'a 100 mk. Les proprietes magnetiques de ce systeme sont associees a l'arrangement d'une majorite de spins de l'ion cr 3 + sur un sous-reseau hautement frustre (le pyrochlore slab) presentant un etat fondamental de type liquide de spin fortement degenere, mais avec certaines proprietes des verres de spin. Les moments magnetiques gelent vers t f4k, mais une large proportion des spins continuent a fluctuer a tres basse temperature. La nature de ce phenomene et l'identification microscopique des spins fluctuants demeurent des questions ouvertes. Le comportement exotique du scgo persiste en presence de fort desordre magnetique et reste a clarifier l'existence de la transition verre de spin pour le compose parfait (non synthetise). Mon travail a consiste a etendre la gamme d'investigation en energie et en temperature (ev a 10 mev, 100mk a 300k) et a etudier l'effet de la dilution magnetique, en utilisant la diffusion de neutrons. Nous avons mis en evidence 3 regimes magnetiques distincts : pour t<t f , on observe une reponse elastique bien marquee. Pour t>t f ,, le systeme presente des correlations dynamiques a courte portee. Pour t>50k, les correlations spatiales disparaissent graduellement et le systeme tend vers un comportement de type paramagnetique. Des echantillons avec differentes concentrations de cr ont ete synthetises pour etudier le role du desordre sur le phenomene de gel. Le moment moyen gele et t f baissent quand la dilution augmente (pour 7<x<8. 6), mais on observe une inversion de comportement pour x>8. 6. L'allure general de <m 2(t)> en fonction de la temperature ne change pas avec la dilution. Cela suggeste que le desordre magnetique n'influence pas fortement le phenomene de gel.

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40

Pouget, Stéphanie. "Contribution à l'étude de l'influence de la dilution sur les propriétés magnétiques de composés isolants frustrés." Toulouse, INSA, 1993. http://www.theses.fr/1993ISAT0039.

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Nous avons principalement etudie le systeme ferromagnetique heisenberg-3d frustre cdcr#2#(#1##x#)in#2#xs#4, dans la limite des faibles dilutions x. La structure des phases ferromagnetiques et verre de spin reentrante a ete exploree par diffraction de neutrons et mesures d'aimantation macroscopiques. Les resultats s'interpretent dans le cadre d'un modele inhomogene du systeme de spins. Par diffusion de neutrons aux petits angles, spectrometries trois-axes et d'echo de spin, nous avons caracterise le comportement critique statique et dynamique des composes x=0 et 0. 05. Cette etude a revele la pertinence de la dilution et ainsi un des effets de la frustration qui est de porter le systeme dans la limite des forts desordres. Nos resultats suggerent l'existence de deux comportements statiques differents du compose cdcr#1#. #9in#0#. #1s#4, de part et d'autre de t#c, concernant la dynamique, nous avons mis en evidence une evolution non monotone du temps de relaxation en fonction du moment transfere, pour des valeurs de celui-ci tres inferieures a l'inverse de la longueur de correlation, et voisines de l'inverse de la distance moyenne entre impuretes in#3#+. La derniere partie de ce travail est consacree au systeme frustre ising-3d fe#1##xmg#xbr#2. Les mesures de la dispersion des ondes de spin pour differentes directions du moment transfere nous ont permis de preciser le modele des interactions d'echange pour le compose febr#2. Nous avons etudie la transition de phase para-antiferromagnetique pour les deux valeurs de la dilution x=0 et 0. 1. Les resultats sont interpretes dans le cadre d'une theorie classique de champ moyen

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41

Filor, Stephan. "A Variational Cluster Approximation for the Heisenberg Model." Doctoral thesis, 2016. http://hdl.handle.net/11858/00-1735-0000-0023-3E15-1.

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Hsu, De-Bang, and 許德邦. "Ground State Properties of the One-dimensional Uniaxial Single-ion Anisotropic Spin-1 XXZ Heisenberg Model." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/56933258370599519508.

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碩士 東海大學 物理學系 103 In this thesis, we investigate the ground state properties of the one-dimensional antiferromagnet Heisenberg model by Exact diagonalization (ED) and Density Matrix Renormalization Group(DMRG). By the exact diagonalization, we calculate the ground state energy and spin correlation function. We employ DMRG to investigate the ground-state phase diagram of the one-dimensional uniaxial single-ion anisotropic Spin-1 XXZ Heisenberg model on different lattice sizes. By the analysis based on the property of symmetry-protected topological order, we obtain the even-Haldane phase, the odd-Haldane phase, and the anti-ferromagnetic, which are phases consistent with the published results.

