  We study energy transport in XXZ spin chains driven to nonequilibrium
configurations by thermal reservoirs of different temperatures at the
boundaries. We discuss the transition between diffusive and subdiffusive
transport regimes in sectors of zero and finite magnetization at high
temperature. At large anisotropies we find that diffusive energy transport
prevails over a large range of disorder strengths, which is in contrast to spin
transport that is subdiffusive in the same regime for weak disorder strengths.
However, when finite magnetization is induced, both energy and spin currents
decay as a function of system size with the same exponent. Based on this, we
conclude that diffusion of energy is much more pervasive than that of
magnetization in these disordered spin-1/2 systems, and occurs across a
significant range of the interaction-disorder parameter phase-space; we suggest
this is due to conservation laws present in the clean XXZ limit.
