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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.

Since the last few decades frustrated spin systems have attracted much interest. These studies are motivated by the rich variety of their unusual magnetic properties and potential applications. In this thesis, excitation spectra of the weakly coupled dimer system Ba3Cr2O8, the spin-1/2 chain material with distorted diamond structure Cu3(CO3)2(OH)2 (natural mineral azurite), and the quasi-twodimensional antiferromagnet with triangle spin structure Cs2CuBr4 have been studied by means of high-field electron spin resonance. Two pairs of gapped modes corresponding to transitions from a spin-singlet ground state to the first excited triplet state with zero-field energy gaps, of 19.1 and 27 K were observed in Ba3Cr2O8. The observation of ground-state excitations clearly indicates the presence of a non-secular term allowing these transitions. Our findings are of crucial importance for the interpretation of the field-induced transitions in this material (with critical fields Hc1 = 12.5 T and Hc2 = 23.6 T) in terms of the magnon Bose-Einstein condensation. The natural mineral azurite, Cu3(CO3)2(OH)2, has been studied in magnetic fields up to 50 T, revealing several modes not observed previously. Based on the obtained data, all three critical fields were identified. A substantial zero-field energy gap, Δ = 9.6 K, has been observed in Cs2CuBr4 above the ordering temperature. It is argued that contrary to the case for the isostructural Cs2CuCl4, the size of the gap can not be explained solely by the uniform Dzyaloshinskii-Moriya interaction, but it is rather the result of the geometrical frustration stabilizing the spin-disordered state in Cs2CuBr4 in the close vicinity of the quantum phase transition between a spiral magnetically ordered state and a 2D quantum spin liquid.

Interactions between the microscopic constituents of a solid---a many-body system--- can lead to novel phases and exotic physical phenomena like fractionalization, topological order, quantum spin liquids, emergent gauge field, etc.. The concept of frustration provides a ground for such exotic phenomena. Frustration can prevent a many-body system from establishing long-range order down to the lowest temperatures due to competing interactions. Instead, competing interactions may result in disordered and liquid-like phases of matter that provide the vacuum for fractional excitations. The absence of any order parameter in strongly frustrated systems---due to not breaking any symmetry spontaneously--- immediately raises the question about possible experimental probes of spin-liquids and their fractional excitations. Dynamic probes, like inelastic neutron scattering or Raman scattering, provide an experimental method to detect signatures of fractionalised quasiparticles. The energy and momentum transferred in a scattering event is split between the fractional quasiparticles. On the theory side, computing such dynamical signatures beyond one spatial dimension is generally a difficult task. In this thesis, numerical methods like density matrix renormalisation group and matrix product states are used to study strongly frustrated magnets and their dynamics in a non-perturbative way. This thesis covers two physical models in the context of frustration and emergent gauge fields. Firstly, the Kitaev model of spin-1/2 degrees of freedom subject to strongly anisotropic spin exchange. The Kitaev model features quantum spin liquid ground states with fractionalization of spins into Majorana fermions and Z_2-fluxes---the visons of an emergent Z_2 gauge theory. The main questions addressed here concern the stability of the quantum spin liquid phase upon adding perturbations relevant in magnetic compounds such as Heisenberg or the symmetric-offdiagonal Gamma exchange. Applying a magnetic field drives the Kitaev model into a topologically ordered phase. The excitations and dynamical signatures within the spin liquid, the topologically ordered phase, and within ordered phases are studied. Secondly, a classical minimal model of the proton configuration in water ice is studied. The ice rules, a local constraint describing the low energy manifold, result in emergent Maxwell's equation. Upon applying an external electric field along certain axis, a polarization plateau occurs in which the remaining degrees of freedom can be described by dimers on two-dimensional lattices.

