耗散稳定螺旋态之间的跃迁
Transition between dissipatively stabilized helical states
摘要：
我们分析了一个$XXZ$自旋为1/2的链，该链在其边界处被耗散驱动。耗散驱动模型由Lindblad跳跃算子，只作用于两个边界自旋。在大耗散的限制下，我们发现边界自旋被钉扎到一定的值，并在特定的相互作用各向异性值，稳定的状态是由秩2混合螺旋状态相反的缠绕数。与先前拓扑状态的稳定性不同，这些螺旋状态不受Lindbladian光谱中的间隙的保护。通过改变各向异性，这些稳定状态之间的过渡发生通过混合状态的更高的秩。特别是，交叉的值的零各向异性的完全混合状态被发现作为稳定状态。在耗散驱动系统中不同拓扑状态之间的转换中，可以看到不同缠绕数之间通过混合状态的转换。结果得到发展的逆耗散耦合强度的微扰理论，并使用数值精确对角化和矩阵乘积状态方法。
英文摘要：
We analyze a $XXZ$ spin-1/2 chain which is driven dissipatively at its boundaries. The dissipative driving is modelled by Lindblad jump operators which only act on both boundary spins. In the limit of large dissipation, we find that the boundary spins are pinned to a certain value and at special values of the interaction anisotropy, the steady states are formed by a rank-2 mixture of helical states with opposite winding numbers. Contrarily to previous stabilization of topological states, these helical states are not protected by a gap in the spectrum of the Lindbladian. By changing the anisotropy, the transition between these steady states takes place via mixed states of higher rank. In particular, crossing the value of zero anisotropy a totally mixed state is found as the steady state. The transition between the different winding numbers via mixed states can be seen in the light of the transitions between different topological states in dissipatively driven systems. The results are obtained developing a perturbation theory in the inverse dissipative coupling strength and using the numerical exact diagonalization and matrix product state methods.
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