  We will review some known exact solutions for the steady state of the open
quantum Heisenberg $XXZ$ spin chain coupled to a pair of baths [Phys. Rev.
Lett. 107, 137201 (2011).]. The dynamics is modelled by the Lindblad master
equation. We also review how to calculate some relevant physical observables
and provide the statistics of spin current assuming the spin chain is weakly
coupled to the baths [Phys. Rev. Lett. 112, 067201 (2014).].
