  In this work we study the heat transport in an XXZ spin-1/2 Heisenberg chain
with homogeneous magnetic field, incoherently driven out of equilibrium by
reservoirs at the boundaries. We focus on the effect of bulk dephasing
(energy-dissipative) processes in different parameter regimes of the system.
The non-equilibrium steady state of the chain is obtained by simulating its
evolution under the corresponding Lindblad master equation, using the time
evolving block decimation method. In the absence of dephasing, the heat
transport is ballistic for weak interactions, while being diffusive in the
strongly-interacting regime, as evidenced by the heat-current scaling with the
system size. When bulk dephasing takes place in the system, diffusive transport
is induced in the weakly-interacting regime, with the heat current
monotonically decreasing with the dephasing rate. In contrast, in the
strongly-interacting regime, the heat current can be significantly enhanced by
dephasing for systems of small size.
