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The competition between the Mott transition and the Anderson localization inone dimensional electron systems is studied based upon the bosonization and therenormalization group method. The beta function is calculated up to the secondorder in the strength of diagonal disorder by using a replica trick. It isfound that the sufficiently strong forward scattering by random impuritiesdestroys the Mott-Hubbard gap, and the backward scattering gives rise to theAnderson localization for the resulting gapless state. On the other hand, ifthe Umklapp interaction is strong enough, the Mott insulating state stilloverwhelms the Anderson localization.Comment: 4 pages, Revtex, figures included, to appear in Phys. Rev. B (Rapid  Communication

Competition between the Mott transition and Anderson localization in one-dimensional disordered interacting electron systems