# Analytical study of the edge states in the bosonic Haldane model

## TL;DR

This paper analytically studies magnon edge states in a ferromagnetic honeycomb lattice with Dzyaloshinskii-Moriya interaction, revealing their spectra, wavefunctions, and dependence on system parameters, with implications for experimental observation.

## Contribution

It provides analytical expressions for bosonic edge states in the Haldane model, extending topological predictions and exploring the effects of external potentials and DMI.

## Key findings

- Edge states are well-defined in certain momentum regions.
- The width of edge states depends on DMI strength.
- External potentials can modify the band structure similarly to fermionic systems.

## Abstract

We investigate the properties of magnon edge states in a ferromagnetic honeycomb spin lattice with a Dzyaloshinskii-Moriya interaction (DMI). We derive analytical expressions for the energy spectra and wavefunctions of the edge states localized on the boundaries. By introducing an external on-site potential at the outermost sites, we show that the bosonic band structure is similar to that of the fermionic graphene. We investigate the region in the momentum space where the bosonic edge states are well defined and we analyze the width of the edge state and their dependence with DMI strength. Our findings extend the predictions using topological arguments and they allow size-dependent confirmation from possible experiments