Spin and charge excitations of the degenerate Hubbard model in one dimension.

Abstract

The degenerate Hubbard chain with N internal degrees of freedom is integrable if site occupations of more than two electrons are excluded. The ground state of the model has several unusual properties; e.g., the magnetic susceptibility has logarithmic singularities as the field H\ensuremath{\rightarrow}0 and also the specific-heat coefficient is singular. An extensive discussion of ground-state properties as a function of U and the band filling is presented. The elemental charge and spin excitations are derived for arbitrary U and band filling. If, on average, there is exactly one electron per site as a function of U, a qualitative change in the low-energy charge excitations is found at a critical value ${\mathit{U}}_{\mathit{c}}$. This change is probably associated with a Mott metal-insulator transition (${\mathit{U}}_{\mathit{c}}$=0 for N=2). The Fermi velocity is finite for U${\mathit{U}}_{\mathit{c}}$ but vanishes for U>${\mathit{U}}_{\mathit{c}}$ (for one electron per site). The spin-wave velocity is inversely proportional to the magnetic susceptibility for all U and band fillings. There are N-1 elemental spin-wave branches. For arbitrary band filling there are then N-1 soft modes at different finite momenta, all related to the Fermi surface. For exactly one electron per site, the spin-excitation spectrum can be mapped onto the one of the SU(N) Heisenberg chain. The implications of the hole states on superconductivity are also discussed.