A class of collective excitations of the Hubbard model: eta excitation of the negative-U model

In this series of papers we present a detailed study of the particle-particle collective excitations of the Hubbard model, and their contribution to the density and spin excitation spectrum. In the first paper, we shall investigate the singlet particle-particle pair with momentum (pi, pi), the eta particle, of the negative-U Hubbard model. We review three previously obtained theorems about the eta particle and develop a self-consistent linear response theory which takes into account its contribution to the density excitation spectrum in the superconducting state. We show that this self-consistent theory agrees with the exact theorems as well as the results of numerical Monte Carlo simulations.