  We describe the use of tensor networks to numerically determine wave
functions of interacting two-dimensional fermionic models in the continuum
limit. We use two different tensor network states: one based on the numerical
continuum limit of fermionic projected entangled pair states obtained via a
tensor network formulation of multi-grid, and another based on the combination
of the fermionic projected entangled pair state with layers of isometric
coarse-graining transformations. We first benchmark our approach on the
two-dimensional free Fermi gas then proceed to study the two-dimensional
interacting Fermi gas with an attractive interaction in the unitary limit,
using tensor networks on grids with up to 1000 sites.