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韓仁傑. "Monte Carlo determination of the low-energy constants — spin wave velocity, spin stiffness and staggered magnetization density —, of the (3+1)-dimensional quantum Heisenberg model." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/995d62.

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Shchelokovskyy, Pavlo. "Solitary objects on quantum spin rings." Doctoral thesis, 2004. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2004121610.

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We investigate whether quantum spin rings with nearest-neighbor Heisenberg or Ising exchange interactions can host solitary states. Using complete diagonalization techniques the system is described without classical or semiclassical approximation. In this case definitions used in connection with classical solitons are not applicable, one needs to redefine what solitary objects on a quantum spin system with translational symmetry ought to be. Thus, we start our contribution by defining which quantum states possess solitary character. In addition we discuss useful observables in order to visualize solitary quantum states. Then we demonstrate for various quantum spin rings that solitary quantum states indeed exist, and that they are moving around the spin ring without changing their shape in the course of time.

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45

Agrapidis, Cliò Efthimia. "Topologically non-trivial states in one- and quasi-one-dimensional frustrated spin systems." Doctoral thesis, 2019. https://tud.qucosa.de/id/qucosa%3A36334.

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Magnetic frustration is a phenomenon arising in spin systems when spin interactions cannot all be satisfied at the same time. A typical example of geometric frustration is a triangle with Ising-spins at its vertices and antiferromagnetic interaction. While we can easily anti-align two neighbouring spins, it is not possible for the third one to simultaneously anti-align with both of them. Another flavour of magnetic frustration is the so called exchange frustration, where different spin components interact in an Ising fashion on different bonds. Moreover, frustrated spin systems give rise to exotic states of matter, such as spin liquids, spin ices and nematic phases. As frustrated systems are rarely analytically solvable, numerical techniques are of the utmost importance in this framework. This dissertation is concerned with a specific class of models, namely one- and quasi-one-dimensional spin systems and studies their properties by making use of the density matrix renormalisation group technique. This method has been shown to be extremely powerful and reliable to study chain and ladder models. We consider examples of both geometric and exchange frustration. For the former, we take into consideration one of the prototypical examples of geometric frustration in one dimension: the J1-J2 model with ferromagnetic nearest-neighbour interaction J1<0 and antiferromagnetic next-nearest-neighbour interaction J2>0. Our results show the existence of a Haldane gap supported by a special AKLT-like valence bond solid state in a specific region of the coupling ratio. Furthermore, we consider the effect of dimerisation of the first-neighbour coupling. This dimerisation affects the critical point and the ground state underlying the spin gap. These models are of interest in the context of cuprate chain materials such as LiVCuO4, LiSbCuO4 and PbCuSO4(OH)2. Concerning exchange frustration, we consider the celebrated Kitaev-Heisenberg model: it is an extension of the exactly solvable Kitaev model with an additional Heisenberg interaction. The Kitaev-Heisenberg model is currently the minimal model for candidate Kitaev materials. The extended model is not analytically solvable and numerics are needed to study the properties of the system. While both the original Kitaev and the Kitaev-Heisenberg models live on a honeycomb lattice, we here perform systematic studies of the Kitaev-Heisenberg chain and of the two-legged ladder. While the chain cannot support a Kitaev spin liquid state, it shows nevertheless a rich phase diagram despite being a one-dimensional system. The long-range ordered states of the honeycomb can be understood in terms of coupled chains within the Kitaev-Heisenberg model. Following this reasoning, we turn our attention to the Kitaev-Heisenberg model on a two-legged ladder. Remarkably, the phase diagram of the ladder is extremely similar to that of the honeycomb model and the differences can be explained in terms of the different dimensionalities. In particular, the ladder exhibits a topologically non-trivial phase with no long-range order, i.e., a spin liquid. Finally, we investigate the low-lying excitations of the Kitaev-Heisenberg model for both the chain and the ladder geometry.

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46

Kalz, Ansgar. "Phase diagrams of two-dimensional frustrated spin systems." Doctoral thesis, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F080-B.

