We find novel site-dependent Lax operators in terms of which we demonstrate exact solvability of a dissipatively driven XYZ spin-$1/2$ chain in the Zeno limit of strong dissipation, with jump operators polarizing the boundary spins in arbitrary directions. We write the corresponding nonequilibrium steady state using an inhomogeneous MPA, where the constituent matrices satisfy a simple set of linear recurrence relations. Although these matrices can be embedded into an infinite-dimensional auxiliary space, we have verified that they cannot be simultaneously put into a tridiagonal form, not even in the case of axially symmetric (XXZ) bulk interactions and general nonlongitudinal boundary dissipation. We expect our results to have further fundamental applications for the construction of nonlocal integrals of motion for the open XYZ model with arbitrary boundary fields, or the eight-vertex model.

中文翻译：

---

大耗散下非均匀矩阵乘积ansatz和边界驱动自旋链的精确稳态

我们发现了新颖的，依赖于位点的Lax运算符，据此我们证明了耗散驱动的XYZ自旋-$\mathrm{1个}/2$在芝诺（Zeno）的强耗散极限中，链跳变操作符使边界自旋极化到任意方向。我们使用不均匀的MPA编写相应的非平衡稳态，其中组成矩阵满足一组简单的线性递归关系。尽管这些矩阵可以嵌入到无限维的辅助空间中，但是我们已经证明，即使在轴对称（XXZ）体相互作用和一般的非纵向边界耗散的情况下，也不能将它们同时放入三对角线形式。我们希望我们的结果对于具有任意边界场的开放XYZ模型或八顶点模型的运动的非局部运动积分的构造具有进一步的基本应用。