Instabilities of the Hubbard chain in a magnetic field

We find and characterize the instabilities of the repulsive Hubbard chain in a magnetic field by studying all response functions at low frequency omega and arbitrary momentum. The instabilities occur at momenta which are simple combinations of the (U=0) sigma = up arrow,down arrow Fermi points, +/-k(F sigma). For finite values of the on-site repulsion U the instabilities occur for single a electron added or removed at momenta +/- k(F sigma), for transverse spin-density wave (SDW) at momenta +/- 2k(F) (when 2k(F)=k(F up arrow) + k(F down arrow)) and for a charge-density wave and SDW at momenta +/- 2k(F up arrow) and +/- 2k(F down arrow). While removing or adding single electrons is dominant at zero magnetic field, the presence of that field brings about a dominance for the transverse +/-2k(F) SDW over all the remaining instabilities for a large domain of U and density n values. We go beyond conformal-field theory and study divergences which occur at finite frequency in the one-electron Green function at half-filling and in the transverse-spin response function in the fully polarized ferromagnetic phase.