One- and two-hole excitation spectra of the Hubbard model in the non-half-filled case

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Abstract
Exact results for the one- and two-hole excitation spectra of the one- dimensional Hubbard model for filling larger than one electron per site are presented. We consider short chains of up to eight atoms and use the so-called modified periodic boundary conditions, with which we are able to extrapolate the results up to infinite chains. The one-hole excitation spectra demonstrate a gradual transition from the band picture to the spectra characterized by new satellite structures, with increasing electron-electron interaction U. The weight of the satellite part of these spectra increases with increasing U, approaching the atomic-limit value. In the ferromagnetic case, a substantial reduction of the exchange splitting is found as compared with the independent-electron approximation. The two-hole excitation spectra exhibit characteristic atomic lines at large values of U, while at intermediate values of U they are much broader in the non-completely-filled chain than the respective ones of the filled chain. The distance between the satellite and the band part is found to be larger than the value of U for small and intermediate values of the interaction. The results obtained support those found with second-order perturbation theory and the t-matrix approximation.