We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.
 H. Maeter, A. Zvyagin, H. Luetkens, G. Pascua, Z. Shermadini, R. Saint-Martin, A. Revcolevschi, C. Hess, B. Büchner, and H. Klauss, J. Phys.: Condensed Matter 25, 365601 (2013).
 T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schausz, S. Hild, D. Bellem, U. Schollwock, T. Giamarchi, C. Gross, I. Bloch, and S. Kuhr, Nat. Phys. 9, 235 (2013).
 S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A. M. Rey, A. Polkovnikov, E. A. Demler, M. D. Lukin, and I. Bloch, Science 319, 235 (2008).
 L. Vidmar, J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodgman, S. Langer, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Phys. Rev. Lett. 115, 175301 (2015).
 J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodgman, S. Langer, I. P. McCulloch, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Phys. Rev. Lett. 110, 205301 (2013).
 H.-P. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University Press, 2002).
 Chu Guo, Ines de Vega, Ulrich Schollwöck, Dario Poletti, "Stable-unstable transition for a Bose-Hubbard chain coupled to an environment", Physical Review A 97, 053610 (2018).
 Wim Casteels, Ryan M. Wilson, Michiel Wouters, "Gutzwiller Monte Carlo approach for a critical dissipative spin model", Physical Review A 97, 062107 (2018).
 Vincenzo Alba, "Entanglement and quantum transport in integrable systems", Physical Review B 97, 245135 (2018).
 Pooja Manasi, Dibyendu Roy, "Light propagation through one-dimensional interacting open quantum systems", Physical Review A 98, 023802 (2018).
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