On the Existence of Bound States of a System of Two Fermions on the Two-Dimensional Cubic Lattice

We construct a two-particle discrete Schrödinger-type operator H_μ(k)=H_0(k)+μV , k∈𝕋^2 associated to a system of two fermions on the two-dimensional cubic lattice ℤ^2 interacting via short-range potential, where the non-perturbed part H_0(k), k∈𝕋^2 is a convolution type operator with dispersion relation ℰ_k(·) defined on the torus 𝕋^2 and having a degenerate minimum at 0∈𝕋^2 . The existence of eigenvalues below the essential spectrum of the operator H_μ(k) is proved in the following two cases: in the case k=0 for all μ>0 and in the case of k≠ 0 for large μ>0 .