Number of Bound States of the Hamiltonian of a Lattice Two-boson System with Interactions up to the Next Neighboring Sites - Lakaev, S. N.; Khamidov, Sh. I.; Akhmadova, M. O. (Lobachevskii journal of mathematics, 2024)
We study the family , of discrete Schrödinger operators, associated to the Hamiltonian of a system of two identical bosons on the two-dimensional lattice interacting through on one site, nearest-neighbor sites and next-nearest-neighbor sites with interaction magnitudes and respectively. We prove there existence an important invariant subspace of operator such that the restriction of the operator on this subspace has at most two eigenvalues lying both as below the essential spectrum as well as above it, depending on the interaction magnitude (only). We also give a sharp lower bound for the number of eigenvalues of .