  At long times residual couplings to the environment become relevant even in
the most isolated experiments, creating a crucial difficulty for the study of
fundamental aspects of many-body dynamics. A particular example is many-body
localization in a cold-atom setting, where incoherent photon scattering
introduces both dephasing and particle loss. Whereas dephasing has been studied
in detail and is known to destroy localization already on the level of
non-interacting particles, the effect of particle loss is less well understood.
A difficulty arises due to the `non-local' nature of the loss process,
complicating standard numerical tools using matrix product decomposition.
Utilizing symmetries of the Lindbladian dynamics, we investigate the particle
loss on both the dynamics of observables, as well as the structure of the
density matrix and the individual states. We find that particle loss in the
presence of interactions leads to dissipation and a strong suppression of the
(operator space) entanglement entropy. Our approach allows for the study of the
interplay of dephasing and loss for pure and mixed initial states to long
times, which is important for future experiments using controlled coupling of
the environment.
