INSTABILITIES OF THE HUBBARD CHAIN IN A MAGNETIC-FIELD

We find and characterize the instabilities of the repulsive Hubbard ch ain in a magnetic field by studying all response functions at low freq uency omega and arbitrary momentum. The instabilities occur at momenta which are simple combinations of the (U=0) sigma = up arrow,down arro w Fermi points, +/-k(F sigma). For finite values of the on-site repuls ion U the instabilities occur for single a electron added or removed a t momenta +/- k(F sigma), for transverse spin-density wave (SDW) at mo menta +/- 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 a t zero magnetic field, the presence of that field brings about a domin ance for the transverse +/-2k(F) SDW over all the remaining instabilit ies for a large domain of U and density n values. We go beyond conform al-field theory and study divergences which occur at finite frequency in the one-electron Green function at half-filling and in the transver se-spin response function in the fully polarized ferromagnetic phase.