Anatomy of open-boundary bulk in multiband non-Hermitian systems

Abstract

Although the non-Bloch band theory is a milestone in elaborating bulk energy bands of non-Hermitian systems under the open-boundary condition (OBC), vital issues related to multivalued functions of non-Hermitian energy bands remain unsolved. In this paper, we anatomize the bulk properties of one-dimensional multiband non-Hermitian systems under OBC. We put forward the energy-band branches (EBBs) to settle the multivalued functions of non-Hermitian energy bands, which become gapped or gapless corresponding to disconnected or connected EBBs in the complex energy plane, where the branch points and branch cuts play a crucial role. We clarify the precise significance of the non-Hermitian skin effect, which illustrates the asymptotic behavior of EBB eigenstates (bulk eigenstates) in the deep bulk and compensates previous non-Bloch band theory. We also obtain a general expression of open-boundary Green's functions based on such EBBs and generalized Brillouin zones, useful for studies on non-Hermitian dynamical evolution.

18 pages, 8 figures

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Cited by in corpus (17)

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• Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays
• Green's functions of multiband non-Hermitian systems
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Nontrivial worldline winding in non-Hermitian quantum systems
• Complex semiclassical theory for non-Hermitian quantum systems
• General theory for infernal points in non-Hermitian systems
• Abnormal Frequency Response Determined by Saddle Points in Non-Hermitian Crystal Systems
• Formal Green's function theory in non-Hermitian lattice systems
• One-dimensional non-Hermitian band structures as Riemann surfaces
• Real-time edge dynamics of non-Hermitian lattices
• Theory for the spectral splitting exponent of exceptional points
• Experimental observation of energy-band Riemann surface
• Recurrence method in Non-Hermitian Systems
• Topology of the generalized Brillouin zone of one-dimensional models