Possible equivalence of Feynman's backflow and spin-dependent correlations

The topic in the title has produced debate about whether spin-dependent correlations should be used in trial wave functions for Hamiltonians that are independent of spin. We investigate this question by calculating the ground-state properties of a small system of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms using the variational Monte Carlo method and trial wave functions, first, with explicit backflow correlations and second, with spin-dependent correlations. We review how backflow and spin-dependent correlations can be made approximately equivalent, and then give Monte Carlo results which demonstrate that spin-dependent correlations can substantially reproduce the effect of backflow correlations.