Recent Results in the Exact Treatment of Fermions at Zero and Finite Temperature

We present release-node quantum Monte Carlo simulations of the first row diatomic molecules and assess how accurately their ground state energies can be obtained with current computational resources. An explicit analysis of the fermion-boson energy difference shows a strong dependence on the nuclear charge, Z, which in turn determines the growth of the variance of the release-node energy. We show that efficiency gains from maximum entropy analysis are modest and that extrapolation to the ground state is tractable only for the low Z elements. For finite temperatures we discuss what can be gleaned from the structure of permutation space for interacting Fermi systems. We then demonstrate improved efficiency in the exact path integral Monte Carlo treatment of liquid He-3 by using importance sampling to deemphasize the contribution of long permutation cycles to the partition function.