Non-Hermitian spectral flows and Berry-Chern monopoles

TL;DR

This paper extends the concept of spectral flow and topological charges to non-Hermitian systems, establishing a topological framework that generalizes Hermitian models and introduces new invariants for complex spectral flows.

Contribution

It introduces a non-Hermitian generalization of spectral flow and topological charges, linking them to a generalized Chern number and demonstrating their topological invariance.

Findings

Spectral flow in non-Hermitian systems can be related to a generalized Chern number.

The topological invariants remain unchanged under homotopic deformations of the Hamiltonian.

A pseudo-Hermitian symmetry captures topology even without a line gap.

Abstract

We propose a non-Hermitian generalization of the correspondence between the spectral flow and the topological charges of band crossing points (Berry-Chern monopoles). A class of non-Hermitian Hamiltonians that display a complex-valued spectral flow is built by deforming an Hermitian model while preserving its analytical index. We relate those spectral flows to a generalized Chern number that we show to be equal to that of the Hermitian case, provided a line gap exists. We demonstrate the homotopic invariance of both the non-Hermitian Chern number and the spectral flow index, making explicit their topological nature. In the absence of a line gap, our system still displays a spectral flow whose topology can be captured by exploiting an emergent pseudo-Hermitian symmetry.