Edge magnetism of Heisenberg model on honeycomb lattice

TL;DR

This paper develops a field-theory model for edge magnons in the Heisenberg model on a honeycomb lattice, showing their relativistic dynamics and robustness against quantum fluctuations, with potential experimental verification.

Contribution

It introduces a relativistic field-theory description of edge magnons and demonstrates their robustness using multiple methods, linking boundary and bulk properties.

Findings

Edge magnons obey a 1D Klein-Gordon equation.

Boundary and bulk magnon dynamics are interconnected.

Edge magnons remain stable despite quantum fluctuations.

Abstract

In our previous study, a single-branch of ferromagnetic magnon with linear dispersion is shown to exist near the (uncompensated) zigzag edge for Heisenberg model on honeycomb lattice. Here we develop a field-theory description for the edge magnon and find its dynamics is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart, described by the two-dimensional Klein-Gordon equation. Furthermore, we also reveal how the parity symmetry relates evanescent modes on opposite edges in a honeycomb nanoribbon. By employing alternative methods, including Schwinger bosons and density-matrix renormalization group, we also demonstrate that the relativistic edge magnon is robust even when the Neel order in the bulk is destroyed by quantum fluctuations. The edge magnon is a direct consequence of uncompensated edge and may be verified in realistic materials by experimental probes.