Instabilities of the Hubbard chain in a magnetic field

Abstract

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, ±${\mathrm{k}}_{\mathrm{F}\mathrm{\sigma }}$. For finite values of the on-site repulsion U the instabilities occur for single σ electron added or removed at momenta ±${\mathrm{k}}_{\mathrm{F}\mathrm{\sigma }}$, for transverse spin-density wave (SDW) at momenta ±${2\mathrm{k}}_{\mathrm{F}}$ (where ${2\mathrm{k}}_{\mathrm{F}}$=${\mathrm{k}}_{\mathrm{F}\mathrm{\uparrow }}$+${\mathrm{k}}_{\mathrm{F}\mathrm{\downarrow }}$), and for a charge-density wave and SDW at momenta ±${2\mathrm{k}}_{\mathrm{F}\mathrm{\uparrow }}$ and ±${2\mathrm{k}}_{\mathrm{F}\mathrm{\downarrow }}$. While removing or adding single electrons is dominant at zero magnetic field, the presence of that field brings about a dominance for the transverse ±${2\mathrm{k}}_{\mathrm{F}}$ 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.