Monte Carlo Study of Four-Spinon Dynamic Structure Function in Antiferromagnetic Heisenberg Model

Using Monte Carlo integration methods, we describe the behavior of the exact four-spinon dynamic structure function $S_{4}$ in the antiferromagnetic spin 1/2 Heisenberg quantum spin chain as a function of the neutron energy $\omega$ and momentum transfer $k$. We also determine the four-spinon continuum, the extent of the region in the $(k,\omega)$ plane outside which $S_{4}$ is identically zero. In each case, the behavior of $S_{4}$ is shown to be consistent with the four-spinon continuum and compared to the one of the exact two-spinon dynamic structure function $S_{2}$. Overall shape similarity is noted.