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The interplay between interaction, disorder, and dissipation has shown a richphenomenology. Here we investigate a disordered XXZ spin chain in contact witha bath which, alone, would drive the system towards a highly delocalized andcoherent Dicke state. We show that there exist regimes for which the naturalorbitals of the single-particle density matrix of the steady state are alllocalized in the presence of strong disorders, either for weak interaction orstrong interaction. We show that the averaged steady-state occupation in theeigenbasis of the open system Hamiltonian could follow an exponential decay forintermediate disorder strength in the presence of weak interactions, while itis 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 oflocalization also with a concatenated inverse participation ratio whichsimultaneously takes into account how localized are the eigenstates of theHamiltonian, and how close is the steady state to an incoherent mixture ofdifferent energy eigenstates.

Localization-delocalization effects of a delocalizing dissipation on disordered XXZ spin chains