A Nonequilibrium quantum phase transition in strongly coupled spin chains

We study a nonequilibrium quantum phase transition in a variant of the boundary driven XXZ spin chain. Spin transport is characterized under strong coupling to non-Markovian baths, and an emergent behavior, both on the transient dynamics and on the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic transport when below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point. Precisely at the critical point, subdiffusive transport is observed. Lastly, we show that the time dependent overlap between two system states is sensible to the phase transition.