Spin Coulomb Drag in the Hubbard Chain

The spin Coulomb drag is the decay of the spin current in a metal as a consequence of the Coulomb interaction between up- and down-spin carriers and is a distinctive feature of spin- polarized transport. The current of majority spins can induce a current of minority spin carriers via the transresistivity. This friction reduces the current but does not change the spin- polarization.\footnote{I. D'Amico and G. Vignale, Phys. Rev. B {\bf 62}, 4853 (2000).} We calculate the critical exponents of the resistivity for up- and down-spin electrons and the transresistivity for the spin-polarized Hubbard chain with nonmagnetic impurities within the Kubo formalism using (1) bosonization techniques\footnote{P. Schlottmann, Phys. Rev. B {\bf 80}, 205110 (2009).} and (2) the Bethe ansatz solution and conformal invariance.\footnote{P. Schlottmann, Phys. Rev. B {\bf 82}, 075103 (2010).} The charge-spin separation in 1D is strictly valid only in the absence of spin-polarization. Due to the Luttinger liquid properties the temperature dependence of the transport correlation functions follow power laws of $T$ with non-universal exponents. A large spin polarization is more favorable for a sustained spin current than a small magnetization.