Low density electron pairs in the extended Hubbard model

We study the extended Hubbard model in the parameter region where it exhibits superconducting instabilities. The model is defined by onsite and nearest-neighbor Coulomb interactions U and V, and hopping integral t. We calculate pair binding energies for various finite clusters by performing exact diagonalization of the Hamiltonian. We show results for one-dimensional chains and discuss results for 4 × 4, 6 × 6, and 8 × 8 two-dimensional square lattices. Results of solving the BCS equation for the pair binding energy as functions of carrier density n, and Coulomb interactions U and V, are compared with the exact diagonalization results. In the dilute concentration limit (n → 0), the BCS equation is expected to be exact and, in the low electron density region, the results for the pair binding energy are found to be in fairly good agreement with the exact solutions.