  Lattice deformation resulting from elastic strain is known to spatially
modulate the wave function overlap of the atoms on the lattice and can
drastically alter the properties of the quasiparticles. Here we elaborate that
a twist lattice deformation in two-dimensional honeycomb quantum magnet
nanoribbons is equivalent to an elastic gauge field giving rise to magnon
Landau quantization. When the ground state is ferromagnetic, dispersive
Dirac-Landau levels are induced in the center of magnon bands, while for
antiferromagnetic nanoribbons, the twist results in dispersive equidistant
Landau levels at the top of magnon bands. The dispersions for both types of
Landau levels are derived in the framework of the band theory.
