The unreasonable accuracy of the Jastrow approach in many-body physics

We investigate in a simple model whether a Jastrow-based approach for a many-body system containing two-body interactions can be exact. By comparison with recent assertions to the contrary, we find that in general the exact wave function is \emph{not} purely two-body correlated. Nonetheless, we show that the energy estimate obtained from the calculations is as accurate as it can possibly be, suggesting why Jastrow wave functions are such a good choice.