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arXiv · 2104.09896

Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics

Liang Mao·Tianshu Deng·Pengfei Zhang
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Abstract

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 thermodynamical limit, the Green's function does not depend on boundary conditions, despite the presence of skin effect. We proffer 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 non-interacting open quantum systems described by the master equation, where we demonstrate that the evolution of the density matrix is independent of the boundary condition.

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Liang Mao, Tianshu Deng, Pengfei Zhang. 2021-04-20. Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics. https://doi.org/10.1103/physrevb.104.125435

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