  In this work we investigate the effect of local dissipation on the presence
of density-wave ordering in spinful fermions with both local and
nearest-neighbor interactions as described by the extended Hubbard model. We
find density-wave order to be robust against decoherence effects up to a
critical point where the system becomes homogeneous with no spatial ordering.
Our results will be relevant for future cold-atom experiments using fermions
with non-local interactions arising from the dressing by highly-excited Rydberg
states, which have finite lifetimes due to spontaneous emission processes.
