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