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

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