Anomalous currents in driven XXZ chain with boundary twisting at weak coupling or weak driving

Abstract: The spin 1/2 XXZ chain driven out of equilibrium by coupling with boundary reservoirs targeting perpendicular spin orientations in XY plane, is investigated. The existence of an anomaly in the nonequilibrium steady state (NESS) at the isotropic point $\Delta=1$ is demonstrated both in the weak coupling and weak driving limits. The nature of the anomaly is studied analytically by calculating exact NESS for small system sizes, and investigating steady currents. The spin current at the points $\Delta=\pm1$ has a singularity which leads to a current discontinuity when either driving or coupling vanish, and the current of energy develops a twin peak anomaly. The character of singularity is shown to depend qualitatively on whether the system size is even or odd.