Tenfold Way for Quadratic Lindbladians.,Physical Review Letters

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Tenfold Way for Quadratic Lindbladians.
Physical Review Letters ( IF 8.1 ) Pub Date : 2020-01-31 , DOI: 10.1103/physrevlett.124.040401
Simon Lieu ₁ , Max McGinley ₁ , Nigel R Cooper ₁

Affiliation

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.

中文翻译：

二次Lindbladians的十倍方式。

我们发现适用于由一般林德布拉德主方程控制的开放费米子系统的拓扑分类。这些“二次Lindbladians”可以被非Hermitian单粒子矩阵捕获，该矩阵描述内部动力学以及系统与环境的耦合。我们表明，该矩阵必须属于十个非Hermitian Bernard-LeClair对称类别之一，该对称类别在封闭范围内可简化为Altland-Zirnbauer类别。Lindblad光谱接受拓扑分类，我们证明了有限寿命的无间隙边缘激励的结果。与先前对纯哈密顿量或纯耗散性演化的研究不同，这些拓扑边缘模式与稳态形式无关。

更新日期：2020-01-27

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