Essential Schrödinger operator spectrum of one system of four particles on a lattice

The energy operator of a system of four particles on a lattice where only two pairs of the particles interact is considered. There exist four mutually orthogonal subspaces, invariant with respect to the energy operator and such that their direct sum is equal to the entire space. The spectra of the restrictions of the energy operator to these invariant spaces are found. The dependence of the essential spectrum on the binary interaction is examined. The absence of bound states of this operator is demonstrated.