# Topological spin phases of trapped Rydberg excitons in Cu$_2$O

## TL;DR

This paper theoretically investigates Rydberg excitons in one-dimensional Cu$_2$O traps, revealing a topological Haldane phase with tunable spin states and rich phase diagrams influenced by trap geometry and interaction anisotropy.

## Contribution

It predicts the emergence of a topological Haldane phase in Rydberg excitons and explores how trap geometry and anisotropy affect the spin phase diagram.

## Key findings

- Presence of topological Haldane phase with long-range string order
- Effect of trap geometry on spin state phases
- High tunability of Rydberg exciton spin states

## Abstract

We study theoretically Rydberg excitons in one-dimensional chains of traps in Cu$_2$O coupled via the van der Waals interaction. The triplet of optically active $p$-shell states acts as an effective spin-$1$ and the interactions between the excitons are strongly spin-dependent. We predict that the system {has the} topological Haldane phase with the diluted antiferromagnetic order, long-range string correlations, and finite excitation gap. We also analyze the effect of the trap geometry and interactions anisotropy on the Rydberg exciton spin states and demonstrate that a rich spin phase diagram can be realized showing high tunability of the Rydberg exciton platform.