Density wave instabilities in a correlated two-dimensional metal

Motivated by recent experimental evidence of charge order in the pseudogap phase of cuprates, we perform a variational analysis of spin-singlet density wave ordering in metals with antiferromagnetic interactions on the square lattice, using a wave function with double occupancy projected out. We examine ordering with and without time-reversal symmetry, with an arbitrary wave vector and a tunable form factor. Depending on parameters, we find d-form factor density wave ordering, with a wave vector either parallel to the lattice generators or diagonally oriented, or a ground state which carries a time-reversal breaking pattern of spontaneous currents.