Some Exact Results in the One-Dimensional Attractive Hubbard Model

The one-dimensional attractive Hubbard model (U << 0) is discussed for the chains of N nodes and the same number of electrons, where N 1 of them have the same spin projection, assuming periodic boundary conditions and the half-filling case. Based on the analysis of the eigenvalue problem we provided the general analytical expression for the eigenvalues, for any number N. This formula implies the existence of two elementary particles with mutually dependent momenta on the ring with N sites the same number of electrons including N - 1 of the same spin projection.