  The interplay between interaction, disorder, and dissipation has shown a rich
phenomenology. Here we investigate a disordered XXZ spin chain in contact with
a bath which, alone, would drive the system towards a highly delocalized and
coherent Dicke state. We show that there exist regimes for which the natural
orbitals of the single-particle density matrix of the steady state are all
localized in the presence of strong disorders, either for weak interaction or
strong interaction. We show that the averaged steady-state occupation in the
eigenbasis of the open system Hamiltonian could follow an exponential decay for
intermediate disorder strength in the presence of weak interactions, while it
is more evenly spread for strong disorder or for stronger interactions. Last,
we show that strong dissipation increases the coherence of the steady states,
thus reducing the signatures of localization. We capture such signatures of
localization also with a concatenated inverse participation ratio which
simultaneously takes into account how localized are the eigenstates of the
Hamiltonian, and how close is the steady state to an incoherent mixture of
different energy eigenstates.
