| We present in this thesis two works aimed at furthering our understanding of the complex interplay possible between quenched disorder and interparticle interaction effects. Specifically, we analyze field theories of novel disordered quantum systems, subject to short-ranged interactions, in d ≥ 2 spatial dimensions. These emerge, for example, as low-energy descriptions of tight-binding models for spinless fermions, at half filling on bipartite lattices, subject to (short-ranged) random hopping. Such lattice models possess a special "sublattice" symmetry (SLS), shared by both the disorder and the interactions. It is known that, in the absence of interactions, these disordered systems are unusual in that they evade the phenomenon of Anderson localization for d ≥ 1, possessing extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states for d ≤ 2. We use the perturbative renormalization group to study the simultaneous effects of disorder and interactions in these field theories.; We first consider the effects of generic short-ranged interactions upon a (class BDI) system of 2D disordered Dirac fermions, possessing SLS and time-reversal invariance (TRI) in every realization of the static disorder. We show that the same mechanism responsible for the divergence of the density of states in the non-interacting system leads to a spectacular instability, in which the interactions are driven strongly relevant by the disorder.; We next analyze a class of "Hubbard-like" models for spinless fermions, with (complex) random hopping and short-ranged interactions on bipartite lattices, in d ≥ 2. SLS is responsible for the special "nesting" instability of the ballistic Fermi liquid phase in the clean, but interacting limit of these models. In a given realization, the hopping disorder breaks TRI, but preserves SLS (class AIII); this is consistent with the application of a random magnetic field to an otherwise clean model. We study these systems using the Finkel'stein non-linear sigma model formalism. Our primary result is the identification of a new instability of the diffusive Fermi liquid phase in d > 2, indicative of a first order metal-insulator transition, arising solely from the competition between disorder and interactions. |