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Gharakhloo, Roozbeh. "Asymptotic Analysis of Structured Determinants via the Riemann-Hilbert Approach." Thesis, 2019. http://hdl.handle.net/1805/19918.

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Indiana University-Purdue University Indianapolis (IUPUI) In this work we use and develop Riemann-Hilbert techniques to study the asymptotic behavior of structured determinants. In chapter one we will review the main underlying definitions and ideas which will be extensively used throughout the thesis. Chapter two is devoted to the asymptotic analysis of Hankel determinants with Laguerre-type and Jacobi-type potentials with Fisher-Hartwig singularities. In chapter three we will propose a Riemann-Hilbert problem for Toeplitz+Hankel determinants. We will then analyze this Riemann-Hilbert problem for a certain family of Toeplitz and Hankel symbols. In Chapter four we will study the asymptotics of a certain bordered-Toeplitz determinant which is related to the next-to-diagonal correlations of the anisotropic Ising model. The analysis is based upon relating the bordered-Toeplitz determinant to the solution of the Riemann-Hilbert problem associated to pure Toeplitz determinants. Finally in chapter ve we will study the emptiness formation probability in the XXZ-spin 1/2 Heisenberg chain, or equivalently, the asymptotic analysis of the associated Fredholm determinant.

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Schnalle, Roman. "Symmetry assisted exact and approximate determination of the energy spectra of magnetic molecules using irreducible tensor operators." Doctoral thesis, 2009. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2009102618.

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In this work a numerical approach for the determination of the energy spectra and the calculation of thermodynamic properties of magnetic molecules is presented. The work is focused on the treatment of spin systems which exhibit point-group symmetries. Ring-like and archimedean-type structures are discussed as prominent examples. In each case the underlying spin quantum system is modeled by an isotropic Heisenberg Hamiltonian. Its energy spectrum is calculated either by numerical exact diagonalization or by an approximate diagonalization method introduced here. In order to implement full spin-rotational symmetry the numerical approach at hand is based on the use of irreducible tensor operators. Furthermore, it is shown how an unrestricted use of point-group symmetries in combination with the use of irreducible tensor operators leads to a reduction of the dimensionalities as well as to additional information about the physics of the systems. By exemplarily demonstrating how the theoretical foundations of the irreducible tensor operator technique can be realized within small spin systems the technical aspect of this work is covered. These considerations form the basis of the computational realization that was implemented and used in order to get insight into the investigated systems.

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譚登瑞. "Monte Carlo simulation of 2-d spatially anisotropic spin-1/2 Heisenberg models." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/15566862694079959505.

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Brüger, Mirko. "Anisotropie und Magnetostriktion als Korrekturen zum Heisenberg-Modell am Beispiel des Moleküls {Ni4Mo12}." Doctoral thesis, 2008. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2008092616.

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Das Standart-Modell zur Beschreibung von Observablen magnetischer Moleküle ist das Heisenberg-Modell. In diesem wird der Magnetismus des Superaustausches der Elektronen durch einfache bilineare Spin-Spin-Kopplungen beschrieben. Zur genaueren Approximation experimenteller Ergebnisse können, der jeweiligen Struktur des Moleküls entsprechend, verschiedene Erweiterungen des Heisenberg-Modells verwendet werden. Diese werden, explizit für das 4-Spin-System {Ni4Mo12}, in ihren Auswirkungen auf die Hochtemperatur-Nullfeldsuszeptibilität, die Nullfeldsuszeptibilität und die Hochfeldmagnetisierung betrachtet. Die wesentlichen Erweiterungen sind dabei die Einzelionen-Anisotropie, die Dzyaloshinskii-Moriya-Anisotropie und die allgemeinen Kopplungen zweiter Ordnung. Letztere stellen eine Verallgemeinerung der bekannten biquadratischen Kopplungen dar und werden im Rahmen eines magneto-elastischen Modells hergeleitet. Dabei ergeben sich unterschiedliche Einschränkungen der Kopplungsmatrix zweiter Ordnung für starre und flexible Molekülstrukturen. Speziell für {Ni4Mo12} entsprechen die Ergebnisse numerischer Simulationen von Messwerten einer Strukturänderung im externen Magnetfeld.

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