Tenfold Way for Quadratic Lindbladians.
Tenfold Way for Quadratic Lindbladians.
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DOI：
10.1103/physrevlett.124.040401
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发表时间：
2019-08
影响因子：
8.6
通讯作者：
S. Lieu;Max McGinley;N. Cooper
中科院分区：
文献类型：
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作者：
S. Lieu;Max McGinley;N. Cooper
我们发现了一个拓扑分类适用于开放的费米子系统所管辖的一般类Lindblad主方程。这些“二次Lindbladian”可以通过描述内部动力学以及系统-环境耦合的非厄米特单粒子矩阵来捕获。我们表明，这个矩阵必须属于10个非埃尔米特Bernard-LeClair对称类减少到Altland-Zirnbauer类的封闭极限。Lindblad频谱承认的拓扑分类，我们在有限寿命的无间隙边缘激发的结果。与以往研究的纯哈密顿或纯耗散演化，这些拓扑边缘模式是无关的形式的稳定状态。我们提供了一维的例子，其中添加耗散可以保持或破坏模型的封闭分类，突出了系统-环境耦合的细节的拓扑特性的敏感性。
We uncover a topological classification applicable to open fermionic systems governed by a general class of Lindblad master equations. These "quadratic Lindbladians" can be captured by a non-Hermitian single-particle matrix which describes internal dynamics as well as system-environment coupling. We show that this matrix must belong to one of ten non-Hermitian Bernard-LeClair symmetry classes which reduce to the Altland-Zirnbauer classes in the closed limit. The Lindblad spectrum admits a topological classification, which we show results in gapless edge excitations with finite lifetimes. Unlike previous studies of purely Hamiltonian or purely dissipative evolution, these topological edge modes are unconnected to the form of the steady state. We provide one-dimensional examples where the addition of dissipators can either preserve or destroy the closed classification of a model, highlighting the sensitivity of topological properties to details of the system-environment coupling.