We investigate with the aid of the 1/N expansion the dispersion relation of the collective mode in the infinite-U Hubbard model in the presence of a long-range Coulomb term. We calculate this numerically in three dimensions and for a parabolic dispersion for the full range of fillings. For moderate fillings the results are consistent with Landau theory and weak-coupling approaches, but for fillings close to one-half the nature of the collective mode is completely changed. In this limit it becomes equivalent to a movement of the electron system as a whole, thereby avoiding the U=∞ restriction. This mode never decays into single-particle excitations, and the mass scale on which it appears is that of the free-electron system.

• Received 9 August 1991

DOI:https://doi.org/10.1103/PhysRevB.45.3995