Department of Physics2024-12-2920240375-960110.1016/j.physleta.2024.1297812-s2.0-85200949346https://doi.org/10.1016/j.physleta.2024.129781https://hdl.handle.net/20.500.14288/22994Considering a spin-up and a spin-down fermion in a generic tight-binding lattice with a multi-site basis, we investigate the two-body problem using a multiband extended-Hubbard model with finite-ranged hopping and interaction parameters. We derive a linear eigenvalue problem for the entire two-body spectrum, alongside a nonlinear eigenvalue problem for the bound states in the form of a self-consistency equation. Our results, based on an exact variational approach, suggest potential applications across various lattice geometries. As an illustration, we apply them to the linear-chain model and show that the resultant spin singlet and triplet bound states align well with the existing literature. Superconductor scienceTopological insulatorsJournal article1873-2429 1294848900001Q241129