  We present a method incorporating biorthogonal orbital-optimization, symmetry
projection, and double-occupancy screening with a non-unitary similarity
transformation generated by the Gutzwiller factor $
n_{i\uparrow}n_{i\downarrow}$, and apply it to the Hubbard model. Energies are
calculated with mean-field computational scaling with high-quality results
comparable to coupled cluster singles and doubles. This builds on previous work
performing similarity transformations with more general, two-body Jastrow-style
correlators. The theory is tested on two-dimensional lattices ranging from
small systems into the thermodynamic limit and is compared to available
reference data.
