  We conjecture that non-equilibrium boundary conditions generically trigger
long range order in non-equilibrium steady states of locally interacting
quantum chains. Our result is based on large scale density matrix
renormalization group simulations of several models of quantum spin 1/2 chains
which are driven far from equilibrium by coupling to a pair of unequal Lindblad
reservoirs attached locally to the ends of the chain. In particular, we find a
phase transition from exponentially decaying to long range spin-spin
correlations in integrable Heisenberg XXZ chain by changing the anisotropy
parameter. Long range order also typically emerges after breaking the
integrability of the model.
