| In this work, strongly correlated systems will be studied using a variety of numerical techniques. The focus will especially be on the Mn-oxides, a class of materials that has attracted considerable interest in the solid-state community both from experimentalists and theorists alike. Their most remarkable property, next to a phase diagram that displays metallic/insulating behavior and a variety of magnetic and/or orbital orderings, is a strong reaction to small changes in the temperature, chemical doping or applied fields. This can lead to so-called “colossal” effects, the most prominent one being the “colossal magnetoresistance” (CMR) in the Mn-oxides. Based on novel ideas which claim that these materials phase-segregate in certain regions, it will be shown how these concepts lead to explanations of many of the characteristic features of the manganites. It will be demonstrated, using quantum as well as classical models, that cluster formation is a natural consequence for systems with phase-separation tendencies and how percolation between these clusters can lead to the aforementioned “colossal” reactions to small perturbations. Many of the experimentally observed properties can be understood in this framework, sometimes taking into account some additional simple ideas and concepts. Furthermore, the connection between manganite and cuprate physics will be highlighted, drawing on new and exciting experiments that support the notion of phase-separation even for the cuprates and an explanation for the resistivity curves in the underdoped regime of the cuprates will be presented.; In the last chapter, only the high-temperature superconductors will be investigated in more detail. They have been at the center of interest of condensed-matter theory for many years by now, without their secrets being unlocked. This is mostly due to the complexity of the models used to describe these compounds. Here we will focus on one of their most spectacular properties, the occurrence of a gap in the quasi-particle spectrum above Tc. Assuming that this gap is due to pair-binding, and that superconductivity itself is triggered by the condensation of these pre-formed pairs, an appropriate model will be studied using extensive numerical calculations, and some interesting conclusions for systems with non-trivial binding symmetries will be drawn. |
