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Boundary condition independence of non-Hermitian Hamiltonian dynamics

Mao, Liang and Deng, Tianshu and Zhang, Pengfei (2021) Boundary condition independence of non-Hermitian Hamiltonian dynamics. Physical Review B, 104 (12). Art. No. 125435. ISSN 2469-9950. doi:10.1103/physrevb.104.125435.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Mao, Liang0000-0003-1878-7166
Zhang, Pengfei0000-0002-7408-0918
Additional Information:© 2021 American Physical Society. Received 28 April 2021; accepted 7 September 2021; published 27 September 2021. We especially thank Hui Zhai for bringing our attention to this problem and for many valuable discussions during the work. We acknowledge helpful discussions with Lei Pan and Zhong Wang. P.Z. acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
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Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Issue or Number:12
Record Number:CaltechAUTHORS:20211025-171528994
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111631
Deposited By: Tony Diaz
Deposited On:25 Oct 2021 17:49
Last Modified:25 Oct 2021 17:49

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