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We derive a lower bound on the ground state energy of the Hubbard model forgiven value of the total spin. In combination with the upper bound derivedpreviously by Giuliani, our result proves that in the low density limit, theleading order correction compared to the ground state energy of anon-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 $a$ isthe scattering length of the contact interaction potential. This result extendsprevious work on the corresponding continuum model to the lattice case.

Ground state energy of the low density Hubbard model