Spin chain in magnetic field: limitations of the large-N mean-field theory

TL;DR

This paper investigates the limitations of the large-N mean-field theory in describing spin chains in magnetic fields, revealing it fails at high polarization levels and indicating more complex physics than spin-orbital chains.

Contribution

It demonstrates that the large-N mean-field approximation cannot accurately capture the spin excitation spectra in high magnetic fields for spin chains.

Findings

Large-N mean-field theory fails at high magnetic fields with >50% spin polarization.

Spin chain physics can be more complex than spin-orbital chains in certain regimes.

Abstract

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.