We investigate the influence of a Markovian environment on the dynamics of interacting spinful fermionic atoms in a lattice. In order to explore the physical phenomena occurring at short times, we develop a method based on a slave-spin representation of fermions which is amenable to the investigation of the dynamics of dissipative systems. We apply this approach to two different dissipative couplings which can occur in current experiments: a coupling via the local density and a coupling via the local double occupancy. We complement our study based on this novel method with results obtained using the adiabatic elimination technique and with an exact study of a two-site model. We uncover that the decoherence is slowed down by increasing either the interaction strength or the dissipative coupling (the Zeno effect). We also find, for the coupling to the local double occupancy, that the final steady state can sustain single-particle coherence.
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