  We explain how to implement, in the context of projected entangled-pair
states (PEPS), the general procedure of fermionization of a tensor network
introduced in [P. Corboz, G. Vidal, Phys. Rev. B 80, 165129 (2009)]. The
resulting fermionic PEPS, similar to previous proposals, can be used to study
the ground state of interacting fermions on a two-dimensional lattice. As in
the bosonic case, the cost of simulations depends on the amount of entanglement
in the ground state and not directly on the strength of interactions. The
present formulation of fermionic PEPS leads to a straightforward numerical
implementation that allowed us to recycle much of the code for bosonic PEPS. We
demonstrate that fermionic PEPS are a useful variational ansatz for interacting
fermion systems by computing approximations to the ground state of several
models on an infinite lattice. For a model of interacting spinless fermions,
ground state energies lower than Hartree-Fock results are obtained, shifting
the boundary between the metal and charge-density wave phases. For the t-J
model, energies comparable with those of a specialized Gutzwiller-projected
ansatz are also obtained.

Strongly Correlated Electrons