Path-integral calculations of normal liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$

The first path-integral calculations of the properties of a strongly correlated continuum fermion system are described. The paths are restricted to the region of phase space with a positive trial density matrix, thereby avoiding the fermion sign problem. This restriction is exact if the nodes of the trial density matrix are correctly placed, but otherwise gives a physically reasonable approximation generalizing the ‘‘fixed-node’’ approximation used at zero temperature. Computations show that restricting the walks with the noninteracting density matrix gives good results for liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ above 1 K. Using imaginary-time-independent nodes or not allowing atomic exchange results in substantially poorer agreement with experimental energies.