Braiding Topology of Non-Hermitian Open-Boundary Bands

TL;DR

This paper introduces a homotopic braiding topology framework for non-Hermitian open-boundary bands, using a sub-GBZ algorithm to characterize spectral properties and topological robustness without degeneracies.

Contribution

It develops a novel topological characterization method for non-Hermitian open-boundary bands, extending the understanding of spectral topology beyond previous studies.

Findings

Homotopic braiding topology characterized by total vorticity.

Topological robustness without transitions or exceptional points.

Open-boundary bands interchange parts at certain exceptional points.

Abstract

There has been much recent interest and progress on topological structures of the non-Hermitian Bloch bands. Here, we study the topological structures of non-Bloch bands of non-Hermitian multiband quantum systems under open boundary conditions, which has received limited attention in prior studies. Using a continuity criterion and an efficient sub-generalized Brillouin zone (sub-GBZ) algorithm, we establish a homotopic characterization -- braiding topology, e.g., characterized by the band's total vorticity -- for open-boundary bands and sub-GBZs. Such topological identification is robust without topological transition and emergent degenerate points, such as exceptional points. We further analyze the transition's impact on bands and spectral flows, including interesting properties unique to open boundaries, and numerically demonstrate our conclusions with tight-binding model examples. We unveil a crucial insight that open-boundary bands interchange their portions after encountering certain exceptional points. Our results enrich the foundational understanding of topological characterizations for generic non-Hermitian quantum systems.