A new class of collective excitations of the Hubbard model I: $η$ excitation of the negative--$U$ model

Abstract

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 $(π,π)$, the $η$ particle, of the negative--$U$ Hubbard model. We review three previously obtained theorems about the $η$ 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.