# Topological Phase Transition Independent of System Non-Hermiticity

## TL;DR

This paper demonstrates that topological phase transitions can occur independently of non-Hermitian effects, preserving topological invariants and bulk-boundary correspondence in certain non-Hermitian systems, which is promising for future applications.

## Contribution

It shows that non-Hermiticity can be introduced without altering the topological properties of chiral symmetric Hermitian systems, revealing a new aspect of non-Hermitian topological physics.

## Key findings

- Topological invariants remain unchanged despite non-Hermitian phase transitions.
- Bulk-boundary correspondence holds in the studied non-Hermitian systems.
- Chern number coincides with topological charge pumping in simulations.

## Abstract

Non-Hermiticity can vary the topology of system, induce topological phase transition, and even invalidate the conventional bulk-boundary correspondence. Here, we show the introducing of non-Hermiticity without affecting the topological properties of the original chiral symmetric Hermitian systems. Conventional bulk-boundary correspondence holds, topological phase transition and the (non)existence of edge states are unchanged even though the energy bands are inseparable due to non-Hermitian phase transition. Chern number for energy bands of the generalized non-Hermitian system in two dimension is proved to be unchanged and favorably coincides with the simulated topological charge pumping. Our findings provide insights into the interplay between non-Hermiticity and topology. Topological phase transition independent of non-Hermitian phase transition is a unique feature that beneficial for future applications of non-Hermitian topological materials.