Density-wave steady-state phase of dissipative ultracold fermions with nearest-neighbor interactions*

In the current 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 [1]. For this purpose we use the recently developed Lindblad dynamical mean-field theory (L-DMFT) [2,3], which allows to study directly steady-state properties of strongly correlated fermionic systems. To take into account nearest-neighbor interactions we perform a mean-field decoupling. We find the density-wave order to be robust against decoherence effects up to a critical point where the system becomes homogeneous with no spatial ordering. These results will be relevant for future cold-atom experiments using fermions with nonlocal interactions arising from the dressing by highly excited Rydberg states, which have finite lifetimes due to spontaneous emission processes.
[1] J. Panas et al., Phys. Rev. B 99, 115125 (2019)
[2] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)
[3] I. Titvinidze et al., Phys. Rev. B 92, 245125 (2015)