  We demonstrate that projected entangled-pair states (PEPS) are able to
represent ground states of critical, fermionic systems exhibiting both 1d and
0d Fermi surfaces on a 2D lattice with an efficient scaling of the bond
dimension. Extrapolating finite size results for the Gaussian restriction of
fermionic projected entangled-pair states to the thermodynamic limit, the
energy precision as a function of the bond dimension is found to improve as a
power law, illustrating that an arbitrary precision can be obtained by
increasing the bond dimension in a controlled manner. In this process, boundary
conditions and system sizes have to be chosen carefully so that
nonanalyticities of the Ansatz, rooted in its nontrivial topology, are avoided.
