Spin transport through a spin-1/2 XXZ chain contacted to fermionic leads

TL;DR

This study uses matrix-product state techniques to analyze zero-temperature spin transport in a spin-1/2 XXZ chain connected to fermionic leads, revealing conditions for optimal conductance and the effects of bias voltage.

Contribution

It provides a detailed numerical investigation of spin transport in XXZ chains with fermionic leads, identifying conducting fixed points and the impact of parameter tuning on current behavior.

Findings

Low-bias spin current is suppressed unless parameters are fine-tuned.

Conductance matches Luttinger-liquid predictions at the fixed point in the XY phase.

Increasing bias voltage causes a crossover to non-linear current-voltage behavior.

Abstract

We employ matrix-product state techniques to numerically study the zero-temperature spin transport in a finite spin-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 N\'eel 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 N\'eel 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 a current-voltage characteristic is no longer linear and the 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.