Does the Heisenberg model describe the multimagnon spin dynamics in antiferromagnetic CuO layers?

We compute the absorption spectrum for multimagnon excitations assisted by phonons in insulating layered cuprates using exact diagonalization in clusters of up to 32 sites. The resulting line shape is very sensitive to the underlying magnetic Hamiltonian describing the spin dynamics. For the usual Heisenberg description of undoped Cu-O planes we find, in accordance with experiment, a two-magnon peak followed by high energy sidebands. However the relative weight of the sidebands is too small to reproduce the experiment. An extended Heisenberg model including a sizable four-site cyclic exchange term is shown to be consistent with the experimental data