Recent refinements of analytical and numerical methods have improved our
understanding of the ground-state phase diagram of the two-dimensional (2D)
Hubbard model. Here we focus on variational approaches, but comparisons with
both Quantum Cluster and Gaussian Monte Carlo methods are also made. Our own
ansatz leads to an antiferromagnetic ground state at half filling with a
slightly reduced staggered order parameter (as compared to simple mean-field
theory). Away from half filling, we find d-wave superconductivity, but confined
to densities where the Fermi surface passes through the antiferromagnetic zone
boundary (if hopping between both nearest-neighbour and next-nearest-neighbour
sites is considered). Our results agree surprisingly well with recent numerical
studies using the Quantum Cluster method. An interesting trend is found by
comparing gap parameters (antiferromagnetic or superconducting) obtained with
different variational wave functions. They vary by an order of magnitude and
thus cannot be taken as a characteristic energy scale. In contrast, the order
parameter is much less sensitive to the degree of sophistication of the
variational schemes, at least at and near half filling.Comment: 18 pages, 4 figures, to be published in New J. Phy