1/S-expansion study of spin waves in a two-dimensional Heisenberg antiferromagnet

TL;DR

This study uses 1/S expansion to analyze quantum fluctuations in a 2D Heisenberg antiferromagnet, revealing energy shifts and spectral changes, especially near the 1D limit, with results aligning with neutron scattering data.

Contribution

It provides a detailed second-order 1/S expansion analysis of spin-wave spectra and dynamical structure factors, including dimensional crossover effects in a 2D Heisenberg antiferromagnet.

Findings

Spin-wave energy at (π,0) is about 2% smaller than at (π/2,π/2).

Second-order corrections grow large near the quasi-1D limit, approaching the des Cloizeaux-Pearson boundary.

The spin-wave peak intensity decreases while the three-spin-wave continuum intensity increases in quasi-1D systems.

Abstract

We study the effects of quantum fluctuations on excitation spectra in the two-dimensional Heisenberg antiferromagnet by means of the 1/S expansion. We calculate the spin-wave dispersion and the transverse dynamical structure factor up to the second order of 1/S in comparison with inelastic neutron scattering experiments. The spin-wave energy at momentum $(\pi,0)$ is found to be about 2% smaller than that at $(\pi/2,\pi/2)$ due to the second-order correction. In addition, we study the dimensional crossover from two dimensions to one dimension by weakening exchange couplings in one direction. It is found that the second-order correction becomes large with approaching the quasi-one dimensional situation and makes the spin-wave energy approach to the des Cloizeaux-Pearson boundary for $S=1/2$. The transverse dynamical structure factor is also calculated up to the second order of 1/S. It is shown that the intensity of spin-wave peak is strongly reduced while the intensity of three-spin-wave continuum becomes large and exceeds that of the spin-wave peak in the quasi-one dimensional situation.