Alternation of sign of magnetization current in driven XXZ chains with twisted XY boundary gradients

TL;DR

This paper studies how boundary-driven XXZ spin chains exhibit alternating magnetization current signs and suppressed heat transport due to symmetries, revealing complex dependence on anisotropy and chain length.

Contribution

It uncovers symmetry-induced effects on transport in XXZ chains, provides exact steady states at strong coupling, and analyzes the influence of anisotropy on magnetization currents.

Findings

Magnetization current alternates with chain length.

Heat transport is completely suppressed by symmetry.

Magnetization current depends nontrivially on anisotropy .

Abstract

We investigate an open XXZ spin 1/2 chain driven out of equilibrium by coupling with boundary reservoirs targeting different spin orientations in XY plane. Symmetries of the model are revealed which appear to be different for spin chains of odd and even sizes. As a result, spin current is found to alternate with chain length, ruling out the possibility of ballistic transport. Heat transport is switched off completely by virtue of another global symmetry. Further, we investigate the model numerically and analytically. At strong coupling, we find exact nonequilibrium steady state using a perturbation theory. The state is determined by solving secular conditions which guarantee self-consistency of the perturbative expansion. We find nontrivial dependence of the magnetization current on the spin chain anisotropy $\Delta$ in the critical region $|\Delta|<1$, and a phenomenon of tripling of the twisting angle along the chain for narrow lacunes of $\Delta$.