# Topological edge states in periodically-driven trapped-ion chains

## TL;DR

This paper explores how long-range interactions in periodically-driven trapped-ion chains influence topological edge states, revealing enhanced localization and survival of edge states within the ground state, with implications for quantum simulation.

## Contribution

It demonstrates the realization of a driven Su-Schrieffer-Heeger model with long-range interactions in trapped-ion systems and analyzes their impact on topological edge states.

## Key findings

- Long-range interactions enhance edge state localization.
- Edge states persist within the ground state.
- Results are experimentally accessible with current technology.

## Abstract

Topological insulating phases are primarily associated with condensed-matter systems, which typically feature short-range interactions. Nevertheless, many realizations of quantum matter can exhibit long-range interactions, and it is still largely unknown the effect that these latter may exert upon the topological phases. In this Letter, we investigate the Su-Schrieffer-Heeger topological insulator in the presence of long-range interactions. We show that this model can be readily realized in quantum simulators with trapped ions by means of a periodic driving. Our results indicate that the localization of the associated edge states is enhanced by the long-range interactions, and that the localized components survive within the ground state of the model. These effects could be easily confirmed in current state-of-the-art experimental implementations.