Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions

Abstract

We study the Schrödinger operators , with the fixed quasimomentum of the particles pair, associated with a system of two identical fermions on the two-dimensional lattice with first and second nearest-neighboring-site interactions of magnitudes and , respectively. We establish a partition of the plane so that in each its connected component, the Schrödinger operator has a definite (fixed) number of eigenvalues, which are situated below the bottom of the essential spectrum and above its top. Moreover, we establish a sharp lower bound for the number of isolated eigenvalues of in each connected component.