Spectral Relations for a Matrix Model in Fermionic Fock Space

Abstract

A matrix model \(\mathcal{A}\) is considered related to a system describing two identical fermions and one particle of another nature on a lattice, interacting via annihilation and creation operators. The problem of the study of the spectrum of a block operator matrix \(\mathcal{A}\) is reduced to the investigation of the spectrum of block operator matrices of order three with a discrete variable, and the relations for the spectrum, essential spectrum, and point spectrum are established. Two-particle and three-particle branches of the essential spectrum of the block operator matrix \(\mathcal{A}\) are singled out.