  We extend our low-scaling variational Monte Carlo (VMC) algorithm to optimize
the symmetry projected Jastrow mean field (SJMF) wavefunctions. These
wavefunctions consist of a symmetry-projected product of a Jastrow and a
general broken-symmetry mean field reference. Examples include Jastrow
antisymmetrized geminal power (JAGP), Jastrow-Pfaffians, and resonating valence
bond (RVB) states among others, all of which can be treated with our algorithm.
We will demonstrate using benchmark systems including the nitrogen molecule, a
chain of hydrogen atoms, and the 2-D Hubbard model that a significant amount of
correlation can be obtained by optimizing the energy of the SJMF wavefunction.
This can be achieved at a relatively small cost when multiple symmetries
including spin, particle number, and complex conjugation are simultaneously
broken and projected. We also show that reduced density matrices can be
calculated using the optimized wavefunctions, which allows us to calculate
other observables such as correlation functions and will enable us to embed the
VMC algorithm in a complete active space self-consistent field (CASSCF)
calculation.
