Exact ground state of the two-dimensional Hubbard model at half-filling for U=0+

We solve analytically the N×N square lattice Hubbard model for even N at half-filling and weak coupling by a new approach. The exact ground-state wave function provides an intriguing and appealing picture of the antiferromagnetic order. Like at strong coupling, the ground state has total momentum Ktot=(0,0) and transforms as an s wave for even N/2 and as a d wave otherwise.