Spectrum of short-wavelength magnons in two-dimensional quantum Heisenberg antiferromagnet on a square lattice: third order expansion in 1/S

Abstract

The spectrum of short-wavelength magnons in two-dimensional quantum Heisenberg antiferromagnet on a square lattice is calculated in the third order in $1/S$ expansion. It is shown that $1/S$ series for $S=1/2$ converges fast in the whole Brillouin zone except for the neighborhood of the point $\mathbf{k}=(\pi ,0)$, at which absolute values of the third and the second order $1/S$-corrections are approximately equal to each other. It is shown that the third order corrections make deeper the roton-like local minimum at $\mathbf{k}=(\pi ,0)$ improving the agreement with the recent experiments and numerical results in the neighborhood of this point. It is suggested that $1/S$ series converges slowly near $\mathbf{k}=(\pi ,0)$ also for $S=1$ although the spectrum renormalization would be small in this case due to very small values of high-order $1/S$ corrections.

arXiv comment11 pages, 2 figures

References in corpus (6)

• Quantum dynamics and entanglement of spins on a square lattice
• High-energy magnon dispersion and multi-magnon continuum in the two-dimensional Heisenberg antiferromagnet
• 1/S-expansion study of spin waves in a two-dimensional Heisenberg antiferromagnet
• Further Series Studies of the Spin-1/2 Heisenberg Antiferromagnet at T=0: Magnon Dispersion and Structure Factors
• Spin-Wave Theory and Finite-Size Scaling for the Heisenberg Antiferromagnet
• Magnetic Excitation Spectrum of the Square Lattice S=1/2 Heisenberg Antiferromagnet K2V3O8

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