# Topological states at exceptional points

## TL;DR

This paper investigates topological states associated with exceptional points in non-Hermitian systems, revealing their robustness and occurrence in both open and closed systems, and defining their topological properties.

## Contribution

It introduces the concept of topological exceptional states at high-order exceptional points and explores their dynamical robustness and interface localization.

## Key findings

- Topological states appear at interfaces of distinct non-Hermitian systems.
- Exceptional states are robust under dynamical evolution.
- Topological states can exist even in closed systems.

## Abstract

We consider an N-level non-Hermitian Hamiltonian with an exceptional point of order N. We define adiabatic equivalence in such systems and explore topological phase. We show that the topological exceptional states appear at the interface of topologically distinct systems. We discuss that topological states appear even in closed systems. We explore dynamical robustness of exceptional edge states.