Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory

Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation, 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.