The structure of essential spectra and discrete spectrum of four-electron systems in the Hubbard model in a singlet state

Abstract

We study the spectral properties of four-electron systems in the Hubbard model in the quintet and singlet states. We proved the essential spectra of the four-electron systems in the quintet state is a single segment, and four-electron anti-bound states or four-electron bound states is absent. In the system exists two four-electron singlet states, and they are different origins. In the singlet states the essential spectra of four-electron systems is consists of the union no more three segments. Furthermore, in the system exists no more one four-electron anti-bound states or no more one bound states.