Spectra of the energy operator of four-electron systems in the triplete state in the Hubbard model

We investigate spectral properties of a four-electron system in the Hubbard Model framework in the v- dimensional lattice Zv. We prove that the essential spectrum of the system in a quintet state consists of a single segment and the four-electron bound state or four-electron anti-bound state is absent. We show that the essential spectrum of the system in a triplete states is the union of at most three segments. We also prove that four-electron bound states or a four-electron anti-bound state exists in triplete states. We prove that in the system exists three triplete states and their spectrum are different.