  We present a method for performing path integral molecular dynamics (PIMD)
simulations for fermions and address its sign problem. PIMD simulations are
widely used for studying many-body quantum systems at thermal equilibrium.
However, they assume that the particles are distinguishable and neglect bosonic
and fermionic exchange effects. Interacting fermions play a key role in many
chemical and physical systems, such as electrons in quantum dots and ultracold
trapped atoms. A direct sampling of the fermionic partition function is
impossible using PIMD since its integrand is not positive definite. We show
that PIMD simulations for fermions are feasible by employing our recently
developed method for bosonic PIMD and reweighting the results to obtain
fermionic expectation values. The approach is tested against path integral
Monte Carlo (PIMC) simulations for up to 7 electrons in a two-dimensional
quantum dot for a range of interaction strengths. However, like PIMC, the
method suffers from the sign problem at low temperatures. We propose a simple
approach for alleviating it by simulating an auxiliary system with a larger
average sign and obtaining an upper bound to the energy of the original system
using the Bogoliubov inequality. This allows fermions to be studied at
temperatures lower than would otherwise have been feasible using PIMD, as
demonstrated in the case of a three-electron quantum dot. Our results extend
the boundaries of PIMD simulations of fermions and will hopefully stimulate the
development of new approaches for tackling the sign problem.
