Moments of the Raman spectrum of the two-dimensional Heisenberg antiferromagnet.

Abstract

Using the spin-1/2 antiferromagnetic Heisenberg model on a square lattice, we calculate the first two cumulants of the Raman scattering intensity by the variational Monte Carlo method. We use a Jastrow variational wave function which includes spin-spin correlations and possesses antiferromagnetic long-range order. This wave function has been self-consistently obtained by minimizing the ground-state energy and by satisfying sum rules of the dynamical structure function; in addition, it gives values for the ground-state energy, the staggered magnetization, and the spin-wave velocity in good agreement with the results of other calculations. The values of the cumulants obtained by our variational Monte Carlo calculation, when extrapolated to the thermodynamic limit (using finite-size scaling forms suggested by spin-wave theory), are ${\mathit{M}}_{1}$=3.69J and ${\mathit{M}}_{2}$=0.72J, in good agreement with those obtained by series expansion. Taking a value of J=1000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, our results also agree with the experimental data on ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$.