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Constraints on the energy spectrum of non-Hermitian models in open environments

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Abstract

Motivated by recent progress on non-Hermitian topological band theories, we study the energy spectrum of a generic two-band non-Hermitian Hamiltonian. We prove rigorously that the complex energy spectrum of such a non-Hermitian Hamiltonian is restricted to the lower complex plane, provided that the parameters of the Hamiltonian satisfy a certain constraint. Furthermore, we consider one specific scenario where such a non-Hermitian Hamiltonian can arise, namely a two-band model coupled to an environment, and show that this aforementioned constraint originates from very general physical considerations. Using this construction we extract the real-space behaviour of the non-hermitian terms. Our findings are relevant in the definition of the energy gap in non-Hermitian topological band theories and also have implications on simulations of such theories using quantum systems.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Aarhus University, 8000, Aarhus C, Denmark

    Jonatan Melkær Midtgaard

  2. Shenzhen Institute for Quantum Science and Engineering (SIQSE) and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen, 518055, P.R. China

    Zhigang Wu

  3. Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen, 518055, P.R. China

    Zhigang Wu

  4. Center for Theoretical Physics and Department of Physics, Capital Normal University, Beijing, 100048, P.R. China

    Yu Chen

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  1. Jonatan Melkær Midtgaard
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Correspondence to Jonatan Melkær Midtgaard.

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Midtgaard, J.M., Wu, Z. & Chen, Y. Constraints on the energy spectrum of non-Hermitian models in open environments. Eur. Phys. J. B 92, 260 (2019). https://doi.org/10.1140/epjb/e2019-100393-5

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