Orientador: Eduardo Miranda / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-10-31T13:24:18Z (GMT). No. of bitstreams: 1 HoyosNeto_JoseAbel_D.pdf: 1434769 bytes, checksum: 70acbb99e5c8d9636d4209b0919b56ca (MD5) Previous issue date: 2005 / Resumo: O propósito desse trabalho é estudar o papel da desordem em sistemas de spins fortemente interagentes de baixa dimensionalidade. Do ponto de vista teórico, cadeias de spin são extremamente atrativas por apresentarem uma nova física de baixas energias que vem da competição entre o ordenamento magnético e as .utuações quânticas. A introdução de desordem, onipresente no contexto experimental, é um elemento que pode desestabilizar as fases puras dando origem a uma nova física. Essa é a motivação principal do estudo de seu papel. Neste trabalho nós estudamos 4 sistemas de spins antiferromagnéticos desordenados:(i ) as escadas de spins-1/2 dos tipos 2 pernas e zig-zag, (ii ) as cadeias isotrópicas de spins SU(N), (iii ) a cadeia anisotrópica de spins SU(4), e (iv ) revisitamos a cadeia de spins-1/2. O estudo destes sistemas foi realizado aplicando generalizações da técnica do grupo de renormalização no espaço real para desordem forte. No caso do primeiro sistema, nós mostramos que as escadas de spins sempre renormalizam em cadeias de spins muito bem conhecidas. A escada de 2 pernas renormaliza para uma cadeia de spins-1/2 dimerizada antiferromagnética desordenada e, portanto, possui duas fases. Para dimerização forte ou equivalentemente desordem fraca, o sistema se encontra na fase de Haldane onde há um "gap" e a desordem é irrelevante. Para dimerização fraca ou equivalentemente desordem forte, o "gap" de Haldane se fecha e o sistema se encontra numa fase de Griffiths onde as quantidades termodinâmicas são controladas por um expoente não universal denominado expoente dinâmico z . Em contraste, a escada zig-zag renormaliza ou para uma cadeia de spins-1/2 antiferromagnética desordenada ou para uma cadeia de spins com acoplamentos ferro e antiferromagnéticos desordenada. Se a desordem e a frustração são suficientemente fracas, a escada renormaliza para a primeira cadeia, caso contrário esta pertence à mesma classe de universalidade da segunda. Além disso, relacionamos o expoente dinâmico da cadeia de spins com acoplamentos ferro e antiferromagnéticos com a distribuição de ponto fixo desses acoplamentos. Finalmente, através de argumentos simples, consideramos dizimações de acoplamentos correlacionados. Nesse caso, torna-se bem claro que a frustração é responsável pelo surgimento de acoplamentos ferromagnéticos que põem a escada na bacia de atração do ponto fixo das cadeias com acoplamentos ferro e antiferromagnéticos. Com relação à cadeia SU(N), desenvolvemos uma generalização do método do grupo de renormalização para desordem forte para uma cadeia isotrópica antiferromagnética de spins que pertencem à representações irredutíveis totalmente anti-simétricas do grupo SU(N), com N maior ou igual a 2. Conseguimos resolver as equações de fluxo analiticamente e descobrimos que essas cadeias pertencem a uma nova classe de universalidade cujos pontos fixos são de desordem infinita e, por tal motivo, nossos resultados se tornam assintoticamente exatos. Próximo a esses pontos fixos, os expoentes característicos são universais, i. e., independentes da desordem inicial da cadeia, e dependem somente do posto N do grupo de simetria. Devido às similaridades entre as regras de aglomeração de spins quando da dizimação de uma cadeia de spins com acoplamentos ferro e antiferromagnéticos e da dizimação da cadeia isotrópica de spins SU(N) no limite N ® µ , fomos capazes de calcular analiticamente, através de expansões de 1/N , a função correlação da primeira cadeia.Com relação à cadeia de spins SU(4), modificamos a generalização do método de grupo de renormalização para levar em conta a anisotropia dos acoplamentos. Conseguimos determinar o diagrama de fases através de cálculos analíticos e numéricos. Todos os pontos fixos encontrados são universais e de desordem infinita, entretanto, os expoentes característicos dependem de uma maneira não trivial da anisotropia do sistema. Por fim, revisitamos a cadeia de spins-1/2 antiferromagnética. Calculamos a amplitude da função de correlação média e a relacionamos com a amplitude da entropia de emaranhamento da mesma. Além disso, argumentamos em favor da universalidade dessas amplitudes / Abstract: The purpose of this thesis is the study of the role of quenched disorder in low-dimensional strongly interacting quantum spin systems. From the theoretical point of view, spin chains are extremely attractive due to their unconventional behavior that originates in the competition between magnetic ordering and quantum fluctuations. The introduction of disorder, ubiquitous in experimental realizations, is an element that can destabilize the clean phases giving rise to new physical behavior. That is the main motivation of this study. In this thesis, we study 4 random antiferromagnetic spin systems: (i ) the spin-1/2 two-leg and zigzag ladders, (ii ) the isotropic SU(N) spin chains, (iii ) the anisotropic SU(4) spin chain, and (iv ) we also revisit the spin-1/2 chain. For such a task, we use generalizations of the strong disorder real-space renormalization group method. Concerning the first systems, we show that the ladders are always renormalized to well-known spin chains. The two-leg ladder is renormalized to a random dimerized antiferromagnetic spin-1/2 chain, hence exhibiting two phases. For strong dimerization or equivalently weak disorder the system is in the gapful Haldane phase where disorder is irrelevant. Otherwise, the Haldane gap closes and the system is driven into a nonuniversal Griffiths phase, where the thermodynamical quantities are controled by the dynamical exponent z. In contrast, the zigzag ladder is renormalized either to a random antiferromagnetic spin-1/2 chain or to a random spin chain with both ferro- and antiferromagnetic couplings. If the randomness and frustration are sufficiently weak, the ladder is renormalized to the former chain, but otherwise it belongs to the same universality class of the latter one. In addition, we related the dynamical exponent of the ferro- and aniferromagnetic spin chain with its fixed point coupling constant distributions. Moreover, through simple qualitative arguments, we determined the phase diagram of the zigzag ladder with correlated disorder. That calculation clearly showed that frustration is responsible for the appearance of ferromagnetic couplings, which place the system in the basin of attraction of the fixed point of the ferro- and antiferromagnetic spin chains. With respect to theSU(N) spin chain, we developed a generalization of the strong-disorder renormalization group method to the case of an antiferromagnetic isotropic spin chain whose spins belong to the totally antisymmetric irreducible representations of the SU(N) group, with N greater than or equal to 2. We solved the flow equations analytically and found that such chains belong to a new universality class whose fixed point distributions are characterized by infinite disorder, rendering our results asymptotically exact. The characteristic exponents of these fixed points are universal, i. e., independent of the bare disorder, and depend only on the symmetry group rank. Due to the similarities of the spin clustering rules between the ferro- and antiferromagnetic spin chain and the isotropic SU(N) spin chain in the limit of N ® µ, we were able to analytically calcu- late, through a 1/N expansion, the mean correlation function of the former chain. In the case of the SU(4) spin chain, we modified the generalization of the renormalization group method to take into account the coupling anisotropy. We determined the phase diagram through analytical and numerical calculations. All fixed points found are universal and of infinite-randomness type. However, the characteristic exponents depend in a nontrivial fashion on the anisotropy. Finally, we revisited the antiferromagnetic spin-1/2 chain. We calculated the amplitude of the mean correlation function and related it with the amplitude of the entanglement entropy of the chain. In addition, we gave arguments in favor of the universality of these amplitudes / Doutorado / Física da Matéria Condensada / Doutor em Ciências

