We employ matrix-product state techniques to numerically study the zero-temperature spin transport in a finite spin-$\frac{1}{2}$ XXZ chain coupled to fermionic leads with a spin bias voltage. Current-voltage characteristics are calculated for parameters corresponding to the gapless XY phase and the gapped Néel phase. In both cases, the low-bias spin current is strongly suppressed unless the parameters of the model are fine tuned. For the XY phase, this corresponds to a conducting fixed point where the conductance agrees with the Luttinger-liquid prediction. In the Néel phase, fine tuning the parameters similarly leads to an unsuppressed spin current with a linear current-voltage characteristic at low bias voltages. However, with increasing the bias voltage, there occurs a sharp crossover to a region where the current-voltage characteristic is no longer linear and a smaller differential conductance is observed. We furthermore show that the parameters maximizing the spin current minimize the Friedel oscillations at the interface, in agreement with the previous analyses of the charge current for inhomogeneous Hubbard and spinless fermion chains.

• Received 23 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.245124