# Emergent localized states at the interface of a twofold $\mathcal{PT}$-symmetric lattice

## TL;DR

This paper explores how non-Hermitian, twofold PT-symmetric lattices exhibit unique localized states at interfaces, protected by symmetry, with potential robustness against external gain and loss, demonstrated through numerical models.

## Contribution

It introduces the concept of twofold PT-symmetry in lattices, revealing new surface exceptional points and symmetry-protected localized states not previously characterized.

## Key findings

- Identification of additional surface exceptional points.
- Existence of symmetry-protected localized states.
- Localization lengths are robust against external gain and loss.

## Abstract

We consider the role of non-triviality resulting from a non-Hermitian Hamiltonian that conserves twofold PT-symmetry assembled by interconnections between a PT-symmetric lattice and its time reversal partner. Twofold PT-symmetry in the lattice produces additional surface exceptional points that play the role of new critical points, along with the bulk exceptional point. We show that there are two distinct regimes possessing symmetry-protected localized states, of which localization lengths are robust against external gain and loss. The states are demonstrated by numerical calculation of a quasi-1D ladder lattice and a 2D bilayered square lattice.