# Relation between $\mathcal{PT}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models

## TL;DR

This paper explores how $\\mathcal{PT}$-symmetry breaking relates to topologically nontrivial phases in the SSH and Kitaev models, revealing model-dependent behaviors influenced by edge states and particle-hole symmetry.

## Contribution

It provides a comparative analysis of $\\mathcal{PT}$-symmetry breaking in topological phases of SSH and Kitaev models, highlighting the role of edge states and symmetries.

## Key findings

- SSH model undergoes immediate $\\mathcal{PT}$-symmetry breaking in TNP with gain/loss
- Kitaev chain's $\\mathcal{PT}$-symmetry breaking is independent of topological phase
- Edge states and particle-hole symmetry influence $\\mathcal{PT}$-symmetry behavior

## Abstract

Non-Hermitian systems with $\mathcal{PT}$ symmetry can possess purely real eigenvalue spectra. In this work two one-dimensional systems with two different topological phases, the topological nontrivial Phase (TNP) and the topological trivial phase (TTP) combined with $\mathcal{PT}$-symmetric non-Hermitian potentials are investigated. The models of choice are the Su-Schrieffer-Heeger (SSH) model and the Kitaev chain. The interplay of a spontaneous $\mathcal{PT}$-symmetry breaking due to gain and loss with the topological phase is different for the two models. The SSH model undergoes a $\mathcal{PT}$-symmetry breaking transition in the TNP immediately with the presence of a non-vanishing gain and loss strength $\gamma$, whereas the TTP exhibits a parameter regime in which a purely real eigenvalue spectrum exists. For the Kitaev chain the $\mathcal{PT}$-symmetry breaking is independent of the topological phase. We show that the topological interesting states -- the edge states -- are the reason for the different behaviors of the two models and that the intrinsic particle-hole symmetry of the edge states in the Kitaev chain is responsible for a conservation of $\mathcal{PT}$ symmetry in the TNP.