# Reply to "Comment on `Winding around non-Hermitian singularities' by Zhong et al., Nat. Commun. 9, 4808 (2018)"

## TL;DR

This paper defends a previously proposed method for analyzing exceptional points in non-Hermitian systems against recent criticism, demonstrating that their approach yields correct results when properly applied.

## Contribution

The authors clarify and validate their method for encircling multiple exceptional points, countering claims of errors and misconceptions in recent commentaries.

## Key findings

- Their method correctly analyzes exceptional points when properly applied.
- Counter-arguments show the criticized approach remains valid.
- The timing of publications indicates independent development.

## Abstract

A comment has been recently posted on the arXiv (arXiv:1902.07504) that discuss our recent work on encircling multiple exceptional points in Nat. Commun. 9, 4808 (2018). In that comment, the authors claim that our approach is prone to errors. In discussing their findings, they also indicate that a method presented by their team in Phys. Rev. A 98, 023818 (2018) (presumed to give correct results in all situations) was published prior to our work. First, we would like to note that both their work and ours were posted on the arXiv within a week from each other. Second and more importantly, as we will show below, their analysis and conclusion concerning the validity of our approach as presented in the comment article (arXiv:1902.07504) are not correct. As we will demonstrate, a proper application of our method does indeed provide the correct results.