A new class of collective excitations of the Hubbard model I: $\eta$ 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 $(\pi ,\pi )$, 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.

arXiv comment30 pages, revtex 3.0 and epsf.sty (optional), 13 PostScript figures. Submitted to Phys. Rev. B. Minor changes, typos corrected, references added

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