  We derive a lower bound on the ground state energy of the Hubbard model for
given value of the total spin. In combination with the upper bound derived
previously by Giuliani, our result proves that in the low density limit, the
leading order correction compared to the ground state energy of a
non-interacting lattice Fermi gas is given by $8\pi a \rho_u \rho_d$, where
$\rho_{u(d)}$ denotes the density of the spin-up (down) particles, and $a$ is
the scattering length of the contact interaction potential. This result extends
previous work on the corresponding continuum model to the lattice case.
