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We study the 1D extended Hubbard model with a weak repulsive short-rangeinteraction in the non-half-filled band case, using non-perturbativeRenormalization Group methods and Ward Identities. At the critical temperature,T = 0, the response functions have anomalous power-law decay withmultiplicative logarithmic corrections. The critical exponents, thesusceptibility and the Drude weight verify the universal Luttinger liquidrelations. Borel summability and (a weak form of) Spin-Charge separation isestablished.

Universal Luttinger Liquid Relations in the 1D Hubbard Model