Since the first discovery of atomically thin sheets of carbon, two-dimensional (2D) materials have captured the interest from scientific community to expand the understanding in fundamental physics and chemistry at low dimensional systems. With extraordinary phenomena only possible at atomically thin limits, there has been high demand to reveal new and unique 2D materials and manipulate their structures and properties. Structural tunability of superatomic solids motivates us to control dimentionality of the materials and construct layered structures which could be exfoliated to 2D materials. The layered crystal [Co6Se8(PEt2phen)6][C60]5 can be used as a template to create a 2D C60-based material with an optical gap in mid-infrared. Re6Se8Cl2 and Mo6S3Br6, are presented as the first examples of covalently linked 2D superatomic solids built from nanoscale building blocks with hierarchical structures and semiconducting properties. We further demonstrate the emergence of hierarchical coherent phonons in a 2D superatomic semiconductor Re6Se8Cl2. Lastly, we explore complex magnetic phases in 2D ferromagnetic semiconductor CrSBr using second harmonic generation and Raman spectroscopy. 2D superatomic semiconductors and 2D magnetic materials provide additional sets of design principles to manipulate structural, electronic, phononic, and magnetic properties at the atomically thin limits. These materials hold promises as model systems to study fundamental physical principles as well as platform for applications with phonon engineering and magnetic optoelectronic devices.

Thesis (Ph. D.)--University of Oregon, 2002. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 118-120). Also available for download via the World Wide Web; free to University of Oregon users.

This thesis investigates the topology and geometry of hyperbolic knot complements that are commensurable with other knot complements. In chapter 3, we provide an infinite family examples of hyperbolic knot complements commensurable with exactly two other knot complements. In chapter 4, we exhibit an obstruction to knot complements admitting exceptional surgeries in conjunction with hidden symmetries. Finally, in chapter 5, we discuss the role of surfaces embedded in 3-orbifolds as it relates to hidden symmetries. / text

The Intrinsic Low-Dimensional Manifold (ILDM) has been adopted as an approximation to the slow manifold representing the long-term evolution of a non-linear chemical system. The computation of the slow manifold simplifies the model without sacrificing accuracy because the trajectories are rapidly attracted to it. The ILDM has been shown to be a highly accurate approximation to the manifold when the curvature of the manifold is not too large. An efficient method of calculating an approximation to the slow manifold which may be equivalent to the ILDM is presented. This method, called Functional Equation Truncation (FET). is based on the assumption that the local curvature of the manifold is negligible, resulting in a locally linearized system. This system takes the form of a set of algebraic equations which can be solved for given values of the independent variables. Two-dimensional and three-dimensional models are used to test this method. The approximations to onedimensional slow manifolds computed by FET are quite close to the corresponding ILDMs and those for two-dimensional ones seem to differ from their ILDM counterparts. / vii, 61 leaves ; 29 cm.

