Finite-size spin-wave theory of a collinear antiferromagnet

The ground-state and low-energy properties of the two-dimensional $J_1{-}J_2$ Heisenberg model in the collinear phase are investigated using finite-size spin-wave theory [Q. F. Zhong and S. Sorella, {\em Europhys. Lett.} {\bf 21}, 629 (1993)], and Lanczos exact diagonalizations. For spin one-half -- where the effects of quantization are the strongest -- the spin-wave expansion turns out to be quantitatively accurate for $J_2/J_1\gtrsim 0.8$. In this regime, both the magnetic structure factor and the spin susceptibility are very close to the spin-wave predictions. The spin-wave estimate of the order parameter in the collinear phase, $m^\dagger\simeq 0.3$, is in remarkable agreement with recent neutron scattering measurements on ${\rm Li_2VOSiO_4}$.