Excitation Spectra of the Negative-U Hubbard Model: A Small-Cluster Study

TL;DR

This study uses exact diagonalization on small clusters to analyze low-energy excitations and superconductivity in the negative-U Hubbard model, revealing how quasiparticle properties evolve with interaction strength.

Contribution

It introduces a detailed numerical approach to examine excitations and pairing in the negative-U Hubbard model, providing insights into intermediate coupling superconductivity.

Findings

Calculated Bogoliubov quasiparticle spectrum and coherence length as functions of U/t.

Evaluated the internal structure and dispersion of Cooper pairs.

Analyzed the dynamical density correlation function of pairs.

Abstract

An exact-diagonalization technique on small clusters is used to study low-lying excitations and superconductivity in the two-dimensional negative-$U$ Hubbard model. We first calculate the Bogoliubov-quasiparticle spectrum, condensation amplitude, and coherence length as functions of the coupling strength $U/t$, thereby working out how the picture of Bogoliubov quasiparticles in the BCS superconductors is affected by increasing the attraction. We then define the Cooper-pair operator as a spatially-extended composite boson and make a variational evaluation of its internal structure. We thereby calculate the single-particle spectral function of the Cooper pair and obtain the dispersion relation for its translational motion. The dynamical density correlation function of the pairs is also calculated. We thus demonstrate the applicability of our numerical method for gaining insight into low-lying excitations of models for the intermediate coupling superconductivity relevant to cuprate materials.