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

Jonatan Melkær Midtgaard (), Zhigang Wu and Yu Chen
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Jonatan Melkær Midtgaard: Aarhus University
Zhigang Wu: Shenzhen Institute for Quantum Science and Engineering (SIQSE) and Department of Physics, Southern University of Science and Technology (SUSTech)
Yu Chen: Center for Theoretical Physics and Department of Physics, Capital Normal University

The European Physical Journal B: Condensed Matter and Complex Systems, 2019, vol. 92, issue 11, 1-7

Abstract: 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

Keywords: Solid; State; and; Materials (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1140/epjb/e2019-100393-5

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