Numerical Studies of Models for Strongly Correlated Electrons Using Monte Carlo Mean Field and Density Matrix Renormalization Group Methods

The interplay of magnetism and superconductivity in the iron-based superconductors is investigated numerically using Monte Carlo mean field and density matrix renormalization group methods. The finite temperature magnetic and transport properties of the 2D oxypnitides are calculated using Monte Carlo mean field methods, capturing many experimentally relevant phases and predicting a new phase dubbed "orbital selective directional conductor". Finally, pairing tendencies are explored using exact diagonalization and density matrix renormalization group for low dimensional iron-based superconductor, BaFe₂S₃, predicting hole pairs arranged along the diagonals or rungs of the ladders in real space. This dissertation further adds to the evidence that superconductivity in the iron based compounds has its origin in the magnetic fluctuations that are driven by correlations.