Absence of spin diffusion in most random lattices

We examine the metallic phase of the positionally disordered Anderson-Hubbard model as a prototype of a strongly correlated disordered metal. We find that the low-temperature thermodynamics is dominated by spin excitations in rare regions, leading to non-Fermi-liquid behavior as T{→}0 with a diverging susceptibility, a specific heat rising faster than T, and a vanishing spin diffusion coefficient. We argue that the results should, in principle, apply throughout the metallic phase of random alloys which undergo a transition, as a function of concentration, to an insulating phase with local moments.