An Exact Monte Carlo Method for Continuum Fermion Systems

We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon Diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs; different functions ``guide’’ walkers of different signs; the Gaussians used for members of a pair are correlated; walkers can cancel so as to conserve their expected future contributions. We report results for free-fermion systems and a fermion fluid with 14 ${}^3$He atoms, where it proves stable and correct. Its computational complexity grows with particle number, but slowly enough to make interesting physics within reach of contemporary computers.