  We study a 1-dimensional XX chain under nonequilibrium driving and local
dephasing described by the Lindblad master equation. The analytical solution
for the nonequilibrium steady state found for particular parameters in
[J.Stat.Mech., L05002 (2010)] is extended to arbitrary coupling constants,
driving and homogeneous magnetic field. All one, two and three-point
correlation functions are explicitly evaluated. It is shown that the
nonequilibrium stationary state is not gaussian. Nevertheless, in the
thermodynamic and weak-driving limit it is only weakly correlated and can be
described by a matrix product operator ansatz with matrices of fixed dimension
4. A nonequilibrium phase transition at zero dephasing is also discussed. It is
suggested that the scaling of the relaxation time with the system size can
serve as a signature of a nonequilibrium phase transition.
