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In the presence of quenched disorder, the competition between localmagnetic-moment formation and Anderson localization for electrons at azero-temperature, metal-insulator transition (MIT) remains a long unresolvedproblem. Here, we study the interplay of these ingredients in a power-lawrandom banded matrix model of spin-1/2 fermions with repulsive Hubbardinteractions. Focusing on the regime of weak interactions, we perform bothanalytical field theory and numerical self-consistent Hartree-Fock numericalcalculations. We show that interference-mediated effects strongly enhance thedensity of states and magnetic fluctuations upon approaching the MIT from themetallic side. These are consistent with results due to Finkel'stein obtainedfour decades ago. Our numerics further show that local moments nucleate fromtypical states at the Fermi energy near the MIT, with a density that growscontinuously into the insulating phase. We identify spin-glass order in theinsulator by computing the overlap distribution between converged Hartree-Fockmean-field moment profiles. Our results indicate that itinerant interferenceeffects can morph smoothly into moment formation and magnetic frustrationwithin a single model, revealing a common origin for these disparate phenomena.

Magnetic instability and spin-glass order beyond the Anderson-Mott transition in interacting power-law random banded matrix fermions