  Tensor networks are a powerful tool to simulate a variety of different
physical models, including those that suffer from the sign problem in Monte
Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero
chemical potential is one such problem. Our method is based on projected
entangled pair states (PEPS) using imaginary time evolution. We demonstrate
that it provides accurate estimators for the ground state of the model,
including cases where Monte Carlo simulations fail miserably. In particular it
shows near to optimal, that is linear, scaling in lattice size. We also present
a novel approach to directly simulate the subspace with an odd number of
fermions. It allows to independently determine the ground state in both
sectors. Without a chemical potential this corresponds to half filling and the
lowest energy state with one additional electron or hole. We identify several
stability issues, such as degenerate ground states and large single particle
gaps, and provide possible fixes.
