  We report a ground-state solution for the two-dimensional fermionic Hubbard
model, which is obtained via a numerical variational method. The two
ingredients in this approach are tensor network states and the time-evolving
block decimation. We easily handle the horizontal hopping in the Hamiltonian,
and we proceed further to observe the fermion-exchange effect caused by the
vertical hopping. By requiring no divergence and no convergence to zero for the
ground state, we successively determine the ground-state energy per site as a
function of the chemical potential and the lattice length. In addition, we
observe saturation in the behavior of the ground-state energy as the lattice
length increases.
