Boundary condition independence of non-Hermitian Hamiltonian dynamics,Physical Review B

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Boundary condition independence of non-Hermitian Hamiltonian dynamics
Physical Review B ( IF 3.2 ) Pub Date : 2021-09-27 , DOI: 10.1103/physrevb.104.125435
Liang Mao _{1,

2} , Tianshu Deng ₁ , Pengfei Zhang _{3,

4}

Affiliation

The non-Hermitian skin effect, namely, that the eigenvalues and eigenstates of a non-Hermitian tight-binding Hamiltonian have significant differences under open or periodic boundary conditions, is a remarkable phenomenon of non-Hermitian systems. Inspired by the presence of the non-Hermitian skin effect, we study the evolution of wave packets in non-Hermitian systems, which can be determined using the single-particle Green's function. Surprisingly, we find that in the thermodynamic limit, the Green's function does not depend on boundary conditions, despite the presence of skin effect. We provide a general proof for this statement in arbitrary dimension with finite hopping range, with an explicit illustration in the non-Hermitian Su-Schrieffer-Heeger model. We also explore its applications in noninteracting open quantum systems described by the master equation. We demonstrate that the evolution of the density matrix is independent of the boundary condition.

中文翻译：

非厄米哈密顿动力学的边界条件独立性

非厄米集肤效应，即非厄米紧束缚哈密顿量的特征值和本征态在开放或周期边界条件下具有显着差异，是非厄米系统的一个显着现象。受非厄米集肤效应的启发，我们研究了非厄米系统中波包的演化，这可以使用单粒子格林函数来确定。令人惊讶的是，我们发现在热力学极限下，格林函数不依赖于边界条件，尽管存在趋肤效应。我们在具有有限跳跃范围的任意维度上为该陈述提供了一般证明，并在非 Hermitian Su-Schrieffer-Heeger 模型中进行了明确说明。我们还探索了它在主方程描述的非相互作用开放量子系统中的应用。我们证明密度矩阵的演变与边界条件无关。

更新日期：2021-09-28

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