Electron concentration and on-site interaction effects for the spin and charge excitation spectra in the two-dimensional Hubbard model

Abstract

Electron concentration and on-site interaction effects for spin and charge excitations in the two-dimensional Hubbard model are investigated. Using the auxiliary boson approach, which takes into account the spin and charge fluctuation effects, we derive an effective model which reproduces qualitatively well electronic states for the weak- and intermediate-coupling Hubbard models. The spin response function shows drastic changes as a function of the interaction and of the electron concentration. For the intermediate coupling regime, the Stoner enhancement around $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ and the spin-density-wave-like collective mode are obtained. In contrast, the charge response function does not have any specific structure for this interaction range. Finally, the electron concentration dependence of the zero sound velocity is discussed for the weak-coupling regime. The zero sound mode is shown to have a specific doping dependence that is associated with the existence of a hopping in the lattice.