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

TL;DR

This paper advances the understanding of bulk properties in multiband non-Hermitian systems under open boundaries by introducing energy-band branches, clarifying the non-Hermitian skin effect, and deriving a general Green's function expression.

Contribution

It introduces energy-band branches to resolve multivalued energy functions, clarifies the non-Hermitian skin effect's role, and provides a general Green's function formula for open-boundary systems.

Findings

Energy-band branches (EBBs) characterize multivalued energy functions.

The non-Hermitian skin effect relates to EBB eigenstate behavior.

Derived a general expression for open-boundary Green's functions.

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.