The simplest way to add interactions to a single-band model of spinful electrons hopping on a crystal lattice is the Hubbard model, and the next simplest model is the extended Hubbard model (EHM). The EHM is useful for modeling superconductive electron pairing and emergent insulating phases including a dimerized phase called the "Bond Order Wave". In this thesis, I present two projects. In the first, I applied the numerical method of Density Matrix Renormalization Group to study the entanglement entropy at critical points of the clean EHM in one dimension near the BOW phase. In the second project, I applied analytical renormalization group approaches to study the phase diagram of the one dimensional model with weak disorder at weak coupling.