  When using Hartree-Fock (HF) trial wave functions in quantum Monte Carlo
calculations, one faces, in case of HF instabilities, the HF symmetry dilemma
in choosing between the symmetry-adapted solution of higher HF energy and
symmetry-broken solutions of lower HF energies. In this work, we have examined
the HF symmetry dilemma in hydrogen rings which present singlet instabilities
for sufficiently large rings. We have found that the symmetry-adapted HF wave
function gives a lower energy both in variational Monte Carlo and in fixed-node
diffusion Monte Carlo. This indicates that the symmetry-adapted wave function
has more accurate nodes than the symmetry-broken wave functions, and thus
suggests that spatial symmetry is an important criterion for selecting good
trial wave functions.
