  We investigate heat transport in a spin-1/2 Heisenberg chain, coupled locally
to independent thermal baths of different temperature. The analysis is carried
out within the framework of the theory of open systems by means of appropriate
quantum master equations. The standard microscopic derivation of the
weak-coupling Lindblad equation in the secular approximation is considered, and
shown to be inadequate for the description of stationary nonequilibrium
properties like a non-vanishing energy current. Furthermore, we derive an
alternative master equation that is capable to describe a stationary energy
current and, at the same time, leads to a completely positive dynamical map.
This paves the way for efficient numerical investigations of heat transport in
larger systems based on Monte Carlo wave function techniques.
