  Quantum Monte Carlo simulations of fermions are hampered by the notorious
sign problem whose most striking manifestation is an exponential growth of
sampling errors with the number of particles. With the sign problem known to be
an NP-hard problem and any generic solution thus highly elusive, the Monte
Carlo sampling of interacting many-fermion systems is commonly thought to be
restricted to a small class of model systems for which a sign-free basis has
been identified. Here we demonstrate that entanglement measures, in particular
the so-called Renyi entropies, can intrinsically exhibit a certain robustness
against the sign problem in auxiliary-field quantum Monte Carlo approaches and
possibly allow for the identification of global ground-state properties via
their scaling behavior even in the presence of a strong sign problem. We
corroborate these findings via numerical simulations of fermionic quantum phase
transitions of spinless fermions on the honeycomb lattice at and below
half-filling.
