Karevski D, Popkov V, Schütz G M
Institut Jean Lamour, Department P2M, Groupe de Physique Statistique, Université de Lorraine, CNRS, B.P. 70239, F-54506 Vandoeuvre les Nancy Cedex, France.
Dipartimento di Fisica, Università di Firenze, via Sansone 1, 50019 Sesto Fiorentino Firenze, Italy and Max Planck Institute for Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Phys Rev Lett. 2013 Jan 25;110(4):047201. doi: 10.1103/PhysRevLett.110.047201. Epub 2013 Jan 24.
We demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ansatz for the nonequilibrium density matrix where the matrices satisfy a quadratic algebra. This algebra turns out to be related to the quantum algebra U(q)[SU(2)]. Coherent state techniques are introduced for the exact solution of the isotropic Heisenberg chain with and without quantum boundary fields and Lindblad terms that correspond to two different completely polarized boundary states. We show that this boundary twist leads to nonvanishing stationary currents of all spin components. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms.
我们证明，由边界林德布拉德算符驱动的一维海森堡XXZ自旋链的精确非平衡稳态可以通过非平衡密度矩阵的矩阵乘积假设明确构建，其中矩阵满足二次代数。事实证明，这种代数与量子代数U(q)[SU(2)]相关。引入了相干态技术来精确求解具有和不具有量子边界场以及对应于两种不同完全极化边界态的林德布拉德项的各向同性海森堡链。我们表明，这种边界扭转导致所有自旋分量的非零稳态电流。我们的结果表明，矩阵乘积假设可以扩展到由林德布拉德边界项保持远离平衡的更一般量子系统。
