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We study spin transport in a boundary driven XXZ spin chain. Driving at thechain boundaries is modeled by two additional spin chains prepared inoppositely polarized states. Emergent behavior, both in the transient dynamicsand in the long-time quasi-steady state, is demonstrated. Time-dependentmatrix-product-state simulations of the system-bath state show ballistic spintransport below the Heisenberg isotropic point. Indications of exponentiallyvanishing transport are found above the Heisenberg point for low energy initialstates while the current decays asymptotically as a power law for high energystates. Precisely at the critical point, non-ballistic transport is observed.Finally, it is found that the sensitivity of the quasi-stationary state on theinitial state of the chain is a good witness of the different transport phases.

A Nonequilibrium quantum phase transition in strongly coupled spin chains