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 {ω} and arbitrary momentum. The instabilities occur at momenta which are simple combinations of the (U=0) {σ}={↑},{↓} Fermi points, ±{}k_Fσ. For finite values of the on-site repulsion U the instabilities occur for single {σ} electron added or removed at momenta ±{}k_Fσ, for transverse spin-density wave (SDW) at momenta ±{}2kF (where 2kF=k_F↑+k_F↓), and for a charge-density wave and SDW at momenta ±{}2k_F↑ and ±{}2k_F↓. While removing or adding single electrons is dominant at zero magnetic field, the presence of that field brings about a dominance for the transverse ±{}2kF 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.