Les atomes froids dans les réseaux optiques permettent d'avoir un contrôle sans précédent des états a N-corps fortement corrélés. Pour cette raison, ils représentent un excellent outil pour l'implémentation d'un « simulateur quantique », utile pour réaliser de manière expérimentale de nombreux hamiltoniens de systèmes d'intérêt physique. En particulier, ils rendent possible la création de champs de jauge artificiels; ces derniers permettant d'accéder à la physique du magnétisme frustré. Dans ce travail, il s'agit de s'intéresser à la thermodynamique des atomes froids, en abordant ce sujet de manière théorique et numérique. A ce jour, le Monte Carlo quantique est la méthode la plus efficace dans ce domaine. Néanmoins, en raison de ce qu'on appelle le « problème du signe », elle ne peut s'appliquer qu'à une classe restreinte de systèmes, et dont par exemple les systèmes frustrés ne font pas partie. L'intérêt de cette thèse est de développer une nouvelle méthode approximée fondée sur une approche Monte Carlo. La première partie de cette thèse est consacrée à des considérations de nature théorique sur la structure spatiale des corrélations classiques et quantiques. Ces résultats nous permettent de développer, dans une deuxième partie, une approximation nommée « champ moyen quantique ». Celle-ci permet de proposer, dans une troisième partie, une méthode numérique qu'on appelle « Monte Carlo du champ auxiliaire » et qu'on applique à des cas d'intérêt physique, notamment au réseau triangulaire frustré. / Cold atoms in optical lattices offer unprecedented control over strongly correlatedmany-body states. For this reason they represent an excellent tool for the implementation ofa “quantum simulator”, which can be used to realize experimentally several Hamiltonians ofsystems of physical interest. In particular, they enable the engineering of artificial gaugefields, which gives access to the physics of frustrated magnetism. In this work, we study thethermodynamics of cold atoms both from a theoretical and a numerical point of view. Atpresent days, the most effective method used in this field is the quantum Monte Carlo. Butbecause of the so-called “sign problem” it can only be applied to a limited class of systems,which for example do not include frustrated systems. The interest of this thesis is to developof a new approximated method based on a Monte Carlo approach. The first part of this workis dedicated to theoretical considerations concerning the spatial structure of quantum andclassical correlations. These results permit to develop, in the second part, an approximationcalled quantum mean-field. This latter allows to propose, in the third part, a numericalmethod that we call “auxiliary-field Monte Carlo” and that we apply to some systems ofphysical interest, among which the frustrated triangular lattice.

Since the last few decades frustrated spin systems have attracted much interest. These studies are motivated by the rich variety of their unusual magnetic properties and potential applications. In this thesis, excitation spectra of the weakly coupled dimer system Ba3Cr2O8, the spin-1/2 chain material with distorted diamond structure Cu3(CO3)2(OH)2 (natural mineral azurite), and the quasi-twodimensional antiferromagnet with triangle spin structure Cs2CuBr4 have been studied by means of high-field electron spin resonance. Two pairs of gapped modes corresponding to transitions from a spin-singlet ground state to the first excited triplet state with zero-field energy gaps, of 19.1 and 27 K were observed in Ba3Cr2O8. The observation of ground-state excitations clearly indicates the presence of a non-secular term allowing these transitions. Our findings are of crucial importance for the interpretation of the field-induced transitions in this material (with critical fields Hc1 = 12.5 T and Hc2 = 23.6 T) in terms of the magnon Bose-Einstein condensation. The natural mineral azurite, Cu3(CO3)2(OH)2, has been studied in magnetic fields up to 50 T, revealing several modes not observed previously. Based on the obtained data, all three critical fields were identified. A substantial zero-field energy gap, Δ = 9.6 K, has been observed in Cs2CuBr4 above the ordering temperature. It is argued that contrary to the case for the isostructural Cs2CuCl4, the size of the gap can not be explained solely by the uniform Dzyaloshinskii-Moriya interaction, but it is rather the result of the geometrical frustration stabilizing the spin-disordered state in Cs2CuBr4 in the close vicinity of the quantum phase transition between a spiral magnetically ordered state and a 2D quantum spin liquid.