Structure of essential spectrum and discrete spectra

We consider five-electron systems for the Hubbard Model and investigate the structure of essential spectrum and discrete spectra of the system in a sextet, and four type quartet states and five type doublet states of the system for the d- dimensional integer valued lattice Zd. We proved the spectrum of the system in the sextet state is purely continuous and in the system five-electron bound states and five-electron anti bound states is absent. In the one- and two-dimensional cases, it is shown that the essential spectrum of the five-electron quartet states operator is the union of seven segments, and the discrete spectrum of the system consists of a no more than one eigenvalue lying the outside domain of the essential spectrum of this operator.