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

TL;DR

This paper investigates the $ ext{eta}$ collective excitation in the negative-$U$ Hubbard model, developing a self-consistent theory that aligns with exact theorems and Monte Carlo simulations, enhancing understanding of particle-particle excitations.

Contribution

It introduces a self-consistent linear response theory for the $ ext{eta}$ excitation, integrating it into the density spectrum of the negative-$U$ Hubbard model, and validates it against established theorems and simulations.

Findings

Self-consistent theory agrees with exact theorems.

Results match Monte Carlo simulations.

Provides new insights into $ ext{eta}$ excitation contributions.

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.