Magnetic effects, dynamical form factors, and electronic instabilities in the Hubbard chain

Abstract

We identify and classify the possible divergences of the charge and spin response functions of the Hubbard chain in a constant external magnetic field H=Hz^. When 0H${\mathit{H}}_{\mathit{c}}$, where ${\mathit{H}}_{\mathit{c}}$ is the critical field for full spin polarization, these divergences occur at the momenta \ifmmode\pm\else\textpm\fi{}2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$ for all values of U and density n=${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$; here ${\mathit{k}}_{\mathit{F}}$=\ensuremath{\pi}n/2 and ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$=\ensuremath{\pi}${\mathit{n}}_{\mathrm{\ensuremath{\sigma}}}$, so that 2${\mathit{k}}_{\mathit{F}}$=${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$. Divergences at \ifmmode\pm\else\textpm\fi{}4${\mathit{k}}_{\mathit{F}}$ show up in the charge function when H=0 and U\ensuremath{\rightarrow}\ensuremath{\infty}. Finally, divergences at \ifmmode\pm\else\textpm\fi{}2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$ appear only for certain regions of these parameters. We discuss the possible connection of our results to the physics of the quasi-one-dimensional metals.