Comments on a boundary-driven open XXZ chain: asymmetric driving and uniqueness of steady states
Comments on a boundary-driven open XXZ chain: asymmetric driving and uniqueness of steady states
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评论边界驱动的开放XXZ链：非对称驱动和稳态的唯一性
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发表时间：
2012
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通讯作者：
T. Prosen
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作者：
T. Prosen
在本文中，我们提供了关于马尔可夫边界驱动的各向异性海森堡 XXZ 自旋 1/2 链的非平衡稳态的矩阵乘积 ansatz 的最新显式结果的两个扩展。我们为系统-浴耦合中的稳态密度矩阵编写了一个微扰解，用于两个链端的任意（不对称）一组四个自旋翻转速率，推广了 Prosen 的对称驱动 ansatz（2011 Phys. Rev. Lett. 106 217206）。此外，我们将两个 Lindblad 通道（左侧自旋向上翻转和右侧自旋向下翻转）的稳态的精确（非微扰）形式概括为任意（不对称）比率的自旋翻转速率（Prosen 2011 Phys. Rev. Lett. 107 137201）。此外，我们还给出了稳态唯一性的简单证明。
In this paper, we provide two extensions of recent explicit results on the matrix-product ansatz for the non-equilibrium steady state of a Markovian boundary-driven anisotropic Heisenberg XXZ spin-1/2 chain. We write a perturbative solution for the steady-state density matrix in the system–bath coupling for an arbitrary (asymmetric) set of four spin-flip rates at the two chain ends, generalizing the symmetric-driving ansatz of Prosen (2011 Phys. Rev. Lett. 106 217206). Furthermore, we generalize the exact (non-perturbative) form of the steady state for just two Lindblad channels (spin-up flipping on the left and spin-down flipping on the right) to an arbitrary (asymmetric) ratio of the spin-flipping rates (Prosen 2011 Phys. Rev. Lett. 107 137201). In addition, we also indicate a simple proof of the uniqueness of our steady states.