Popkov V, Karevski D, Schütz G M
Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy and Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, D-50937 Cologne, Germany.
Institut Jean Lamour, dpt. P2M, Groupe de Physique Statistique, Université de Lorraine, CNRS, B.P. 70239, F-54506 Vandoeuvre les Nancy Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):062118. doi: 10.1103/PhysRevE.88.062118. Epub 2013 Dec 10.
We consider an open isotropic Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. Using a matrix product ansatz, we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady state of a chain with N sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle θ. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady-state currents scale as 1/N^{2} for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to 2θ/N.
我们考虑一个开放的各向同性海森堡量子自旋链，其两端与沿不同方向极化的边界库耦合，这在链上建立了一个扭转梯度。使用矩阵乘积假设，我们计算了具有(N)个格点的链在非平衡稳态下的精确磁化分布和磁化电流。磁化分布是频率与扭转角(\theta)成正比的调和函数。位于扭转平面内和正交方向上的磁化分量的电流表现出质的不同：对于固定且足够大的边界耦合，平面内稳态电流按(1/N^{2})缩放，并且随着耦合增加而消失，而横向电流随耦合增加并饱和到(2\theta/N)。
