Wang, Xiaoyu2017-11-272017-11-272017-08https://hdl.handle.net/11299/191405University of Minnesota Ph.D. dissertation.August 2017. Major: Physics. Advisor: Rafael Fernandes. 1 computer file (PDF); x, 140 pages.Superconductivity (SC) is an electronic phase of matter in which certain condensed matter systems conduct electricity without resistance and completely expel magnetic fields from their interiors. Since the initial discovery in mercury over a century ago, great advances have been made to deepen our understanding of the SC phenomenon and its microscopic mechanism. In two families of layered materials, namely, the cuprates and the iron pnictides/chalcogenides, the superconducting transition temperatures can be higher than the boiling point of liquid Nitrogen. Furthermore, the microscopic origin is not due to electron-phonon coupling, as is the case for low-temperature superconductors. In addition to SC, the phase diagram of these systems exhibit several other electronic phases of matter, such as antiferromagnetism, nematicity and charge density wave. The normal state also exhibits properties different than those of normal metals. In this thesis, I use analytical and numerical Quantum Monte Carlo (QMC) methods to shed light on the interplay between these ordered states. In particular, I will study the novel magnetic phases in iron pnictides, and attribute their origin to the itineracy of electrons. I will discuss the magnetic origin of electronic nematicity in these materials, and describe the spectroscopic manifestations. I will elaborate on the origin and prop- erties of SC and charge density wave orders near a metallic antiferromagnetic quantum critical point, as well as its relevance to both cuprate and iron pnictide/chalcogenide superconductors.enThesis or Dissertation