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

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  • Jonatan Melkær Midtgaard
  • ,
  • Zhigang Wu, Southern University of Science and Technology, Center for Quantum Computing, Peng Cheng Laboratory
  • ,
  • Yu Chen, Capital Normal University

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. Graphical abstract: [Figure not available: see fulltext.].

TidsskriftEuropean Physical Journal B
Antal sider7
StatusUdgivet - 2019

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