  Using a nearest-neighbor tight-binding model we investigate quantum effects
of plasmons on few-nanometer wide graphene nanoribbons, both for zigzag and
armchair edge terminations. With insight from the Dirac description we find an
emerging scale-invariant behavior that deviates from the classical model both
for zigzag and armchair structures. The onset of the deviation can be related
to the position of the lowest parabolic band in the band structure. Dirac
theory is only valid in the parameter subspace where the scale invariance holds
that relates narrow ribbons with high doping to wide ribbons with low doping.
We also find that the edge states present in zigzag ribbons give rise to a
blueshift of the plasmon, in contrast to earlier findings for graphene
nanodisks and nanotriangles.
