# Monopoles in non-Hermitian systems

## TL;DR

This paper investigates the properties of monopoles in non-Hermitian systems, revealing their dependence on branch cuts and invariance under gauge transformations, with implications for understanding geometric curvature in such systems.

## Contribution

It introduces the concept of monopoles in non-Hermitian systems, highlighting their branch-cut dependence and gauge invariance, and compares them to Hermitian systems.

## Key findings

- Monopoles include exceptional points and branch cuts.
- Monopoles depend on the choice of branch cut in the complex plane.
- Monopoles are invariant under $GL(l,\mathbb{C})$ gauge transformations.

## Abstract

The monopole for the geometric curvature is studied for non-Hermitian systems. We find that the monopole contains not only the exceptional points but also branch cuts. As the mathematical choice of branch cut in the complex plane is rather arbitrary, the monopole changes with the branch-cut choice. Despite this branch-cut dependence, our monopole is invariant under the $GL(l,\mathbb{C})$ gauge transformation that is inherent in non-Hermitian systems. Although our results are generic, they are presented in the context of a two-mode non-Hermitian Dirac model. A corresponding two-mode Hermitian system is also discussed to illustrate the essential difference between monopoles in Hermitian systems and non-Hermitian systems.