Monte Carlo study of four-spinon dynamic structure function in antiferromagnetic Heisenberg model

Using Monte Carlo integration methods, we describe the behaviour of the exact four-spinon dynamic structure function S₄ in the antiferromagnetic spin 1/2 Heisenberg quantum spin chain as a function of the neutron energy ω and momentum transfer k. We also determine the four-spinon continuum, the extent of the region in the (k, ω) plane outside which S₄ is identically zero. In each case, the behaviour of S₄ is shown to be consistent with the four-spinon continuum and compared to that of the exact two-spinon dynamic structure function S ₂. Overall shape similarity is noted.