Antiferromagnetism of the two-dimensional Hubbard model at half-filling: the analytic ground state for weak coupling

We derive explicit spin and charge correlation functions of the N×N Hubbard model from a recently obtained weak-coupling analytic ground state |Ψ[0]AFrangle. The spin correlation function shows an antiferromagnetic behaviour with different signs for the two sublattices and its Fourier tranform is peaked at Q = (π,π). The charge correlation function presents two valleys at 45° from the axes. Both functions behave in a smooth way with increasing N; the results agree well with the available numerical data.