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.Comment: 47 pages, 25 figures; submitted to Phys. Rev. B. Long version of
arXiv:cond-mat/060757