Current fluctuations in boundary-driven quantum spin chains

Boundary-driven quantum spin chains are paradigmatic nonequilibrium systems featuring the presence of particle currents. In general, it may not be possible to distinguish an incoherent type of particle transport from a truly quantum coherent one through monitoring the mean current, as both ballistic as well as diffusive regimes occur in either setting. Here, we show that genuine coherent features become manifest in large fluctuations which allow a discrimination between incoherent and coherent quantum transport: in the former case, realizations that are characterized by atypically large boundary activity are associated with larger than typical currents, i.e., an enhanced number of events at the boundaries goes together with a large current. Conversely, in the coherent case the Zeno effect leads to the suppression of current in trajectories with large activity at the boundary. We analyze how these different dynamical regimes are reflected in the structure of rare fluctuations. We show moreover that realizations supporting a large current are generated via weak long-range correlations within the spin chain, typically associated with hyperuniformity. We further observe critical time-coexistence behaviors with intermittent currents in rare fluctuations of the strongly interacting XXZ chain for completely asymmetric drivings.