  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.
