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

Midtgaard，Jonatan Melkær1; Wu，Zhigang2,3; Chen，Yu4

2019-11-01

10.1140/epjb/e2019-100393-5

EUROPEAN PHYSICAL JOURNAL B   影响因子和分区

1434-6028

1434-6036

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.].

Solid State and Materials

SCI ; EI

英语

其他

Foundation of Beijing Education Committees[KM201710028004]

Physics

Physics, Condensed Matter

WOS:000499252800001

Springer

20194807738363

Quantum optics ; Spectroscopy ; Topology

Light/Optics:741.1 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

PHYSICS

2-s2.0-85075399073

Scopus

1.Department of Physics and Astronomy,Aarhus University,Aarhus C,8000,Denmark
2.Shenzhen Institute for Quantum Science and Engineering (SIQSE) and Department of Physics,Southern University of Science and Technology (SUSTech),Shenzhen,518055,China
3.Center for Quantum Computing,Peng Cheng Laboratory,Shenzhen,518055,China
4.Center for Theoretical Physics and Department of Physics,Capital Normal University,Beijing,100048,China

Midtgaard，Jonatan Melkær,Wu，Zhigang,Chen，Yu. Constraints on the energy spectrum of non-Hermitian models in open environments[J]. EUROPEAN PHYSICAL JOURNAL B,2019,92(11).

Midtgaard，Jonatan Melkær,Wu，Zhigang,&Chen，Yu.(2019).Constraints on the energy spectrum of non-Hermitian models in open environments.EUROPEAN PHYSICAL JOURNAL B,92(11).

Midtgaard，Jonatan Melkær,et al."Constraints on the energy spectrum of non-Hermitian models in open environments".EUROPEAN PHYSICAL JOURNAL B 92.11(2019).