The structural architecture found in low-dimensional materials can lead to a number of interesting physical properties including anisotropic conductivity, magnetic frustration and non-linear optical properties. There is no standard synthesis concept described thus far to apply when searching for new low-dimensional compounds, and therefore control on the design of the new materials is of great importance.This thesis describes the synthesis, crystal structure and characterization of some new transition metal oxohalide compounds containing p-elements having a stereochemically active lone-pair. First row transition metal cations have been used in combination with SeIV, SbIII and TeIV ions as lone-pair elements and Cl- and Br- as halide ions. The lone-pairs do not participate in covalent bonding and are responsible for an asymmetric one-sided coordination. Lone-pair elements in combination with halide ions have shown to be powerful structural spacers that can confine transition metal building blocks into low-dimensional arrangements. The halide ions and lone-pairs reside in non-bonded crystal volumes where they interact through weak van der Waals forces. The transition metal atoms are most often arranged to form sheets, chains or small clusters; most commonly layered compounds are formed.To further explore the chemical system and to separate the transition metal entities even more the possibility to include tetrahedral building blocks such as phosphate-, silicate-, sulphate- and vanadate building blocks into this class of compounds has been investigated. Tetrahedral building blocks are well known for their ability of segmenting structural arrangements by corner sharing, which often leads to the formation of open framework structures. The inclusion of tetrahedral building blocks led to the discovery of interesting structural features such as complex hydrogen bonding, formation of unusual solid solutions or faulted stacking of layers.Compounds for which phase pure material could be synthesized have been characterized in terms of their magnetic properties. Most compounds were found to have antiferromagnetic spin interactions and indications of magnetic frustration could be observed in some of them. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 6: Manuscript. Paper 9: Manuscript. Paper 10: Manuscript.</p>

Transport properties of the two-dimensional electron gas (2DEG) in high magnetic fields are used to investigate scattering processes affecting the resistivity of GaAs-GaAlAs and GaInAs-InP heterojunctions and quantum wells: especially coupling of electrons to acoustic and optic phonons; and transitions between electric subbands. The experiments fall into two groups: A systematic study of magnetophonon resonance (MPR) between 30K and 300K. Resonance positions indicate a coupling substantially below the LO phonon energy, expected from 3D measurements. GaAs-GaAlAs hetero junctions show amplitudes varying smoothly with electron density (n_s) and closely related to the 4K mobility. On rotation in magnetic field they decrease rapidly as the resonance position returns to the LO value. In modulation doped structures the damping factor is determined by remote impurity scattering. As n_s is increased in GaInAs-InP the coupling frequency decreases dramatically from the GaAs-like LO at 272cm^-1 to the InAs-like TO at 226cm^-1. At higher electric fields the 'normal' MPR maxima invert, starting at low magnetic fields, to form 'hot electron' MPR minima, with maximum amplitude at ~60K. This is the first direct observation of HEMPR in 2D and is explained in a diffusion picture. At lower electric fields, additional resonances are identified with resonant cooling by inter-subband scattering. Comparisons are made with calculations and explanations sought including consideration of interface phonons; coupled plasmon-phonon modes; and shifts of the resonance positions due to the shape of the density of states. Low temperature magnetoresistance measurements in GaAs-GaAlAs heterojunctions with more than one occupied electric subband. Shubnikov-de Haas oscillations in perpendicular magnetic fields contain non-additive terms at electron temperatures > 2K where acoustic phonon mediated inter-subband scattering is comparable to intra-subband scattering. Subband separations and greatly enhanced g-factors [largest for electrons in the upper subband ] are deduced from the oscillations. Damping of the oscillations in field, gives values for quantum lifetimes (τ_s), much smaller than τ_tʼ, deduced from mobility. With two subbands occupied τ_s is always largest for the upper subband, while relative sizes of τ_t depend on sample quality. Study of electron energy loss rates, from thermal damping of the oscillations, shows enhancement in the region kT_e ~ ħω_cʼ, which is evidence for cyclotron phonon emission. Depopulating subbands in parallel fields causes the resistance to drop, by up to 60%, due to suppression of inter-subband scattering. Systematic studies show this scattering rate is independent of n_s.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2009. / Includes bibliographical references (p. 100-107).

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2007. / Landman, Uzi, Committee Member ; Yannouleas, Constantine, Committee Member ; Bunimovich, Leonid, Committee Member ; Chou, Mei-Yin, Committee Member ; Pustilnik, Michael, Committee Member.

Thesis (M.S.)--Boise State University, 2010. / Includes abstract. Includes bibliographical references (leaf 55).