Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping

We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in d = 3 spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices, in d > 1. In a given realization, the hopping disorder breaks time reversal invariance, but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein non-linear sigma model [A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983), Sov. Phys. JETP 57, 97 (1983)]. We analyze the Finkel'stein sigma model using a perturbative, one-loop renormalization group analysis controlled via an epsilon-expansion in d = 2 + epsilon dimensions. We find that, in d = 2 dimensions, the interactions destabilize the conducting phase known to exist in the disordered, non-interacting system. The metal-insulator transition that we identify in d > 2 dimensions occurs for disorder strengths of order epsilon, and is therefore perturbatively accessible for epsilon << 1. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase, and the transition into it, can only appear due to the presence of the interactions.