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

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Using Monte Carlo integration methods, we describe the behavior 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 behavior of S₄ is shown to be consistent with the four-spinon continuum and compared to the one of the exact two-spinon dynamic structure function S₂. Overall shape similarity is noted.