We study the Schrödinger operators H λµ (K), with K ∈ T 2 the fixed quasi-momentum of the particles pair, associated with a system of two identical fermions on the two-dimensional lattice Z 2 with first and second nearest-neighboring-site interactions of magnitudes λ ∈ R and µ ∈ R, respectively. We establish a partition of the (λ, µ)−plane so that in each its connected component, the Schrödinger operator H λµ (0) 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 H λµ (K) in each connected component.

We study the Schroedinger operators H_{λµ}(K), with K ∈T_2 the fixed quasimomentum of the particles pair, associated with a system of two identical fermions on the two-dimensional lattice Z_2 with first and second nearest-neighboring-site interactions of magnitudes λ ∈ R and µ ∈ R, respectively. We establish a partition of the (λ,µ)−plane so that in each its connected component, the Schroedinger operator H_{λµ}(0) 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 H_{λµ}(K) in each connected component.

No abstract