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In this work we analyze the magnetization properties of an antiferromagnetic Kagomé stripe lattice, motivated by the recent synthesis of materials exhibiting this structure. By employing a variety of techniques that include numerical methods as Density Matrix Renormalization Group and Monte Carlo simulations, as well as analytical techniques, as perturbative low energy effective models and exact solutions, we characterize the magnetization process and magnetic phase diagram of a Kagomé stripe lattice. The model captures a variety of behaviors present in the two dimensional Kagomé lattice, which are described here by analytical models and numerically corroborated. In addition to the characterization of semiclassical intermediate plateaus, it is worth noting the determination of an exact magnon crystal phase which breaks the underlying symmetry of the lattice. This magnon crystal phase generalizes previous findings and according to our knowledge is reported here for the first time.

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Localized magnons states, due to flat bands in the spectrum, is an intensely studied phenomenon and can be found in many frustrated magnets of different spatial dimensionality. The presence of Dzyaloshinskii-Moriya (DM) interactions may change radically the behavior in such systems. In this context, we study a paradigmatic example of a one-dimensional frustrated antiferromagnet, the sawtooth chain in the presence of DM interactions. Using both path integrals methods and numerical Density Matrix Renormalization Group, we revisit the physics of localized magnons and determine the consequences of the DM interaction on the ground state. We have studied the spin current behavior, finding three different regimes. First, a Luttinger-liquid regime where the spin current shows a step behavior as a function of parameter D, at a low magnetic field. Increasing the magnetic field, the system is in the Meissner phase at the m = 1/2 plateau, where the spin current is proportional to the DM parameter. Finally, further increasing the magnetic field and for finite D there is a small stiffness regime where the spin current shows, at fixed magnetization, a jump to large values at D = 0, a phenomenon also due to the flat band.

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La estructura del texto es la siguiente. El capítulo 1 comienza con una introducción general a algunos aspectos centrales en teorías de campos en materia condensada. Luego continúa desarrollando el formalismo de integrales de camino a partir de estados coherentes de espín, y finaliza dando un ejemplo concreto; la teoría de campos efectiva para una cadena de Heisenberg antiferromagnética. El capítulo 2 se centra en el estudio analítico y numérico de antiferromagnetos cuánticos frustrados y agrupa tres de nuestros trabajos, ordenados cronológicamente y a la vez por nivel de complejidad, en tres geometrías diferentes; la cadena Kagomé, la cadena diente de sierra y la bicapa hexagonal (panal de abejas). El capítulo 3 comienza con una introducción a las redes neuronales artificiales y continúa desarrollando nuestros dos trabajos relacionados con la aplicación de técnicas de aprendizaje automático al estudio de sistemas magnéticos en el límite de alta anisotropía de Ising, con el mismo orden que en el capítulo anterior. Para finalizar, el capítulo 4 presenta las conclusiones globales, y el capítulo 5, el apéndice.