# Topological spin excitations in Harper-Heisenberg spin chains

## TL;DR

This paper demonstrates that engineered superlattice modulations in one-dimensional spin chains can produce observable topological boundary modes in their excitation spectrum, even with many-body interactions, relevant for cold atoms and layered materials.

## Contribution

It reveals that superlattice modulations induce topological boundary modes in many-body spin chains, persisting with interactions and large spins, linking to quantum Hall edge states.

## Key findings

- Topological boundary modes appear in modulated spin chains.
- Many-body interactions do not close topological gaps.
- Boundary modes persist in the large-spin limit.

## Abstract

Many-body spin systems represent a paradigmatic platform for the realization of emergent states of matter in a strongly interacting regime. Spin models are commonly studied in one-dimensional periodic chains, whose lattice constant is on the order of the interatomic distance. However, in cold atomic setups or functionalized twisted van der Waals heterostructures, long-range modulations of the spin physics can be engineered. Here we show that such superlattice modulations in a many-body spin Hamiltonian can give rise to observable topological boundary modes in the excitation spectrum of the spin chain. In the case of an XY spin-$1/2$ chain, these boundary modes stem from a mathematical correspondence with the chiral edge modes of a two-dimensional quantum Hall state. Our results show that the addition of many-body interactions does not close some of the topological gaps in the excitation spectrum, and the topological boundary modes visibly persist in the isotropic Heisenberg limit. These observations carry through when the spin moment is increased and a large-spin limit of the phenomenon is established. Our results show that such spin superlattices provide a promising route to observe many-body topological boundary effects in cold atomic setups and functionalized twisted van der Waals materials.