  Motivated by the recent success in describing the spin and orbital spectrum
of a spin-orbital chain using a large-N mean-field approximation [Phys. Rev. B
91, 165102 (2015)], we apply the same formalism to the case of a spin chain in
the external magnetic field. It occurs that in this case, which corresponds to
N=2 in the approximation, the large-N mean-field theory cannot qualitatively
reproduce the spin excitation spectra at high magnetic fields, which polarize
more than 50% of the spins in the magnetic ground state. This, rather
counterintuitively, shows that the physics of a spin chain can under some
circumstances be regarded as more complex than the physics of a spin-orbital
chain.
